Assessment of Biofuel Industry Sustainability Factors Based on the Intuitionistic Fuzzy Symmetry Point of Criterion and Rank-Sum-Based MAIRCA Method

Abstract

Biofuel production from biomass resources can significantly contribute to greenhouse gas mitigation and clean energy generation. This paper aims to develop a new decision analysis approach under an intuitionistic fuzzy set (IFS) setting to rank suitable biomass resources for biofuel production. For this purpose, an intuitionistic fuzzy Symmetry Point of Criterion (IF-SPC) tool was introduced to obtain the objective weight of the indicators and an IF-rank sum (IF-RS) was applied to find the subjective weight of the indicators under an IFS setting. Then, an integrated multi-attributive ideal real comparative assessment (MAIRCA) approach was introduced using aggregation operators and a proposed weight-determining tool to rank suitable biomass resources for biofuel production. Further, the usability of the proposed model was tested with a case study of the selection of biomass resources for biofuel production under the context of IFS. From the obtained outcomes, we found that the most important indicators for selecting suitable biomass resources for biofuel production are cost of biomass supply (EC-3), maturity (T-3), local acceptability (SP-1), cost of the biomass conversion process (EC-2), and reduction of GHG emissions (EN-1), respectively. From this perspective, globally existing sustainable biomass resources for biofuel production were recognized and then ranked over thirteen diverse indicators including environmental, economic, technical, and social-political pillars of sustainability. It was found that municipal solid waste and sewage, forest and wood farming waste, and livestock and poultry waste achieve higher overall utility scores over the other biomass resources for biofuel production in India. Furthermore, comparison with extant models and sensitivity analysis are discussed to present the usefulness and stability of the presented model.

1. Introduction

In the economic and social advances of all societies, access to energy has had a decisive impact [1,2]. Biofuel, as sustainable energy produced from a biomass resource, does not release as many GHGs as fossil-based fuels, generally is not a risk to food security, especially for non-edible-based feedstock, and does not threaten biodiversity [3]. Biomass is a sustainable and eco-friendly renewable energy resource (RES) with a significant potential to be a substitute for fossil fuel energy sources [4]. In fact, the amount of comparable energy from existing resources of biomass is about eight times larger than current global energy requirements [2,5].

Biomass resources are categorized into three prime groups as first-, second-, and third-generation [6], considering the feedstock and conversion procedure utilized for their production [7]. First-generation biofuels are produced from crop-based plants, which can be considered as food, such as biodiesel generation from peanuts and rice [8]. Second-generation biofuels are produced from food, agricultural, forest, and municipal solid waste [9,10]. The prime concern related to first-generation biofuel resources is that there is a competition between energy generation and food production for arable land use [11]. First-generation biofuel may also pay raise the net GHG emissions of energy generation structures as a result of deforestation and chemical-based input consumption such as chemical fertilizer [12]. Alternatively, the drawbacks of second-generation biofuels are their high costs and numerous technical concerns [13].

Third-generation biofuels generate energy from algae and seaweed [14]. The biofuels produced in this manner primarily comprise the production of bio-diesel, bio-ethanol, and bio-hydrogen with green algae [15]. The bio-diesel production potential of microalgae is apparently 15–300 times greater than that of conventional crops in terms of land-use source; furthermore, microalgae has a short harvesting sequence [16]. However, biofuel production from third-generation biofuel resources (algal biomass) encounters specific complications such as high water requirements on an industrial scale, several technical issues such as lipid extraction, dewatering, and geographical-based difficulties in various regions where the temperature is below freezing for a significant duration of the year [17].

In this context, India is the world’s third-largest energy-consuming country, and a significant portion of India’s energy needs are met through fossil fuels, which continue to depend mostly on imports. India’s share of global energy consumption is projected to double by 2050 [18]. A growing energy demand and high dependence on imports raise substantial energy security concerns. It is also evidence of a huge foreign cash outflow. Additionally, excessive utilization of fossil fuels raises maximum GHG emissions and related health issues. Biofuels in India are of tactical significance as they augur well with current initiatives of the government, namely Make in India (MII) and Swachh Bharat Abhiyan (SBA), and provide great prospects for incorporation with ambitious goals of doubling farmers’ revenue, import reduction, job creation, waste-to-wealth generation, and decreasing air pollution [18]. Consequently, it is extremely crucial to rank biomass resources in terms of energy production in this region.

