A Fuzzy-Based Approach for Flexible Modeling and Management of Freshwater Fish Farming

Abstract

Most populated developing countries having water resources, like Egypt, are interested in aquaculture since it supplies around 30% of the cheap protein consumed by customers. Increasing the production of aquaculture, specifically fish farming, in such countries represents an essential need. One candidate water resource for freshwater fish farming in Egypt is the Nile River (1530 km long). Yet, this represents a challenging task due to the existing variations in its water quality (WQ) parameters, such as dissolved oxygen, acidity, and temperature, at different sites. Climate change and pollution negatively affect many water quality parameters. This work provides a fuzzy-based approach for modeling WQ requirements for a set of fish types and evaluates the suitability of a water site for farming them. Thus, it greatly helps managing and planning fish farming in a set of water sites. It benefits from the flexibility of fuzzy logic to model the farming requirements of each fish type. Consequently, it evaluates and clusters the water sites with respect to their degrees of suitability for farming various fish types. The illustrative case study considers 27 freshwater sites spread along the Nile River and 17 freshwater fish types. The result incorporates a set of suitable clusters and a set of unsuitable ones for farming each fish type. It greatly helps managing and planning fish farming, to maximize the overall productivity and prevent probable catastrophic damage. In addition, it shows how to enhance each unsuitable site. We believe that eliminating the causes of pollution in the polluted freshwater sites along a water source could cause a significant boom in the cultivation of multiple freshwater fish types.

1. Introduction

Fishing is one of the main pillars of human food security. Humans get 14% of their animal protein from fish. In 2020, global fish production reached around 178 million tons, which was the highest worldwide annual rate of production. Accordingly, fish farming has received a lot of attention in recent times due to its importance in fish production. Egypt represents one of the developing countries that produced around 1.59 million tons of fish. Fish farming accounts for more than 50% of the overall production of fisheries and aquaculture [1]. Human population in Egypt is growing rapidly. As a result, the demand from middle- and low-income peoples for fish is significantly increasing as it represents a cheaper alternative to other more expensive food items rich in protein like meat and chicken. As a result, farming some cheap types of fish, like tilapia and catfish, is more suitable and common in Egypt. The fish farming process in fresh water has less cost and is more sustainable than that in the seas or oceans [2]. Commonly, modeling the evaluation and selection process of the most suitable sites for fish farming is one of the hardest and most challenging management tasks. Water quality (WQ) mainly depends on measuring physical, chemical, and biological properties of water. Spatial water sites differ according to their WQ parameters’ states. Hence, it is required to select the best WQ sites before starting fish farming, or to adjust abnormal parameters to make the site suitable for farming a specific type of fish. Generally, almost all types of fish need appropriate degrees of WQ parameters, particularly the following parameters: dissolved oxygen (DO), acidity (PH), and temperature (Temp) [3,4]. DO is the amount of dissolved oxygen gas present in a water site measured in mg/L. Very low levels of DO catastrophically harm fish life and affect the WQ itself [5]. Naturally, DO should not be less than 5 mg/L for most fish types. On the other hand, the potential of hydrogen (PH) parameter describes the acidity or alkalinity of water. The value of PH represents the instantaneous hydrogen that affects the biological and chemical properties of water. Most fish require water with PH between 6 and 9 [6]. Usually, values of PH lower than 4.8 or higher than 9.2 harm most fish types. In addition, the temperature of a water site greatly affects fish breading and health. A very low or very high temperature at a water site causes diseases, mortality, and loss of fish weight. Most fish types have various suitable fuzzy ranges of WQ parameter values, rather than being precise crisp values. Therefore, there is a need to model the requirements of fish types for farming at a water site in a flexible manner [6].

The novelty of this work is that it concentrates on evaluating water quality for a set of water sites spread along a water resource like the Nile River with variations in their WQ parameters’ values. Then, it assesses the suitability of these sites for farming a set of interesting fish types. Rationally, a freshwater natural resource consists of a set of consecutive sites, which may have different water quality parameters’ values due to many reasons, like climate change and industrial factories. This work deals with sites such as a set of aquariums or freshwater fishponds. Hence, selecting a more suitable fish type to farm in each of them, or in a cluster of similar sites, represents a great benefit. This greatly helps in managing and planning fish farming, to decrease the cost of farming, since freshwater represents a renewable resource for fish food plus other water parameters. In addition, farming each fish type in a more suitable water site increases the overall yield and profitability. In addition, this work gives indications for enhancing each unsuitable site to make it suitable for farming a specific fish type. It facilitates the choice of multiple farming of a set of non-contradicting fish types together in a suitable site or cluster of sites.

Fuzzy logic, as a soft computing technique, provides a powerful approach for handling uncertainty and approximate reasoning in a flexible and reliable fashion. It is more accurate in modeling uncertainty compared with traditional methods [7,8]. Fuzzy set theory represents a generalization of crisp set theory, and allows partial membership. While an element either belongs fully to a crisp set or does not belong to it at all, an element can belong to a fuzzy set with a membership value between 0 and 1. Many membership functions allow a flexible definition of fuzzy sets. Some of these membership functions are triangular, trapezoidal, bill-shaped, and sigmoid functions. The trapezoidal membership function is common and flexibly defines a fuzzy set. It can be modified to be a left- or right-shouldered membership function. Figure 1 shows the use of trapezoidal FMF to define three linguistic terms—“Low”, “Medium”, and “High”—over the universe of discourse X, which are defined as right-shouldered, ordinary, and left-shouldered trapezoidal FMF, respectively.

The smooth boundaries of a fuzzy set mean it can be flexibly used to model, in a human-like style, the requirements of WQ parameters to farm a specific fish type. That is, there are some ideal values of each WQ parameter and the rest of the values are partially suitable. WQ parameters with partial membership values greater than the predefined threshold value are considered acceptable, otherwise they are considered inacceptable. For the trapezoidal fuzzy membership function, the ideal range of values for a specific WQ parameter becomes the core of the adopted fuzzy membership function, with a full membership value of 1. The other values less than and greater than the ideal range of values will lie on the left and right smooth boundaries of the fuzzy set, with partial membership values. Due to such smooth boundaries, fuzzy sets represent reliable approaches for modeling the requirements of WQ for farming each fish type. Each WQ parameter has an ideal range of values and an accepted threshold value for values outside of this ideal range. On the other hand, fuzzy evaluation and queries have appeared to cope with the necessity to soften the Boolean crisp logic in database queries through using fuzzy sets with smooth boundaries and fuzzy operators [9,10]. Therefore, storing WQ parameter values for a set of water sites in a database, as well as fish types’ requirements, gives the first step for querying about which fish type is suitable for farming in which water site. Generating and executing a fuzzy query against the considered water sites stored in the database for farming a specific fish type returns sites with a matching degree for each site. This degree value ranges between 0 and 1, and indicates the suitability of the site’s WQ parameters for farming the specified fish type.

The aim of this work is to provide a fuzzy-based approach for evaluating the suitability of various water sites for farming various types of fish. These results greatly help in both managing and planning the fish farming process. The rest of this paper includes the following sections: Section 2 introduces the problem definition. Related works are given in Section 3. Section 4 presents the proposed fuzzy-based approach for managing fish farming. Section 5 illustrates a case study. Finally, Section 6 gives the conclusion.

2. Challenges of Fish Farming

Generally, the success of the fish farming process at a water site depends on the prevailing water quality conditions, namely WQ parameters. Farming of each fish type needs suitable values of WQ main parameters, like DO, PH, and Temp [3,11,12,13]. WQ differs from site to site due to the surrounding environment conditions, like factories with huge amounts of wastewater, sanitary, and agricultural drainage, as well as climate change. Therefore, such heterogeneity in WQ parameters for a set of sites spread along a water source creates a big challenge in selecting suitable fish types for farming in each site [14]. Therefore, using a reliable approach, it is very important to find and evaluate sites with suitable values of WQ parameters before start to farm a specific fish type. Unfortunately, traditional searching and querying methods for identifying water characteristics matching the requirements of a specific fish type suffer from the commonly adopted assumption of bivalent crisp set theory and binary logic [15]. In other words, decisions made regarding the suitability of water sites regarding a specific fish type requirement are mostly restricted to the crisp traditional binary logic values, namely true and false. Accordingly, a site with a matching degree less than 1 for fish farming is not suitable, although 90% matching is somewhat suitable for fish farming [7]. Therefore, it is very important to find a flexible approach to deal with this problem rather than the classic crisp solutions. In addition, there is a need to determine the required enhancements in the WQ parameters of the unsuitable sites to make them suitable for farming the considered fish types. Therefore, such an approach helps avoid a catastrophic loss in fish weight, reduce the killed fish percentage, reduce fish diseases, and increase fish production.

3. Related Works

Many approaches have worked on the problems concerned with WQ parameters and fish farming. Some of these approaches were presented in [5,16,17] for WQ assessment. Although they help in the assessment of WQ, they do not introduce a method for solving the problems of inappropriate WQ parameters for fish farming. On the other hand, the works [18,19] show the effects of the changes in WQ parameters like dissolved oxygen and PH on fish farming. A simulation of the effects of cage fish farming on the environment appears in [20]. In addition, the authors in [19,20] evaluate WQ in different sites using fuzzy logic to test if they reach the standard levels of WQ parameters. Most of these previous works evaluate the water quality with respect to the standard measures of fish farming. On the other hand, the authors in [21] showed the impacts of changes in temperature, pollution, and harvesting of juvenile Hilsa on the production of mature Hilsa fishes. Their study did not consider some other main parameters that affect most types of fish, like DO and PH. In addition, the study was limited to only one type of fish, namely Hilsa, without considering the fact that temperature and pollution changes in WQ may be suitable for other types of fish farming.