Numerous models have been utilized to find suitable biomass resources for biofuel production. However, conventional single-attribute decision analysis (SADA) models are no longer capable of solving these complex problems [2], and, accordingly, ranking the local biomass resources alternatives for biofuel production must be taken from a multi-attribute decision analysis (MADA) perspective. MADA is one of leading innovative and practical models for assessment and can be utilized to rank diverse biomass resources in terms of biofuel production. Numerous MADA tools have been implemented for treating this complex problem in the bioenergy and biofuel sectors [19,20,21]. Each MADA model has its cons and pros, and the procedure could be enhanced with the hybridization and implementation of two or more models [22]. Consequently, this study aims to rank suitable biomass resources for biofuel production in India by unifying diverse MADA tools under uncertainty.

The doctrine of IFS is an influential and appropriate way to manage the uncertainty and fuzziness occurring in various realistic MADA issues. Considering the flexibility and applicability of IFSs, the aim of this study is to develop an integrated framework for evaluating the MADA problem on IFSs. For the first time, a hybridized MADA model created by uniting the IFSs, the IF-symmetric-point-criterion (SPC)-rank sum (RS) weighting model, and the multi-attributive ideal real comparative assessment (MAIRCA) model, referred to as the IF-SPC-RS-MAIRCA model, is presented. The IF-SPC-RS model is utilized the integrated weighting of parameters by combining objective and subjective weights. The objective parameters are determined from the decision matrices and derived based on the information presented by the “decision-making experts” (DMEs). The IF-SPC approach has been presented to estimate attribute weights using the utility of the attribute that is described by its symmetry, that is, using the absolute rating of symmetry of the attribute to measure its impact on the weight of attribute. The symmetry point is located in the middle of interval [a, b], where a and b present the lower and upper degrees of the criterion, respectively. The subjective criteria weights offer the DMEs subjective opinions on the relative significance of the criteria. For the subjective weighting model, a “rank-sum” (RS) weighting method was applied to assist DMEs in giving their preference ratings for the considered criteria [22]. Further, the combined MAIRCA method is introduced for the sake of prioritizing appropriate biomass resources for biofuel production under the context of IFS, which combines the benefits of criteria weighting model, aggregation function, and the gap between the ideal ratings and empirical ratings of options with intuitionistic fuzzy information. The novel contributions of this work are as follows:

• Identifying the key indicators of sustainability for prioritizing biomass resource options for biofuel production using the literature survey method.
• Estimating the indicator weights and proposing an IF-SPC-RS model by considering the symmetry of criteria and the rank-sum model.
• Introducing a MAIRCA model integrated with the IF-SPC-RS model to rank the biomass resource options for biofuel production.
• Completing a case study of selection biomass resource options for biofuel production to exemplify the performance and advantages of the developed IF-SPC-RS-MAIRCA method.
• Certifying the developed IF-SPC-RS-MAIRCA model, we present its sensitivity and undertake comparative discussions.

The rest of the study is arranged thusly: Section 2 confers the literature associated with the biofuel sector and IFSs and MADA models under uncertain settings. Section 3 introduces fundamental notions of IFSs. Section 4 introduces a hybrid intuitionistic fuzzy-SPC-RS-MAIRCA method for MADA problems to rank the biomass resource options for biofuel production. Section 5 implements the developed model with a case study of the selection of biomass resource options for biofuel production. Section 6 concludes the whole study and provides further research recommendations.

2. Literature Review

2.1. Decision Analysis Model for the Biofuel Sector

Recently, numerous models have been established to rank and choose the most appropriate biomass resources for biofuel production from a sustainability viewpoint. Kataki et al. [10] reviewed biomasses’ accessibility, conversion tools, and biofuel production potential in the northeastern states of India. Khishtandar et al. [23] presented an MADA based on HFTLSs information for the assessment of bioenergy production technology (BPT). Additionally, a hybrid MADA tool was presented by Mishra et al. [21] using the SWARA COPRAS models from the perspective of IFSs. Recently, Firouzi et al. [2] utilized a hybrid MADA to rank suitable biomass resources for biofuel production. Abdel-Basset et al. [24] discussed an MADA tool using the DEMATEL and the EDAS models for assessing sustainable BPTs on trapezoidal neutrosophic sets. Afkharni et al. [25] used BWM and TOPSIS models on FSs for site selection for biofuel production from farm practices in Fars region. Kengpol et al. [26] presented fuzzy AHP and TOPSIS tools for sustainably assessing sites for biomass power plants. Mishra et al. [27] introduced an ARAS tool to choose sustainable biomass crops on PFSs. Da Silva Romero et al. [28] discussed a GIS-based fuzzy system for region identification for biorefineries with spatial and multifactor information. Hezam et al. [22] developed the SVN-MEREC-SWARA-COPRAS model for selecting bioenergy production technologies (BPTs) with sustainability indicators.