Other approaches presented in [22,23,24] were concerned with the assessment of WQ parameters. They introduce some solutions to decrease water pollution and to improve the suitability of WQ parameters for fish farming, like that presented in [22]. Another approach considered searching the eastern region of Red Sea, surveying and selecting the cage farming sites in the eastern Red Sea in Saudi Arabia that have the most suitable WQ for fish farming [23]. In addition, the work presented in [25] attempts to evaluate the sustainability of capture-based aquaculture practices in Egypt. Based on the two-valued logic, the authors of [21,23,24] present methods to select the suitable sites for fish farming based on the hard crisp evaluation of sites according to some WQ parameters, that is, any evaluated site either wholly suitable or unsuitable at all for fish farming without giving a matching degree for the considered fish requirements. Finally, none of these previous works attempted to evaluate and cluster a set of water sites spread along a water source with respect to farming different sets of fish types. Selecting the most suitable sites for each fish type, to maximize production and prevent damage, is a challenging task.

4. The Proposed Fuzzy-Based Approach for Modeling Fish Farming

Generally, the proposed approach allows modeling fish farming requirements in a human-like flexible manner. It benefits from the smooth boundaries of fuzzy set theory to model the WQ requirements for farming each type of fish. Consequently, it evaluates and measures the spatial water sites’ suitability degree, which ranges between 0 (unsuitable at all) and 1 (completely suitable) for each considered fish type. Figure 2 shows the architecture of the proposed approach, which incorporates five phases. The first phase considers preparing and predicting the water quality parameters of spatial sites. The second defines the suitable values of water quality parameters for farming each fish type as a set of fuzzy membership functions (FMFs) in a human-like behavior. Consequently, the third phase evaluates the suitability of each water site for farming each considered type of fish. The fourth phase performs fuzzy clustering of sites according to their suitability degree, resulting in a set of suitable clusters and another set of unsuitable clusters for farming a specific fish type. The last phase gives the required enhancement percent for the unsuitable sites’ water quality parameters. The following subsections present these phases.

4.1. Preparation and Prediction of WQ Parameters

This phase is responsible for collecting and preparing the data of WQ parameters of the selected sites and the WQ parameter values suitable for fish farming. Data preparation tackles the problem of missing, noisy, extreme values and inconsistent data. The predication process takes place using Algorithm 1 and the prepared data of WQ parameters gathered for the previous five years of the considered site 1. It predicts the WQ parameter values for every day in the next year. As a result, the process of evaluating the sites’ suitability for farming each type of the considered fish takes place with respect to the average values of the predicted WQ parameter values.

Algorithm 1. Weight-based WQ parameter value prediction.

input: Historical WQ parameters of the considered set of sites of last N years. output: Predicted WQ parameters values of the next year ${\mathbf{Y}}_{\mathbf{m}}$. begin: let  $\mathbf{P}=\sum _{\mathbf{i}=1}^{\mathbf{N}}\mathbf{i}$; // P is used for the weighting years in the prediction process let  m = |N|+1;   // |N| is the cardinality of the set of years for each year Yi in N   // Compute the prediction weight ${\mathbf{W}}_{\mathbf{i}}$ of year ${\mathbf{Y}}_{\mathbf{i}}$:    ${\mathbf{W}}_{\mathbf{i}}=(\left|\mathbf{N}\right|-\left({\mathbf{Y}}_{\mathbf{m}}-{\mathbf{Y}}_{\mathbf{i}}+1\right))/\mathbf{P}$; end for for each day Di in the next year Ym    ${\mathbf{Y}}_{\mathbf{m}}^{\mathbf{P}\mathbf{H}}$(${\mathbf{D}}_{\mathbf{i}}$)=$\sum _{\mathbf{i}=1}^{\left|\mathbf{N}\right|}{\mathbf{Y}}_{\mathbf{i}}^{\mathbf{P}\mathbf{H}}\left({\mathbf{D}}_{\mathit{i}}\right)\mathbf{\ast }\left({\mathbf{W}}_{\mathbf{i}}\right)$;    ${\mathbf{Y}}_{\mathbf{m}}^{\mathbf{D}\mathbf{O}}$(${\mathbf{D}}_{\mathbf{i}}$)=$\sum _{\mathbf{i}=1}^{\left|\mathbf{N}\right|}{\mathbf{Y}}_{\mathbf{i}}^{\mathbf{D}\mathbf{O}}\left({\mathbf{D}}_{\mathit{i}}\right)\mathbf{\ast }\left({\mathbf{W}}_{\mathit{i}}\right)$;    ${\mathbf{Y}}_{\mathbf{m}}^{\mathbf{T}\mathbf{e}\mathbf{m}\mathbf{p}}$(${\mathbf{D}}_{\mathbf{i}}$)=$\sum _{\mathbf{i}=1}^{\left|\mathbf{N}\right|}{\mathbf{Y}}_{\mathbf{i}}^{\mathbf{T}\mathbf{e}\mathbf{m}\mathbf{p}}\left({\mathbf{D}}_{\mathbf{i}}\right)\mathbf{\ast }\left({\mathbf{W}}_{\mathbf{i}}\right)$; end for end Algorithm 1.

4.2. Defining the Suitability FMFs for Each Fish Type

Commonly, the fuzzy membership function for a fuzzy set A on the universe of discourse X is defined as μ A: X → [0, 1], where each element of X is mapped into a value between 0 and 1. This value, called the membership value or degree of membership, quantifies the grade of membership of the element in “X” to the fuzzy set “A” [8]. In this phase, we define the suitability FMFs for each fish type that represent the suitability degree for each possible value for the considered water quality parameters, namely DO, PH and Temp.

4.2.1. Defining PH and Temp Suitable FMFs

We adopt the trapezoidal FMF for modeling the suitability degree of PH and Temp at a water site for farming a fish type. To define the suitability fuzzy membership for PH shown in Figure 3, we use Equation (1). This definition implies the following:

• PH degrees in [${\mathbf{F}}_{\mathbf{i}}^{\mathbf{f}\mathbf{r}\mathbf{o}\mathbf{m}\mathbf{P}\mathbf{H}},{\mathbf{F}}_{\mathbf{i}}^{\mathbf{t}\mathbf{o}\mathbf{P}\mathbf{H}}$] are the most suitable values with full membership of 1.
• PH degrees in the right-side opened interval [${\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{i}\mathbf{n}\mathbf{P}\mathbf{H}},{\mathbf{F}}_{\mathbf{i}}^{\mathbf{f}\mathbf{r}\mathbf{o}\mathbf{m}\mathbf{P}\mathbf{H}}$) and left-side opened interval $({\mathbf{F}}_{\mathbf{i}}^{\mathbf{t}\mathbf{o}\mathbf{P}\mathbf{H}},{\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{a}\mathbf{x}\mathbf{P}\mathbf{H}}$] are partially suitable PH values with membership values in [0, 1).
• PH degrees greater than ${\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{a}\mathbf{x}\mathbf{P}\mathbf{H}}$ or less than ${\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{i}\mathbf{n}\mathbf{P}\mathbf{H}}$ are not suitable at all, with a membership value of 0.

$${\mathsf{\mu }}_{\mathrm{P}\mathrm{H}}^{{\mathrm{F}}_{\mathrm{i}}}(\mathrm{x})=\left\{\begin{array}{cc}\hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{P}\mathrm{H}}\\ \frac{{\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{P}\mathrm{H}}}{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{P}\mathrm{H}}},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{P}\mathrm{H}}<{\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}\\ \hspace{1em}\hspace{1em}\hspace{1em}1\hspace{1em}\hspace{1em},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}\le {\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}\\ \frac{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{P}\mathrm{H}}-{\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}}{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{P}\mathrm{H}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}<{\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{P}\mathrm{H}}\\ \hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{p}\mathrm{h}}>{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{P}\mathrm{H}}\end{array}\right.$$

(1)

where ${\mathsf{\mu }}_{\mathrm{P}\mathrm{H}}^{{\mathrm{F}}_{\mathrm{i}}}\left(\mathrm{x}\right)$ represents the suitability degree of the $\mathrm{P}\mathrm{H}$ water quality parameter value x for farming fish type ${\mathrm{F}}_{\mathrm{i}}$ at water site ${\mathrm{S}}_{\mathrm{k}}$.

In the same way, Equation (2) and Figure 4 present the adopted definition of the suitability FMF for the Temp water quality parameter. Therefore, the temperature suitability degree for farming a fish type $F_{\mathrm{i}}$ is as follows:

• Temp degrees in [${\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{T}\mathrm{E}\mathrm{M}\mathrm{P}},{\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{T}\mathrm{E}\mathrm{M}\mathrm{P}}$] are suitable, with full membership of 1.
• Temp degrees in [${\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}$, ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}$p) and $({\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}},{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}$] are partially suitable temperature values, with membership values in [0, 1).
• Temp degrees greater than ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{E}\mathrm{M}\mathrm{P}}$ or less than ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{E}\mathrm{M}\mathrm{P}}$ are not suitable at all, with a membership value of 0.

$${\mathsf{\mu }}_{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}^{F_{\mathrm{i}}}(\mathrm{x})=\left\{\begin{array}{cc}\hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\\ \frac{{\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}}{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}<{\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\\ \hspace{1em}\hspace{1em}\hspace{1em}1\hspace{1em}\hspace{1em},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\le {\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\\ \frac{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}-{\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}}{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}<{\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\\ \hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}>{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}\end{array}\right.$$

(2)

where ${\mathsf{\mu }}_{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}^{F_{\mathrm{i}}}\left(\mathrm{x}\right)$ represents the suitability degree of the $\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}$ WQ parameter value x for farming fish type $F_{\mathrm{i}}$ at water site S_k.

Assuming that the ideal Temp range of values for farming fish type Grass Crap is between 20 and 30, then this range is represented as the core of the defined Temp suitability membership function for farming the Grass Crap fish type. The tolerance degree with little variations in water temperature means that the values near the core with suitability greater than or equal to the defined threshold value are considered suitable. Accordingly, the values of Temp from 10 to 20 and from 30 to 40 lie on the left and right smooth boundaries of the function, respectively.

Table 1. Trapezoidal FMF’s control points of suitable PH and Temp for Grass Carp fish type.

Considered WQ Parameters	Trapezoidal FMF Control Points
	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{i}\mathbf{n}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{f}\mathbf{r}\mathbf{o}\mathbf{m}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{t}\mathbf{o}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$
PH	4	6	8.6	10.6
Temp	12	22	30	40

gives the control points values of the FMF representing the suitability of PH and Temp for farming the Grass Carp fish type in fresh water. It shows that the value of PH between 6 and 8.6 is quite suitable. In addition, any other value outside this range, but greater than 4 and less than 10.4, is partially suitable. The rest of PH values are completely unsuitable for farming the Grass Carp fish type. On the other hand, a temperature between 22 and 30 is ideal, while other values between 12 and 22 or between 30 and 40 are partially suitable. The rest of the water temperature values are wholly unsuitable for farming the Grass Carp fish type. Any partially suitable values of either PH or Temp are acceptable for fish farming if they exceed the predefined threshold value for both of them with respect to the specified fish type. The specified threshold value for each fish type reflects its tolerance degree for the water quality parameter.

4.2.2. Defining the DO Suitable FMF

There is a minimum suitable DO value for farming a specific fish type $F_{\mathrm{i}}$. So, the left-shouldered trapezoidal FMF, shown in Equation (3) and Figure 5, is used to define the suitability of water site values of DO for each fish type, as follows:

• DO greater than or equal ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}$ is wholly suitable, with a full membership value of 1.
• DO degrees in [${\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{D}\mathrm{O}}$, ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}$) are partially suitable, with membership values in [0, 1).
• DO degree less than ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{D}\mathrm{O}}$ are not suitable DO values, with a 0 membership value.

$${\mathsf{\mu }}_{\mathrm{D}\mathrm{O}}^{F_{\mathrm{i}}}(\mathrm{X})=\left\{\begin{array}{cc}\hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em},& S_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}<{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{D}\mathrm{O}}\\ \frac{{\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{D}\mathrm{O}}}{{\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}-{\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{D}\mathrm{O}}},& {\mathrm{F}}_{\mathrm{i}}^{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{P}\mathrm{H}}\le {\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}<{\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}\\ \hspace{1em}\hspace{1em}\hspace{1em}1\hspace{1em}\hspace{1em},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}\ge {\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}\end{array}\right.$$

(3)

where ${\mathsf{\mu }}_{\mathrm{D}\mathrm{O}}^{F_{\mathrm{i}}}\left(\mathrm{X}\right)$ represents the suitability degree of the DO parameter value x for farming fish type $F_{\mathrm{i}}$ at water site ${\mathrm{S}}_{\mathrm{k}}$.

4.3. Fuzzy Evaluation of Fish Farming Sites’ Suitability

This phase applies Algorithm 2 to compute the suitability of each water site for farming each of the considered fish types. For each fish type and for each site, it applies the predicted WQ parameter values to the predefined suitability FMF for the considered fish type. As a result, it gives an average suitability that measures the suitability of the water site for farming the considered fish type. Commonly, each WQ parameter is a dominant variable for fish life; so, the adopted conjunction operator, the S-norm fuzzy operator, in this work, is the MIN operator. The final output of this phase is a two-dimensional array, named Suitability [S][F], having one dimension for sites (S) and the other for fishes (F), which includes the suitability degree for fish farming. The rows with suitability degrees greater than the specified threshold value, Suitability [S_k][${\mathrm{F}}_{\mathrm{i}}$] ≥ θ_i, indicate the suitability of each site S_k for farming fish type ${\mathrm{F}}_{\mathrm{i}}$. On the other hand, the rest of the rows, where [S_k][${\mathrm{F}}_{\mathrm{i}}$] < ${\mathsf{\theta }}_{\mathrm{i}}$, represent unsuitable sites S_k for farming a specific fish type f_i, with suitability degrees less than the predefined threshold value set by domain experts for each fish type.

Algorithm 2. Fuzzy evaluation of sites’ suitability for fish farming

Inputs: a set of sites S, a set of fish F, WQ parameters of sites, each fish type requirements of WQ parameters, accepted threshold for suitability membership function. Outputs: an array Suitability[S][F] storing the suitability degree of each site $S_k$∈ S for farming each fish type $F_i$∈ F. begin Suitability [|S|][|F|] = 0; or each site $S_k$ in S  for each fish $F_i$ in F   // compute the suitability of PH, DO and Temp   $phSuit\left(S_k^{PH},F_i\right)=Max\left(min\left(\frac{S_k^{PH}-F_i^{minPH}}{F_i^{fromPH}-F_i^{minPH}},1,\frac{F_i^{maxPH}-S_k^{PH}}{F_i^{maxPH}-F_i^{toPH}}\right),0\right)$;   $doSuit\left(S_k^{DO},F_i\right)=Max\left(min\left(\frac{S_k^{DO}-F_i^{minDO}}{F_i^{greatDO}-F_i^{minDO}},1\right),0\right)$;   $tempSuit\left(S_k^{Temp},F_i\right)=Max\left(min\left(\frac{S_k^{Temp}-F_i^{minTemp}}{F_i^{fromTemp}-F_i^{minTemp}},1,\frac{F_i^{maxTemp}-S_k^{Temp}}{F_i^{maxTemp}-F_i^{toTemp}}\right),0\right)$;   // compute and store the overall suitability of site $s_k$ for farming fish type $f_i$   $Suitability\left[S_k\right]\left[F_i\right]=Min(suit\left(s_k^{PH},F_i\right),suit\left(s_k^{DO},F_i\right),suit\left(s_k^{Temp},F_i\right))$;  end for end for end Algorithm 2.

4.4. Suitability-Based Fuzzy Clustering of Consecutive Sites

In the literature, clustering is the assignment of objects to groups of similar objects with respect to their attributes, which can be numerical or categorical [26]. The assignment can be hard, where each object belongs to one cluster only [27]. In contrast, this assignment can be fuzzy, where an object can belong to several clusters, with a membership degree in [0, 1]. The membership degree indicates how much the object satisfies the cluster properties. Accordingly, fuzzy clusters can be overlapping [28]. This work achieves consecutive site clustering according to their suitability degrees for farming each fish type, as presented in Algorithm 3. The resulting clusters, which are a series of homogenous consecutive sites, give decision makers and fish farmers the suitable water site clusters for each fish type. In addition, they give a panoramic view indicating the sites that are not suitable for farming each fish type. Equation (4) computes the suitability degree of site $s_k$∈ S for farming fish type ${\mathrm{F}}_{\mathrm{i}}$ ∈ F.

$$\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{S}}_{\mathrm{k}},{\mathrm{F}}_{\mathrm{i}}\right)=\mathrm{T}\_\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}(\mathrm{p}\mathrm{h}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}},{\mathrm{F}}_{\mathrm{i}}\right),\mathrm{d}\mathrm{o}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}},{\mathrm{F}}_{\mathrm{i}}\right),\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}},{\mathrm{F}}_{\mathrm{i}}\right))$$

(4)

where T-norm is the fuzzy operator for the intersection or conjunction operation. We adopt the Minimum operator in this study since we assume that the values of WQ parameters less than the specified threshold disrupts fish farming process.

Algorithm 3. Suitability-based fuzzy clustering of consecutive sets of sites

Inputs: The suitability degrees of the considered water sites S respecting each fish type $F_i$ and the suitability threshold value ${\theta }_i$ for fish type $F_i$. Outputs: Clusters of consecutive sites with average suitability degree for each cluster for farming each fish type. Begin: struct clustNode{clustId, fromSite, toSite, clustType; float avgSuit; node *next;}; clustNode sitesClusters[]; int newFlag, clustId, clustType, fId, sId, firstSite, lastSite, sitesCount; float $sSuit$, avgSuit, augSuit; for each fish type f with fish id fId in the set of fish types F  { newFlag = 1; clustType = 1; clusId = 0;  // Clusters sites respecting their suitability for farming each fish type   for each water site s identified by sId in the set of water sites S   { // evaluate the suitability of farming fish type f at site s    $sSuit=siteSuit(s,f)=Min\left(phSuit\right(s,f),doSuit(s,f),tempSuit(s,f\left)\right);$    if ((newFlag==1) or ($sSuit\ge$ ${\theta }_i$ and clustType == 0) or     ($sSuit<$ ${\theta }_i$ and clustType ==1)) then     { sitesCount = 1; clustId++;     augSuit = avgSuit = $sSuit$;     firstSite = lastSite = sId;     clustType = (clustType==1)? 0 : 1;     sitesClusters[fid].addNew(clusId, firstSite, lastSite, avgSuit, clustType);     newFlag = 0;}    else     { augSuit+=sSuit; sitesCount++;     avgSuit= augSuit/sitesCount;     lastSite = sId;     sitesClusters[fid].update(clusId, lastSite, avgSuit);}    end if;  } end for  sitesClusters[fId].display();} end for return sitesClusters[]; end Algorithm 3.

After computing the suitability of each site for farming each fish type, the fuzzy clustering process takes place. Each cluster of suitable sites j includes a set of consecutive suitable sites ${\mathrm{S}}_{\mathrm{k}}∊\mathrm{S}$ for farming a fish type $F_i∊\mathrm{F}$, denoted by ${\mathrm{C}\mathrm{S}\mathrm{S}}_{\mathrm{j}}^{F_i}$, as shown in Equation (5). It indicates that a suitable site node belongs to a cluster of consecutive sites as an intermediate node, first node, or last node in the cluster.

$${CSS}_j^{F_i}=\left\{S_k\right|\forall S_k∊S,Suit\left(S_k,F_i\right)\ge {\theta }_i\wedge \left({\{S}_{k-1,}{S}_{k+1}\right\}\subseteq {CSS}_j^{F_i}\vee S_k should be the first or last site in the cluster\left)\right\}$$

(5)

where ${\mathsf{\theta }}_{\mathrm{i}}$ represents the predefined threshold value for accepted suitability of WQ parameters for farming fish type ${\mathrm{F}}_{\mathrm{i}}$.