2.2. Review of IFSs and MADA

Uncertainty and ambiguity are intrinsic features of information. In numerous scientific and industrial implementations, we make decisions in settings with various types of uncertain information. The fuzzy set (FS) has effectively been utilized in various settings and revealed its dominant facility for treating vague and ambiguous information. Considering the literature, numerous models and theories have been proposed within the FS doctrine. Further, Atanassov [29] generalized the FS to the “intuitionistic fuzzy set” (IFS), which handles vague data more correctly. In IFS, each element is described with a membership grade, a non-membership grade, and an indeterminacy grade. Researches on the IFS doctrine and its applications in diverse fields are progressing rapidly, and many significant results have been achieved. For instance, De et al. [30] first constructed the credit risk evaluation index system, and, further, suggested a hybrid tool using the AHP with IFS. Mishra and Rani [31] discussed a collective framework for choosing a cloud service provider from an intuitionistic fuzzy perspective. Liang et al. [32] first proposed some new intuitionistic fuzzy distance measures and aggregation operators, and further applied them to extend a “multi-attribute border approximation area comparison” (MABAC) framework for treating correlative MCDM problems. Zhang et al. [33] put forward a novel intuitionistic fuzzy UTASTAR model for treating the selection of “low-carbon tourism destinations” (LCTDs). Liu et al. [34] recommended the latest intuitionistic fuzzy “partitioned Bonferroni mean” (PBM) operator to treat the MCDM process in order to assess rooftop photovoltaic project sites. Gao et al. [35] recommended an MCDM methodology by combining the intuitionistic fuzzy score function, prospect theory, “analytical network process” (ANP), and linear weighting technique. Ocampo et al. [36] suggested the TOPSIS-Sort method using IFSs and demonstrated it in arranging restaurants by the objective experiences of clients in the context of COVID-19. Hezam et al. [22] put forward an incorporated MCDM framework with the MEREC model with a “double normalization-based multiple aggregation” (DNMA) tool to solve MADA problems.

Recently, numerous MADA tolls have been established, such as IF-TOPSIS [37], IF-VIKOR [38], IF-COPRAS [39], IF-CODAS [40], IF-MABAC [41], IF-MULTIMOORA [42], etc. These decision-making methods are not appropriate for our purposes in and of themselves, and their applications are limited in diverse settings. For instance, the relative closeness degree from the distances between each option and the reference points are ignored in the IF-TOPSIS model. The preferences which are derived from the “group utility” degree and the “individual regret” degree are not considered in the IF-VIKOR model. A similar inadequacy occurs in the IF-COPRAS, IF-CODAS, and IF-MABAC models. The IF-MULTIMOORA model does not consider the relative significance of aggregation operators. The IF-ELECTRE model suffers from complex computations and high time requirements due to it deriving consistency and inconsistency ratings based on the subdivision preferences between options.

The MAIRCA [43] is an elegant MADA model. Its main objective is to determine the gap between the ideal ratings and the assessment ratings [44]. For each option, the sum of the gaps for all attributes provides the overall gap, and the option with the lowest utility score is taken as the appropriate option. The MAIRCA approach is more stable than the TOPSIS or ELECTRE models because it uses a diverse linear normalization procedure described by simple mathematical computations and result permanence [45]. Pamucar et al. [44] combined the classical MAIRCA method with the DEMATEL tool to assess locations for sustainable multimodal logistic centers. Kaya [46] evaluated the effect of COVID-19 on nations’ sustainable development using the MAIRCA model. Boral et al. [45] proposed a hybrid fuzzy failure modes and effects analysis tool by combining the AHP and MAIRCA method with fuzzy information. Recently, Ecer [47] presented an integrated IF-MAIRCA model for solving the vaccine selection period during the of COVID-19 pandemic. In this work, a hybrid IF-SPC-RS-MAIRCA model with a new criteria weighting model has been developed to handle MADA problems.

3. Preliminaries

The idea of IFSs, score function, and aggregation operators are discussed.