In the same way, Equation (6) defines the cluster j of unsuitable sites denoted by ${\mathrm{C}\mathrm{U}\mathrm{S}}_{\mathrm{j}}^{F_{\mathrm{i}}}$ for farming fish type ${\mathrm{F}}_{\mathrm{i}}$.

$${CUS}_j^{F_i}=\left\{S_k\right|\forall S_k∊S,Suit\left(S_k,F_i\right)<{\theta }_i\wedge \left({\{S}_{k-1,}{S}_{k+1}\right\}\subseteq {CSS}_j^{F_i}\vee S_k should be the first or last site in the cluster\left)\right\}$$

(6)

Accordingly, the average suitability of farming fish type ${\mathrm{f}}_{\mathrm{i}}$ at cluster ${\mathrm{C}\mathrm{S}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}}$ of consecutive sites is obtained using Equation (7).

$$\mathrm{a}\mathrm{v}\mathrm{g}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}({\mathrm{C}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}})={\sum }_{{\mathrm{S}}_{\mathrm{k}}∊{\mathrm{C}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}}}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{S}}_{\mathrm{k}},{\mathrm{F}}_{\mathrm{i}}\right)/\mathrm{n}$$

(7)

where ${\mathrm{C}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}}$ denotes either a suitable or unsuitable cluster, ${\mathrm{n}=|\mathrm{C}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}}|$, and ${\mathrm{S}}_{\mathrm{k}}$ represents each site belonging to the cluster.

Consequently, the set of suitable clusters of the list of sites S for farming a fish type $F_i$ denoted by ${\mathrm{S}\mathrm{C}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}^{F_i}$ is defined as shown in Equation (8).

$$\begin{gathered} {SC}_{Suit}^{F_i}=\{{(CSS}_j^{F_i},avgSuit{(CSS}_j^{F_i})\left)\right|{CSS}_j^{F_i}\subseteq S^{*}, {CSS}_j^{F_i} is consective suitable sites set \\ \wedge \mathrm{a}\mathrm{v}\mathrm{g}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}\left({\mathrm{C}\mathrm{S}\mathrm{S}}_{\mathrm{j}}^{{\mathrm{F}}_{\mathrm{i}}}\right)\ge {\mathsf{\theta }}_{\mathrm{i}}\} \end{gathered}$$

(8)

where ${\mathrm{S}}^{\mathrm{*}}$ is the power set of the set of all considered sites $\mathrm{S}$.

In addition, Equation (9) defines the set of unsuitable clusters for farming a given fish type.

$${SC}_{unSuit}^{F_i}=\{{(CSS}_j^{F_i},avgSuit\left({CSS}_j^{F_i}\right)|{CSS}_j^{F_i}\subseteq S^{*},{CSS}_j^{F_i} consective unsuitable sites set\wedge avgSuit\left({CSS}_j^{F_i}\right)<{\theta }_i\}$$

(9)

Accordingly, two sets of suitable and unsuitable clusters for all types of fish, ${\mathrm{G}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}$ and ${\mathrm{G}}_{\mathrm{u}\mathrm{n}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}$, are constructed using Equations (10) and (11), respectively.

$${\mathrm{G}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}={\bigcup }_{\mathrm{i}=1}^{\left|\mathrm{F}\right|}{\mathrm{S}\mathrm{C}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}^{{\mathrm{F}}_{\mathrm{i}}}$$

(10)

where ${\mathrm{G}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}$ is the set of suitable clusters and |F| is the count of considered fish types.

$${\mathrm{G}}_{\mathrm{u}\mathrm{n}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}={\bigcup }_{\mathrm{i}=1}^{\left|\mathrm{F}\right|}{\mathrm{S}\mathrm{C}}_{\mathrm{u}\mathrm{n}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}^{{\mathrm{F}}_{\mathrm{i}}}$$

(11)

where $G_{unSuit}$ denotes the set of unsuitable clusters.

Finally, Equation (12) gives the set of all generated clusters.

$$\mathrm{G}={\mathrm{G}}_{\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}\cup {\mathrm{G}}_{\mathrm{u}\mathrm{n}\mathrm{S}\mathrm{u}\mathrm{i}\mathrm{t}}$$

(12)

where G represents the set of all generated clusters, either suitable or unsuitable.

4.5. Required Enhancement for Unsuitable Sites

This phase considers the problem of the unsuitable sites. It is responsible for detecting the existing unsuitable WQ parameter values for farming each type of fish. As a result, it determines the required enhancement in each parameter as a percentage to reach a predefined accepted threshold (${\mathsf{\theta }}_{\mathrm{i}}$) value of each parameter for each fish type. Commonly, a site enhancement may include one or more parameters. Figure 6 shows the computation of the required change (±Δ) in an unsuitable PH or Temp value of a water site to reach the considered fish type threshold value (${\mathsf{\theta }}_{\mathrm{i}}$). In additon, Equations (13) and (14) calculate the required enhancement for unsuitable values of PH and DO, respectively.

$$\pm \mathsf{\Delta }{\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}=\left\{\begin{array}{ll}\left({\mathsf{\theta }}_{\mathrm{i}}\mathrm{*}{\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}-{\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}\right)/{\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}<{\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}\\ \left({\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}-{\mathsf{\theta }}_{\mathrm{i}}\mathrm{*}{\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}\right)/{\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}},& {\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}>{\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}\\ \hspace{1em}\hspace{1em}0\hspace{1em},\hspace{1em}\hspace{1em}otherwise\end{array}\right.$$

(13)

where the range of values between ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{P}\mathrm{H}}$ and ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{t}\mathrm{o}\mathrm{P}\mathrm{H}}$ represents the PH values with full suitability. The rest of PH values have partial suitability degrees for farming fish type ${\mathrm{F}}_{\mathrm{i}}$,$\mathsf{\Delta }{\mathrm{s}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}$ is the required enhancement in PH value for site S_k, ${\mathrm{s}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}$ is the value of PH at site S_k, and ${\mathsf{\theta }}_{\mathrm{i}}$ is the accepted threshold value of PH for farming fish type ${\mathrm{F}}_{\mathrm{i}}$.

$$\pm \mathsf{\Delta }{\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}=\left\{\begin{array}{l}\left({\mathsf{\theta }}_{\mathrm{i}}\mathrm{*}{\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}-{\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}\right)/{\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}, {\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}\le {\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}\\ \hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em}\hspace{1em}, {\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}>{\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}\end{array}\right.$$

(14)

where any DO value greater than ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{D}\mathrm{O}}$ has a full suitability degree for farming a fish type ${\mathrm{F}}_{\mathrm{i}}$ and the rest of the DO values have partial suitability degrees, is the required enhancement in DO values for site S_k, ${\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}$ is the current DO value, and ${\mathsf{\theta }}_{\mathrm{i}}$ is the accepted threshold value for farming fish type ${\mathrm{F}}_{\mathrm{i}}$.

5. An Illustrative Case Study

This section illustrates the applicability and benefits of the proposed approach using a case study. A set of water spatial sites spread from south to north on the Nile River of Egypt and a set of fish types are applied in this case study. In addition, this case study adopts a database including the domain knowledge describing the requirements for farming each considered freshwater fish type that can live in the Nile River. Figure 7 shows a map of the considered spatial water site locations along the Nile River (1539 km long) in Egypt. These water sites start from Nasser Lake (S₁) in the south, to Desouk (S₂₄) and Domietta (S₂₈) in the north, through the Rashid and Domietta branches, respectively. In this work, 28 different spatial sites sequenced on the Nile River and 17 fish types suitable for farming in fresh water are considered. In addition, the database includes a minimum threshold value for the suitability of each WQ parameter required for farming each fish type.

5.1. Prediction of WQ Parameter Values

The historical data of WQ parameters of the considered sites from S₁ to S₂₈ within the last 5 years (from 2019 to 2023) are considered. Each incorporated year has a weight reflecting its importance in the prediction process for the upcoming year, such that the most recent year has the higher weight and vice versa. Algorithm 1 predicts the considered WQ parameters’ values for PH, DO, and Temp for the upcoming year 2024.

Table 2. A set of Nile River site locations and the average of predicted values of the considered WQ parameters.

Site Name	Site Id	Latitude (N)	Longitude (E)	${\mathbf{S}}_{\mathbf{k}}^{\mathbf{P}\mathbf{H}}$	${\mathbf{S}}_{\mathbf{k}}^{\mathbf{D}\mathbf{O}}$(Mg/L)	${\mathbf{S}}_{\mathbf{k}}^{\mathbf{T}\mathbf{e}\mathbf{m}\mathbf{p}}$(°C)
Nasser Lake1	S1	22°15	31°50	7.62	7.09	27.32
Nasser Lake2	S2	22°45	32°40	7.28	6.29	26.88
Nasser Lake3	S3	23°30	32°50	8.37	5.78	26.46
Aswan	S4	24°14	32°52	7.93	5.24	26.25
Kom Ombo	S5	24°49	32°54	5.03	3.44	24.92
Edfu	S6	25°11	32°42	6.39	4.07	24.38
Esna	S7	25°25	32°32	6.76	5.48	21.40
Luxor	S8	25°42	32°38	6.84	4.78	24.10
Qena	S9	26°08	32°42	7.63	6.69	23.36
Girga	S10	26°20	31°54	6.48	6.24	20.30
Sohag	S11	26°33	31°42	6.99	6.29	23.89
Tima	S12	26°55	31°27	6.33	6.05	21.63
Asyut	S13	27°11	31°11	6.81	7.21	21.10
Abnub	S14	27°15	31°07	5.52	6.74	22.38
Mallawi	S15	27°44	30°51	6.55	6.42	21.19
El Minya	S16	28°05	30°46	6.94	6.24	20.93
Samalut	S17	28°18	30°44	6.98	5.84	21.66
Beni Suef	S18	29°03	31°06	7.34	5.78	21.62
Atfih	S19	29°24	31°13	5.95	6.35	20.46
Helwan	S20	29°50	31°17	7.36	4.02	20.54
Giza	S21	30°02	31°13	7.01	5.91	21.72
Menuf	S22	30°28	30°50	7.47	5.16	23.94
Kafrzayat	S23	30°49	30°48	6.40	5.35	21.52
Desouk	S24	31°07	30°38	7.11	4.63	20.64
Banha	S25	30°28	31°10	6.73	3.89	22.76
Zefta	S26	30°42	31°14	6.68	5.21	24.20
Mansura	S27	31°02	31°23	5.89	4.16	20.13
Domietta	S28	31°24	31°48	7.66	4.99	19.42

shows the average of the predicted WQ parameter values, PH, DO, and Temp, for the considered water sites with each site’s latitude and longitude.

5.2. Defining Fish Farming Requirements

Table 3. Control points of suitability membership functions for freshwater PH, DO and Temp for farming a set of fish types.

Fish ID	Fish Type Name	Fish Image	PH (0–14)				DO Mg/L		Temp °C
			${\mathbf{F}}_{\mathbf{i}}^{\mathbf{minPH}}$	Optimum		${\mathbf{F}}_{\mathbf{i}}^{\mathbf{maxPH}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{minDO}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{greatDO}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{minTemp}}$	Optimum		${\mathbf{F}}_{\mathbf{i}}^{\mathbf{maxTemp}}$
				${\mathbf{F}}_{\mathbf{i}}^{\mathbf{fromPH}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{toPH}}$					${\mathbf{F}}_{\mathbf{i}}^{\mathbf{fromTemp}}$	${\mathbf{F}}_{\mathbf{i}}^{\mathbf{toTemp}}$
F1	Shrimp		4	6	8	10	4	5.5	15	20	30	38
F2	African Sharp Tooth Catfish		4	6	9	12	3	5.3	10	23	28	39
F3	Anguilla		5	7.4	8	10	2.8	5	9	23	30	39
F4	Fresh Water Sardines		3.3	5	6.8	8.5	3.8	5	10	15	22	33
F5	Sharp Tooth Catfish		4	6.5	8	12	4	6	9	20	30	40
F6	Electric Catfish		4.5	7	8	12	2.9	4	11	23	30	39
F7	Bagrus Docmac		4.4	6.4	8.2	10	3	4.5	10	21	27	38
F8	Lates Niloticus		3.7	6.2	8.5	10.2	3	4	11	21	27	37
F9	Bottle Nose		3.5	5.5	8	10	3.5	5	13	23	30	38
F10	Hypoph Thalmichthys		3.5	5.5	7.5	9.5	2.5	4	13	20	24	33
F11	Barbus Bynni		4	6	8	10	2.7	4	10	22	27	35
F12	Nile Lebeo		5	7	8.5	10.5	4	6	10	22	28	38
F13	Grass Carp		4	6	8.6	10.4	4	6	12	22	30	40
F14	Tilabia Zillii		3	5	7.5	9	3.8	5.5	12	19	28	38
F15	Tilabia Galilea		3	5	8.4	10	4	6	15	20	30	38
F16	Tilabia Aurea		3.7	5	8	11	3	6	14	19	30	38
F17	Tilabia Niletica		3.5	5	8.2	10.5	3.5	6	15	20	30	38

shows the WQ parameters’ control points used to define the requirements of each WQ parameter for farming each considered freshwater fish type [29,30,31,32,33]. The requirements for farming each fish type of both PH and Temp are represented using a trapezoidal FMF. The implications of the values of the control points for the PH suitability MSF to farm a fish type ${\mathrm{F}}_{\mathrm{i}}$ are as follows:

• The control point “$F_i^{minPH}$” indicates 0 suitability for any PH value less than or equal to it;
• In contrast, any value of PH belonging to the closed period [${F_i^{minPH},F}_i^{fromPH}$] has a full suitability degree for farming fish type $F_i$;
• The control point “$F_i^{maxPH}$” indicates 0 suitability for PH values greater than or equal to it;
• Any PH value belonging to [$F_i^{minPH}$,$F_i^{fromPH}$) or (${f_i^{toPH},F}_i^{maxPH}$] has a partial suitability degree in [0, 1) for farming fish type $F_i$, which is computed using Equation (1).

In the aquaculture literature, the WQ international standards of PH, Temp, and DO for fish farming are in the ranges [6.0–9.0], [15.0–30.0 °C], and [4.0–6.0 Mg/L] respectively [11,12]. Accordingly, the right-shouldered trapezoidal FMF flexibly represents the suitability of the site’s DO value for farming a specific fish type such that:

• The control point “$F_i^{minDO}$” indicates 0 suitability for DO values less than or equal to it;
• In contrast, any value of DO greater than or equal to $F_i^{greatDO}$ has a full suitability degree for farming fish type $F_i$;
• Any value of DO belonging to the opened period [$F_i^{minDO}$,$F_i^{greatDO}$) has a partial suitability degree in [0, 1] for farming fish type $F_i$, which is computed using Equation (2).

5.3. Fuzzy-Based Evaluation of Sites for Fish Farming

In this phase, an evaluation process using Algorithm 2 takes place with respect to the predefined domain knowledge of the requirements for farming each fish type. For each fish type, it evaluates the suitability of each water site for farming this type of fish. As a result, a fuzzification process takes place in order to map the computed suitability degree for farming each fish type in each site to a linguistic value. In aquaculture, WQ parameter values greatly affect the process of fish farming, and severe unsuitable values can cause catastrophic damage in aquaculture production [6,34]. Therefore, it is essential to set a threshold value stating the tolerance of each considered fish type to variations in WQ parameter values.

Suitable sites for farming a specific fish type include all sites with a suitability degree greater than or equal to the specified threshold value ${\mathsf{\theta }}_{\mathrm{i}}$ for fish type ${\mathrm{F}}_{\mathrm{i}}$.

Table 4. Fish farming suitability degrees for a series of Nile River sites sequenced from south (S₁) to north (S₂₈).

	Fish Id	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	F13	F14	F15	F16	F17
Site Id
S1		1	1	1	0.52	1	1	0.97	0.97	1	0.63	0.96	1	1	0.92	1	1	1
S2		1	1	0.95	0.56	1	1	1	1	1	0.68	1	1	1	1	1	1	1
S3		0.82	1	0.82	0.08	0.89	0.91	0.91	1	0.82	0.57	0.82	0.89	0.89	0.42	0.89	0.88	0.91
S4		0.82	0.97	1	0.34	0.62	1	1	1	1	0.75	1	0.62	0.62	0.72	0.62	0.75	0.69
S5		0.00	0.19	0.01	0.73	0.00	0.21	0.30	0.44	0.00	0.63	0.57	0.00	0.00	0.00	0.00	0.15	0.00
S6		0.05	0.46	0.58	0.23	0.03	0.76	0.71	1	0.38	0.96	1	0.03	0.04	0.16	0.03	0.36	0.23
S7		0.98	0.88	0.73	1	0.74	0.87	1	1	0.84	1	0.95	0.74	0.74	0.99	0.74	0.83	0.79
S8		0.52	0.77	0.77	0.81	0.39	0.94	1	1	0.85	0.99	1	0.39	0.39	0.57	0.39	0.59	0.51
S9		1	1	1	0.51	1	1	1	1	1	0.93	1	1	1	0.91	1	1	1
S10		1	0.79	0.62	1	0.99	0.77	0.94	0.93	0.73	1	0.86	0.81	0.83	1	1	1	1
S11		1	1	0.83	0.83	1	1.00	1	1	1	1	1	1	1	1	1	1	1
S12		1	0.89	0.55	1	0.93	0.73	0.96	1	0.86	1	0.97	0.76	0.96	1	1	1	1
S13		1	0.85	0.75	0.99	1	0.84	1	1	0.81	1	0.92	0.92	0.91	1	1	1	1
S14		0.76	0.76	0.22	0.97	0.61	0.41	0.56	0.69	0.94	1	0.81	0.47	1	1	1	1	1
S15		1	0.86	0.65	1	1	0.82	1	1	0.82	1	0.93	0.84	0.92	1	1	1	1
S16		1	0.84	0.81	0.92	1	0.83	0.99	0.99	0.79	1	0.91	0.91	0.89	1	1	1	1
S17		1	0.90	0.83	0.89	0.92	0.89	1	1	0.87	1	0.97	0.92	0.92	1	0.92	0.95	0.94
S18		1	0.89	0.90	0.68	0.89	0.89	1	1	0.86	1	0.97	0.89	0.89	1	0.89	0.93	0.91
S19		0.97	0.80	0.40	1	0.78	0.58	0.77	0.89	0.75	1	0.87	0.62	0.85	1	1	1	1
S20		0.01	0.44	0.55	0.18	0.01	0.79	0.68	0.95	0.35	1	0.88	0.01	0.01	0.13	0.01	0.34	0.21
S21		1	0.90	0.84	0.88	0.96	0.89	1	1	0.87	1	0.98	0.96	0.96	1	0.96	0.97	0.97
S22		0.78	0.94	1	0.61	0.58	1	1	1	1	1	1	0.58	0.58	0.80	0.58	0.72	0.67
S23		0.90	0.89	0.58	1	0.67	0.76	1.00	1	0.85	1	0.96	0.67	0.68	0.91	0.67	0.78	0.74
S24		0.42	0.71	0.83	0.69	0.31	0.80	0.97	0.96	0.75	1	0.89	0.31	0.32	0.49	0.31	0.54	0.45
S25		0.00	0.39	0.49	0.07	0.00	0.89	0.59	0.89	0.26	0.93	0.91	0.00	0.00	0.05	0.00	0.30	0.16
S26		0.81	0.96	0.70	0.80	0.61	0.87	1	1	1	0.98	1	0.61	0.61	0.83	0.61	0.74	0.68
S27		0.10	0.50	0.37	0.30	0.08	0.56	0.74	0.86	0.44	1	0.84	0.08	0.08	0.21	0.08	0.39	0.26
S28		0.66	0.72	0.74	0.50	0.49	0.70	0.86	0.84	0.64	0.92	0.78	0.49	0.50	0.70	0.49	0.66	0.60

shows the calculated suitability degrees for a series of sites with respect to a set of fish types. The shaded cells represent suitable sites with suitability ≥ 0.9. In contrast, the unshaded cells represent unsuitable sites for farming the corresponding fish type. As shown, some sites have full suitability of 1.0 for farming a specific fish type, while some other sites have partial suitability values that range from zero to less than one. Accordingly, the proposed approach greatly helps in ranking the considered sites for farming a specific type of fish with respect to their suitability. The results greatly help in the process of managing and strategic planning for fish farming. Table 4 shows that sites S₁ and S₂ are best suited to farming all types of fish, except F₄ (Fresh Water Sardine) and F₁₀ (Hypoph Thalmichthys).

Figure 8 shows the suitability degrees of the considered water sites for farming fish types F₁, F₂, and F₃. On the other hand, Figure 9 shows the suitability degrees for farming fish types F₇, F₈, and F₉ at the considered water sites along the Nile River. In addition, Figure 10 shows the suitability degree of sites for farming fish types F₁₁, F₁₂, and F₁₃.

Therefore, the greater the suitability degree of a freshwater site for farming a specific fish type, the higher the production and outcome rates, and vice versa. Thus, the result of applying the proposed approach greatly facilitates managing and planning fish farming along the considered Nile River sites. This approach ranks the resulted spatial clusters of water sites with respect to their average suitability of farming each considered fish type. Hence, it enables deciding which type of fish to farm in which water sites based on their computed suitability degrees. With respect to Figure 11, which shows a subset of the considered set of sites, we conclude that the more suitable sites for farming fish type F₃ (Anguilla) include S₄ and S₂₂. In addition, sites S₇ and S₂₃ are more suitable sites for farming fish type F₄ (Fresh Water Sardines). As shown in Figure 12, the more suitable sites for farming fish type F₁₄ (Tilabia Zillii) are S₇ (Esna), S₂₁ (Giza) and S₂₃ (Kafrzayat). Although fish types (F₁₄:F₁₇) have the same main category, namely Tilabia fish, they have different tolerance degrees with variations in water quality. It can be noted that F₁₄ has the highest suitability in most sites compared with the other types (F₁₅:F₁₇) of Tilabia fish. Accordingly, it is more appropriate to farm Tilabia Zillii rather than other Tilabia types in these freshwater sites. In addition, it can be noted that the sites S₅ (Kom Ombo), S₆ (Edfu), S₂₀ (Helwan), S₂₄ (Desouk), S₂₅ (Banha), and S₂₇ (Mansura) are unsuitable sites for farming not only “Tilabia Zillii”, but also most fish types. Some of these sites suffer from sewage waste and/or factories wastes [35]. These water sites are located alongside industrial cities occupied by factories, such as cement factories at site S₂₀ (Helwan) and a sugar factory at S₅ (Kom Ombo), which have huge quantities of wastewater. Some studies proved the negative effect of such wastewater on the quality of water resources near to them [14,35]. This wastewater greatly affects the water quality and causes pollution, at least to some extent. These effects pass into the consequent sites following the polluted site from south to north, which is the natural direction of the water flow.

5.4. Suitability-Based Water Site Clustering with Respect to a Fish Type

As the water sites along a water resource like a river are naturally consecutive, it is rational to cluster them with respect to their suitability for farming each considered fish type. Such clustering adds valuable knowledge for fish farmers and managerial in both short-term and long-term fish farming managing and planning. As shown in Figure 13, a set of five linguistic values, namely “Unfit”, “Bad”, “Fair”, “Good”, and “Fit”, are defined for the universe of discourse “Suitability degree”. As a result, the computed suitability degree for farming a fish type in a specific water site is fuzzily mapped into one of these linguistic values. Commonly, for each fish type, the clustering process aims mainly to determine two sets of clusters. The first set includes all suitable clusters of consecutive water sites spread along the consider water source for farming a specific fish type. On the other hand, the second set incorporates the rest of clusters, which are unsuitable for farming the specified fish type.

For each fish type, Algorithm 3 receives the evaluated water sites for farming the considered fish types as input. Consequently, it starts a suitability-based spatial clustering process with respect to the predefined suitability threshold value.

Table 5. Suitability-based fuzzy clustering of Nile River spatial sites for farming a set of fish types (F₁–F₁₂).

Fish Id	Suitability-Based Clusters of Consecutive Water Sites in Terms of (Range of Sites, Their Average Suitability)	Average Suitability	Linguistic Values
F1	(S1:S2, 1); (S7, 0.98); (S9:S13, 1); (S15:S19, 0.99); (S21, 1); (S23, 0.9)	0.99	Fit
	(S3:S4, 0.82); (S14, 0.76); (S22, 0.78); (S26, 0.81)	0.80	Good
	(S28, 0.66)	0.66	Bad
	(S5:S6, 0.025); (S8, 0.52); (S20, 0.01); (S24:S25, 0.21); (S27; 0.1)	0.16	Unfit
F2	(S1:S4, 0.99); (S7, 0.88); (S9, 1); (S11, 1); (S17:S18, 0.89); (S21:S23, 0.91); (S26, 0.96)	0.94	Fit
	(S12:S13, 0.87); (S15: S16, 0.85);	0.86	Good
	(S8, 0.77); (S10, 0.79); (S14, 0.76); (S19, 0.80); (S24, 0.71); (S28, 0.72)	0.79	Fair
	(S5:S6, 0.325); (S20, 0.44); (S25, 0.39); (S27, 0.50)	0.40	Unfit
F3	(S1:S2, 0.975); (S4, 1); (S9, 1); (S18, 0.90); (S22, 1)	0.98	Fit
	(S3, 0.82); (S11, 0.83); (S16:S17, 0.82); (S21, 0.84); (S24, 0.83)	0.83	Good
	(S8, 0.77); (S13, 0.75); (S26, 0.70); (S28, 0.74)	0.74	Fair
	(S6:S7, 0.655); (S10, 0.62); (S12, 0.55); (S15, 0.65); (S20, 0.55); (S23, 0.58);	0.63	Bad
	(S5, 0.01); (S14, 0.22); (S19, 0.40); (S25, 0.49); (S27, 0.37)	0.30	Unfit
F4	(S7, 1.0); (S10, 1.0); (S12:S17, 0.965); (S19, 1.0); (S21, 0.88); (S23, 1.0)	0.99	Fit
	(S8, 0.81); (S11, 0.83);	0.82	Good
	(S5, 0.73); (S18, 0.68); (S24, 0.80); (S26, 0.69)	0.73	Fair
	(S2, 0.56); (S22, 0.61);	0.56	Bad
	(S1, 0.52); (S3, 0.08); (S4, 0.34); (S6, 0.23); (S9, 0.51); (S20, 0.18); (S25, 0.07); (S27, 0.3); (S28, 0.5)	0.30	Unfit
F5	(S1:S3, 0.97); (S9:S13, 0.984); (S15:S18, 0.95); (S21, 0.96)	0.98	Fit
	(S19, 0.78)	0.78	Fair
	(S4, 0.62); (S7, 0.74); (S14, 0.61); (S22:S23, 0.625); (S26, 0.61)	0.64	Bad
	(S5:S6, 0.015); (S8, 0.39); (S20, 0.01); (S24, 0.31); (S25, 0); (S27:S28, 0.285)	0.16	Unfit
F6	(S1:S4, 0.98); (S8:S9, 0.97); (S11, 1); (S17:S18, 0.89); (S21:S22, 0.95), (S25:S26, 0.88)	0.96	Fit
	(S7, 0.87); (S13, 0.84); (S15:S16, 0.825);	0.88	Good
	(S6, 0.76); (S10, 0.77); (S12, 0.73); (S20, 0.79); (S23:S24, 0.78);	0.79	Fair
	(S19, 0.58); (S27:S28, 0.63)	0.62	Bad
	(S5, 0.21); (S14, 0.41)	0.31	Unfit
F7	(S1:S4, 0.97); (S7:S13, 0.985); (S15:S18, 0.997); (S21:S24, 0.99); (S26, 1)	0.99	Fit
	(S28, 0.86)	0.86	Good
	(S19, 0.77)	0.77	Fair
	(S6, 0.71); (S14, 0.56); (S20, 0.68); (S25, 0.59); (S27, 0.74)	0.67	Bad
	(S5, 0.30)	0.30	Unfit
F8	(S1:S4, 0.99); (S6:S13, 0.99); (S15:S26, 0.97)	0.98	Fit
	(S27,: S28, 0.85)	0.85	Good
	(S14, 0.69)	0.69	Fair
	(S5, 0.44)	0.44	Unfit
F9	(S1:S2, 1); (S4, 1); (S9, 1); (S11, 1); (S14, 0.94); (S22, 1); (S26, 1)	0.99	Fit
	(S7:S8, 0.845); (S12, 0.86); (S15:S18, 0.84); (S21, 0.87); (S23, 0.85)	0.85	Good
	(S3, 0.8); (S10, 0.72); (S13, 0.8); (S19, 0.75); (S24, 0.75)	0.76	Fair
	(S28, 0.64)	0.64	Bad
	(S5:S6, 0.19); (S20, 0.35); (S25, 0.26); (S27, 0.44)	0.29	Unfit
F10	(S6:S28, 0.99)	0.99	Fit
	(S4,0.75)	0.75	Fair
	(S1:S3,0.63); ( S5, 0.63)	0.63	Bad
F11	(S1:S2,0.98); (S4,1); (S6:S9,0.98); (S11:S13,0.96); (S15:S18,0.95); (S21:S23,0.98); (S25:S26,0.95); (S24,0.89)	0.96	Fit
	(S3,0.82); (S10,0.86); (S14,0.81); (S19:S20,0.87); (S27:S28,0.81)	0.84	Good
	(S5,0.57)	0.57	Bad
F12	(S1:S3,0.96); (S9,1); (S11,1); (S13,0.92); (S16:S18,0.91)	0.95	Fit
	(S10,0.81); (S15,0.84)	0.83	Good
	(S7,0.74); (S12,0.76);	0.75	Fair
	(S4,0.62); (S19,0.62); (S22:S23,0.63); (S26,0.61)	0.62	Bad
	(S5:S6,0.015); (S8,0.39); (S14,0.47); (S20,0.01); (S24,0.32); (S25,0); (S27:S28,0.29)	0.20	Unfit

shows the resulting set of spatial clusters of consecutive water sites with an average suitability for each cluster with respect to a specific type of fish. Figure 14a–d show the resulting clusters with respect to their suitability for farming fish types (F₁, F₂ and F₃), (F₄, F₅ and F₆), (F₇, F₈ and F₉), and (F₁₀, F₁₁ and F₁₂), respectively.

Regarding farming fish type F₁ (“Shrimp”), Table 5 and Figure 14a show different types of clusters as follows:

• Best fit clusters include {(S₁:S₂, 1), (S₇, 0.98), (S₉:S₁₃, 1), (S₁₅:S₁₉, 0.99), (S₂₁, 1), (S₂₃, 0.9)}. They are ideally suitable for the farming process of “Shrimp” fish type.
• Good clusters include {(S₃:S₄, 0.82), (S₁₄, 0.76), (S₂₂, 0.78), (S₂₆, 0.81)}. They need little enhancements in their water quality parameters to reach the threshold value.
• Bad clusters include one site {(S₂₈, 0.66)} that needs great enhancements in WQ.
• Unfit clusters include {(S₅:S₆, 0.025), (S₈, 0.52), (S₂₀, 0.01), (S₂₄:S₂₅, 0.21), (S₂₇, 0.1)}. These clusters are unsuitable at all for farming “Shrimp”.

The result presented in Table 4, shows that the water sites from S₉ (Qena) to S₁₉ (Atfih) with around 492 km long, is highly suitable for farming all types of Tilabia fish, one of the most popular consumed fish types in Egypt, including F₁₄ (Tilabia Zillii), F₁₅ (Tilabia Galilea), F₁₆ (Tilabia Aurea), and F₁₇ (Tilabia Nilotica). In consequence, Table 5 and Figure 14 show and visualize the result of the clustering process of the considered consecutive water sites along the Nile River based on their suitability degrees for farming each considered fish type. The resulting clusters greatly help fish farmers and managers in managing and planning the farming process of the considered fish types.

Figure 14a shows the resulted suitability-based clusters for farming fish types (F₁:F₃). As noted, there is a shared best fit suitable cluster (S₁:S₂) for farming fish types F₁ (Shrimp), F₂ (African Sharp Tooth catfish), and F₃ (Anguilla), with average suitability degree of 100%, 100%, and 97.5%, respectively. In addition, there are many suitable clusters for farming Shrimp including (S₁:S₂, 1); (S₇, 0.98); (S₉:S₁₃, 1); (S₁₅:S₁₉, 0.99); (S₂₁, 1) and (S₂₃, 0.9). On the other hand, Figure 14b shows the resulted suitability-based clusters for farming fish types (F₄:F₆). It shows that there are four clusters, namely (S₁:S₃, 0.97), (S₉:S₁₃, 0.98), (S₁₅:S₁₈, 0.95), and (S₂₁, 0.96), that are best fit farming fish type F5 (Sharp Tooth Catfish), one of the most popular and cheap fish types in Egypt. In addition, Figure 14c shows the resulting suitability-based clusters for farming fish types (F₇:F₉). As shown, fish types F₇ (Bagrus Docmac) and F₈ (Lates Niloticus) have many suitable clusters, including {(S₁:S₄, 0.97); (S₇:S₁₃, 0.98); (S₁₅:S₁₈, 0.99); (S₂₁:S₂₄, 0.99); (S₂₆, 1)} and {(S₁:S₄, 0.99), (S₆:S₁₃, 0.99), (S₁₅:S₁₈, 0.99), (S₂₀:S₂₄, 0.98), (S₂₆, 1)}, respectively. In contrast, fish type F₉ (Bottle Nose) has a set of short-distance suitable water clusters, including {(S₁:S₂, 1); (S₄, 1); (S₉, 1); (S₁₁, 1); (S₁₄, 0.94); (S₂₂, 1); (S₂₆, 1)}. Finally, Figure 14d shows the resulting suitability-based clusters for farming fish types (F₁₀:F₁₂). It shows that there is a very long water cluster of about 800 KM that is more suitable for farming fish type F₁₀ (Hypoph Thalmichthys), from site S₆ (Edfu) in the south until the end of the Nile River in the north, on both of its two branches, Rashid and Domietta. In addition, for farming fish type F₁₁ (Barbus Bynni), there is one unfit cluster, namely S₅ (Kom Ombo), which has a suitability degree of 0.57. The rest of the clusters, either fit or good, need little enhancements to reach the predefined threshold value, like {(S₃, 0.82), (S₁₀, 0.86), (S₁₄, 0.81), (S₁₉:S₂₀, 0.875), (S₂₄, 0.89), and (S₂₇, 0.84)}. We believe that these resulted clusters for each fish type enable fish farmers and decision makers to select the most suitable clusters of sites, from among the alternatives, to farm a specific fish type. As a result, it facilitates the maximization of the overall productivity of fish farming along the considered water resource by farming each fish type at its most suitable sites. In addition, it flags the unsuitable sites with indications of the abnormal WQ parameters and the required enhancements to make them suitable for farming a specific fish type.

5.5. Required Enhancements of Unsuitable Sites for Fish Farming

This work helps determine the polluted water sites as a subset of unsuitable sites for fish farming. It gives estimated values for the required enhancements for each of these sites. The results presented in Table 4 and Figure 11 show a significant problem regarding the water quality for sites S₅, S₆, S₂₀, S₂₁, S₂₅, S₂₇, and S₂₈ for farming fish types F₁, F₅, and F₁₄. In addition, one of most popular fish types in Egypt, namely Tilabia Zillii (F₁₄), is not suitable for farming at the water sites S₃–S₆, S₂₀, S₂₄, S₂₅, S₂₇, and S₂₈. As investigated, some of these sites, like S₅ and S₆, correspond to industrial cities that create several pollutants, such as chemical and biological pollution. For example, the discharged wastewater resulting from wood and sugar factories, and agricultural and domestic drainage water, greatly pollute the Nile River water at site S₅ (Kom Ombo) [34,35]. In addition, site S₆ (Edfu) is one of the sites most affected by this pollution, since Edfu city has paper, phosphate, sugar, and ferrosilicon factories. The wastewater resulting from these factories greatly affects the quality of Nile River water at this site. Factory wastewater affects not only the aquatic environment, but also humans and plants, causing the emergence of some diseases for each of them [36].

The proposed approach adopts Equation (12) to compute the required enhancements for the under-threshold PH and/or Temp for each unsuitable site. In addition, Equation (13) computes the required enhancement in the under-threshold DO in each water site. As a result,

Table 6. A sample of the required enhancements for some unsuitable sites’ WQ parameters.

Fish ID	${\mathit{S}}_5$ (Kom Ombo)			${\mathit{S}}_6$ (Edfu)			${\mathit{S}}_{25}$ (Banha)
	$\mathsf{\Delta }{\mathit{S}}_5^{\mathit{P}\mathit{H}}$	${\mathsf{\Delta }\mathit{S}}_5^{\mathit{D}\mathit{O}}$	$\mathsf{\Delta }{\mathit{S}}_5^{\mathit{T}\mathit{e}\mathit{m}\mathit{p}}$	$\mathsf{\Delta }{\mathit{S}}_6^{\mathit{P}\mathit{H}}$	${\mathsf{\Delta }\mathit{S}}_6^{\mathit{D}\mathit{O}}$	$\mathsf{\Delta }{\mathit{S}}_6^{\mathit{T}\mathit{e}\mathit{m}\mathit{p}}$	$\mathsf{\Delta }{\mathit{S}}_{25}^{\mathit{P}\mathit{H}}$	${\mathsf{\Delta }\mathit{S}}_{25}^{\mathit{D}\mathit{O}}$	$\mathsf{\Delta }{\mathit{S}}_{25}^{\mathit{T}\mathit{e}\mathit{m}\mathit{p}}$
F1	+7%	+44%	0%	0%	+22%	0%	0%	+27%	0%
F2	+7%	+39%	0%	0%	+17%	0%	0%	+23%	0%
F3	+32%	+31%	0%	+4%	+11%	0%	0%	+16%	0%
F4	0%	+31%	−3%	0%	+11%	−1%	−2%	+16%	0%
F5	+16%	+57%	0%	0%	+33%	0%	0%	+39%	0%
F6	+25%	+5%	0%	0%	0%	0%	0%	0%	0%
F7	+15%	+18%	0%	0%	0%	0%	0%	+4%	0%
F8	+11%	+5%	0%	0%	0%	0%	0%	0%	0%
F9	0%	+31%	0%	0%	+11%	0%	0%	+16%	0%
F10	0%	+5%	0%	0%	0%	0%	0%	0%	0%
F11	+7%	+5%	0%	0%	0%	0%	0%	0%	0%
F12	+25%	+57%	0%	0%	+33%	0%	0%	+39%	0%
F13	0%	+57%	0%	0%	+33%	0%	0%	+39%	0%
F14	0%	+44%	0%	0%	+22%	0%	0%	+27%	0%
F15	0%	+57%	0%	0%	+33%	0%	0%	+39%	0%
F16	0%	+57%	0%	0%	+33%	0%	0%	+39%	0%
F17	0%	+57%	0%	0%	+33%	0%	0%	+39%	0%

shows the needed enhancement in each unsuitable WQ parameter at a specific site, where the “+” sign indicates a required positive change needed to increase the WQ parameter value; in contrast, the ‘−’ sign indicates a required negative change needed to decrease the WQ parameter value. In fact, improving the water quality parameters in such sites is a very complicated problem. It should start by studying the causes of pollution in such sites and attempting to remove them or at least reduce them to be under the safe level. In aquaculture, some fish types have tolerance to some extent for variations in WQ parameter values [6,30]. Accordingly, some water sites with a suitability degree of less or more than 5–10% of the specified standard value may be accepted for fish farming with respect to the tolerance degree of each fish type. On the other hand, sites with suitability less than 0.75 represent bad sites for farming of fish other than some fish types with a high tolerance degree. Finally, sites with suitability less than 0.55 need careful analysis to realize the reasons for such abnormal WQ parameter values, and are almost not suitable at all for fish farming. Table 6 shows the required enhancements as a percentage of the unsuitable sites’ WQ parameters to reach the predefined suitability threshold for farming each fish type.

5.6. Discussion

The illustrated case study shows the benefit of the proposed approach in managing and planning the fish farming process of a specific set of fish types through given water source sites. It evaluates the suitability of a set of considered spatial water sites for fish farming. As a result, it clusters the considered sites based on their suitability degree into a set of suitable sites and a set of unsuitable sites for each fish type. Some clusters of sites are ideally best suited for farming some types of fish. In contrast, some other clusters of sites are not suitable at all for farming a specific fish type due to abnormal values of the considered WQ parameters PH, DO, and/or Temp. Unfortunately, a set of water sites is not at all suitable due to the water pollution problem caused by the surrounding environment. It incorporates various types of polluters like sewage drainage and factories (sugar, wood, paper, phosphate, and ferrosilicon factories) with huge amounts of wastewater. Figure 14a–d illustrate the results of this work. They give clear, transparent geographical maps for real opportunities for farming a set of considered fish types in a set of consecutive spatial water sites spread over the Nile River in Egypt. These maps clearly show the fish types that are most suitable for farming in each spatial water cluster of sites, and those that are not. As shown in Figure 11 and Figure 12, the suitability degrees for farming two groups of selected fish types (F₁, F₃, F₄, F₅, and F₁₂) and (F₁₃:F₁₇) at Nile River sites (S₅, S₆, S₈, S₂₀, S₂₅ and S₂₇) and (S₄:S₆, S₈, S₂₀, S₂₂ and S₂₄:S₂₈), respectively, are lower than the specified threshold value (0.9). Therefore, farming these fish types at these water sites is not recommended until enhancing their WQ parameters, otherwise, we would expect failure in fish growth and great reduction in the overall production. For instance, the suitability degrees for cluster (S₅:S₆), S₂₀ and site S₂₅ range from 0 to 0.73, from 0.01 to 0.55 and from 0 to 0.49, respectively, for farming fish types (F₁:F₅ and F₁₂:F₁₇), as shown in Table 3. On the other hand, Table 4 and Table 6 show that the fish types (F₁, F₅, F₇, and F₈) are best suited for farming at sites (S₁:S₂, S₉:S₁₃, S₁₅:S₁₈, and S₂₁) as these sites have sufficient suitability degrees greater than the specified threshold value (0.9). In addition, the spatial water cluster (S₉:S₁₉), which starts at Qena and ends at Atfih, is ideal for farming fish types (F₁₀:F₁₇). We expect that farming some non-conflicting suitable fish types together is appropriate and may greatly enhance the overall production in such long spatial water clusters. As noted, both of water sites S₅ and S₆ may remedy the side effects of factories wastewater that affects the quality of fresh water causing abnormal WQ parameters like dissolved oxygen and salinity. In addition, chemical pollution resulting from agriculture wastes, factories, and individuals directly affects the water sites’ suitability for fish farming.

This study also considers the unsuitable sites with suitability degrees less than the specified threshold value indicating that they have shortages in one or more WQ parameters. The suitability degree of a site ${\mathrm{S}}_{\mathrm{k}}$ is calculated as the minimum suitability of potential of hydrogen $({\mathrm{S}}_{\mathrm{k}}^{\mathrm{P}\mathrm{H}}$), dissolved oxygen (${\mathrm{S}}_{\mathrm{k}}^{\mathrm{D}\mathrm{O}}$), and water temperature (${\mathrm{S}}_{\mathrm{k}}^{\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}}$) using Equations (1) and (2) and Algorithm 2. If the suitability of a WQ parameter is less than the predefined threshold θ_i for farming fish type F_i then this parameter becomes critical and needs an enhancement to reach the predefined threshold value. The required enhancement may be positive (+Δ) or negative (−Δ) indicating a required increase or decrease in the WQ parameter value respectively.

Table 7. Comparison between the proposed approach and some other related works.

Work	Considered Aspects	Methodology	Contribution Outputs
[4]	▪ PH, DO, and ammonia. ▪ Requirements of Mandarin fish farming.	▪ Define a set of fuzzy sets for each considered WQ parameter, namely PH, DO, and ammonia. ▪ Construct a set of fuzzy if–then rules to represent the effect of the parameters on farming Mandarin fish type. ▪ Achieve inference using Mamdani fuzzy inference system. ▪ The results give indications of needed improvements in the considered WQ parameters to reach the standard values.	▪ Evaluation of WQ for aquaculture.
[15]	▪ DO, biological oxygen demand (BOD), chemical oxygen demand (COD), total suspended solid (TSS), (PH), and ammoniacal nitrogen (NH3 N).	▪ Define a set of fuzzy sets for each considered WQ parameter. ▪ Define the output fuzzy sets (adequate, acceptable, and highly acceptable) of inputs and outputs. ▪ Construct a set of fuzzy if–then rules to represent the effect of parameters on water quality index. ▪ Inference using Mamdani fuzzy inference system. ▪ Assess fish pond water quality index (WQI).	▪ Evaluates a water pond and assigns to it a water quality index (WQI) in terms of (adequate, acceptable, highly acceptable).
[20]	▪ Temperature, water pollution, and harvesting of Hilsa fishes. ▪ Hilsa fish production.	▪ Define a set of fuzzy sets for each considered WQ parameter namely Temp, pollution, and harvesting. ▪ Construct a set of fuzzy if–then rules using Mamdani model ▪ Inference using Mamdani fuzzy inference system. ▪ Investigate the impacts of water temperature, water pollution, and harvesting of juvenile Hilsa on the production of mature Hilsa fishes.	▪ The impacts of water temperature, pollution, and harvesting on the production of Hilsa fish.
This work	▪ A set of 27 freshwater sites S, with their historical WQ parameter values including PH, DO, and Temperature parameter values. ▪ A set of 17 fish types F with their requirements of WQ parameters in addition to a threshold value indicating the tolerance degree of each fish type to sites’ low suitability degrees.	▪ Predict the WQ parameters for the considered spatial water sites spread along a freshwater source given a set of historical data. ▪ Store the requirements of WQ parameters for each considered fish type in the database as a trapezoidal FMFs. ▪ Evaluate the matching degree of each water site to the requirements of each specified fish type in terms of site suitability. ▪ Start suitability-based clustering of the sequenced spatial sites with respect to each fish type, resulting in two sets of suitable and unsuitable clusters with an average suitability degree. ▪ Determine the critical parameters that have suitability less than the predefined threshold value of a spatial water site. ▪ Detect the required enhancement in each critical parameter in each unsuitable site as a percentage to reach the accepted predefined threshold value (θ) for farming the fish type.	▪ Predicted values of the WQ parameters in each site for the incoming year. ▪ Suitability degree of each considered water site for farming each considered fish type in terms of a percent and a linguistic term. ▪ A set of suitable clusters as well as another set of unsuitable clusters for farming each fish type. ▪ The required enhancements in WQ parameters for each unsuitable water site.

compares the proposed approach against some other fuzzy-based approaches. The proposed approach has many advantages; firstly, it evaluates every parameter suitability degree, in addition to evaluating the sites’ suitability degree. The evaluation of the parameters’ suitability degree helps fish farmers and decision makers to determine a site’s WQ problems. This leads to enhancement in the management process and solutions for the site’s WQ problems. The approach compares the sites’ WQ parameters with the WQ parameters required for fish farming. In addition to this, the proposed approach does not only consider the suitable sites for fish farming, but also considers the unsuitable sites and determines the required enhancement percent in the sites’ effective parameters to reach the required threshold. Additionally, the proposed approach also determines the clusters of sites based on the sites’ suitability degree.

The work presented in [15] concentrates on developing a fuzzy model for monitoring the water quality of fishponds resulting in one water quality index or three quantifiers, namely “Adequate”, “Acceptable”, and “Highly Acceptable”. The authors of [21] built a fuzzy-based model to assess water warming, harvesting, and pollution of the production of a specific type of fish, namely Hilsa fish. In contrast, this work provides a flexible fuzzy-based model for measuring the suitability of freshwater sites spread along a water source for farming of fish types. Additionally, it clusters these sequenced water sites with respect to their suitability degrees, resulting in a set of suitable and unsuitable clusters for farming of fish types. Finally, for the unsuitable sites, it gives the required enhancement for each unsuitable water parameter.

6. Conclusions

This paper presents a fuzzy-based approach for managing and planning the fish farming process at a set of consecutive spatial sites spread through a freshwater source with respect to their WQ parameters. A prediction process takes place for the WQ parameter values for the upcoming year. This adopts an importance weight for each year of the considered set of most recent historical years. The proposed approach benefits from the smooth boundaries of the fuzzy set as a soft computing approach. It enables human-like modeling of the domain knowledge concerning the requirements of WQ parameters for farming each fish type. Consequently, for each fish type, an evaluation process takes place for each site to measure its suitability for farming the specified fish type. After that, a clustering process takes place, resulting in a set of suitable clusters rather than a set of unsuitable clusters. An average suitability degree is associated with each resulting cluster, which shows its suitability for farming the specified fish type. Each cluster represents a distance within the considered water source. The resulting clusters, with their computed average suitability degree, help decision makers and fish farmers in selecting the most suitable sites for farming each considered fish type. The proposed approach helps determine the set of fish types allowed for farming together in a consecutive set of water sites through a conjunction operation of their suitable clusters. In addition, it detects the required enhancements in WQ parameters for each unsuitable water site for farming each considered type of fish. For each unsuitable WQ parameter value, it detects the required percentage increase or decrease to reach the preset accepted threshold value. An illustrative case study of fish farming in the Nile River of Egypt was undertaken. This showed the benefit of the proposed approach against traditional crisp approaches, rather than a set of previous approaches. This case study considered 17 freshwater fish types and 28 different spatial freshwater sites sequenced on the Nile River in Egypt, from Nasser Lake (S₁) in the south, to Desouk (S₂₄) and Domietta (S₂₈) in the north.

The achieved result provides a representative geographical map visualizing the suitability degree of each water site for farming a specific fish type. This shows which fish types are best suited to farming in each spatial water cluster of the sites, and which are not. Therefore, it shows the real opportunities for water sites along the Nile River for farming a set of considered fish types. Accordingly, it obviously helps in fish farming managing and planning, to maximize the overall productivity and prevent probable catastrophic damage. In addition, it shows the causes of the abnormality of unsuitable sites and the required enhancements. Hence, it helps in detecting the most polluted freshwater sites spread along the considered water source, which need enhancements in their WQ at least for some extent to reach the predefined threshold value for each considered fish type. Accordingly, it helps protect the fish farming process from probable damage as a result of the sites’ unsuitability. Finally, we believe that eliminating the causes of pollution in the polluted freshwater sites along the considered freshwater source could cause a significant boom in the cultivation of multiple types of freshwater fish and prevent from probable catastrophic damage.