Definition 1

[29]. An IFS R on fixed set $Z=\{z_1,z_2,\dots ,z_s\}$ is given as

$$R=\left\{\langle z_i,{\mu }_R(z_i),{\nu }_R(z_i)\rangle :z_i\in Z\right\},$$

where  ${\mu }_R:Z\to [0,1]$ and  ${\nu }_R:Z\to [0,1]$ present the MF and NF of an object  $z_i$ to R in Z, respectively, satisfying

$0\le {\mu }_R\left(z_i\right)\le 1,0\le {\nu }_R\left(z_i\right)\le 1$ and  $0\le {\mu }_R\left(z_i\right)+{\nu }_R\left(z_i\right)\le 1,\forall z_i\in Z.$

The degree of indeterminacy of an object $z_i\in Z$ to R is discussed as ${\pi }_R\left(z_i\right)=1-{\mu }_R\left(z_i\right)-{\nu }_R\left(z_i\right)$ and $0\le {\pi }_R\left(z_i\right)\le 1,\forall z_i\in Z.$

For ease, Xu [48] defined the “intuitionistic fuzzy number” (IFN) $\omega =\left({\mu }_{\omega },{\nu }_{\omega }\right)$, which satisfies ${\mu }_{\omega },{\nu }_{\omega }\in \left[0,1\right]$ and $0\le {\mu }_{\omega }+{\nu }_{\omega }\le 1.$

Definition 2

[48]. Consider  $\omega =\left(\mu ,\nu \right)$ to be an IFN. Then

$$\overline{\mathbb{S}}\left(\omega \right)=\left(\mu -\nu \right)andh\left(\omega \right)=\left(\mu +\nu \right),where\overline{\mathbb{S}}\left(\omega \right)\in \left[-1,1\right]and\hslash \left(\omega \right)\in \left[0,1\right],$$

(1)

are said to be the score and accuracy values of  $\omega$, respectively.

As $\overline{\mathbb{S}}\left(\omega \right)\in \left[-1,1\right],$ Xu et al. [49] gave a normalized score and accuracy functions, shown as:

Definition 3

[49]. For an IFN  $\omega =\left(\mu ,\nu \right),$ a normalized score value of ω is given as

$$\mathbb{S}\left(\omega \right)=\frac{1}{2}\left(\overline{\mathbb{S}}\left(\omega \right)+1\right)$$

(2)

where  $\mathbb{S}\left(\omega \right)\in \left[0,1\right].$

Definition 4

[48]. Let  ${\zeta }_j=\left({\mu }_j,{\nu }_j\right),$ $j=1,2,\dots ,n$ be IFNs. Then, the IFWA and the IFWG operators on the IFNs are given by

$$IFW{A}_w\left({\zeta }_1,{\zeta }_2,\dots ,{\zeta }_n\right)=\underset{j=1}{\overset{n}{\oplus }}{w}_j{\zeta }_j=\left[1-{\displaystyle \prod _{j=1}^n{\left(1-{\mu }_j\right)}^{w_j}},{\displaystyle \prod _{j=1}^n{\nu }_j{}^{w_j}}\right],$$

(3)

$$IFW{G}_w\left({\zeta }_1,{\zeta }_2,\dots ,{\zeta }_n\right)=\underset{j=1}{\overset{n}{\otimes }}{w}_j{\zeta }_j=\left[{\displaystyle \prod _{j=1}^n{\mu }_j{}^{w_j}},1-{\displaystyle \prod _{j=1}^n{\left(1-{\nu }_j\right)}^{w_j}}\right],$$

(4)

where  $w_j={\left(w_1,w_2,\dots ,w_n\right)}^T$ is a weight of the values of  ${\zeta }_j,j=1,2,\dots ,n,$ with  ${\displaystyle {\sum }_{j=1}^n{w}_j=1},$ $w_j\in \left[0,1\right].$

4. An Integrated IF-SPC-Rank-Sum-MAIRCA Model

In this section, the IF-SPC-RS-MAIRCA model using the IF-SPC model and IF-rank-sum model is introduced. Here, the IF-SPC model is presented to generate the objective weight of the indicators and the IF-RS is applied to estimate the subjective weight of the indicators. Finally, the preference for the option is obtained using the IF-SPC-RS-MAIRCA model. The procedural steps of the developed model are given as follows:

Step 1: Construct an intuitionistic fuzzy decision-matrix (IFDM).

A team $E=\left\{e_1,e_2,\dots ,e_l\right\}$ of DMEs is formed to assess a set of options $M=\left\{m_1,m_2,\dots ,m_s\right\}$ with respect to criteria set $N=\left\{n_1,n_2,\dots ,n_t\right\}.$ A team offers assessment ratings for each option $m_i$ over different indicator $n_j\left(j=1,2,\dots .,t\right)$ in the form of “linguistic ratings” (LRs). Consider $\mathsf{\Upsilon }=\left(y_{ij}^{(k)}\right)$, to be the IFDM offered by the DMEs, where $y_{ij}^{(k)}$ denotes the LR of each option $m_i$ over an indicator $n_j$ provided by the $k^{\mathrm{th}}$ DME.

Step 2: Evaluate the weights of the DMEs.

The significance ratings of the DMEs are described in the form of LRs and converted into IFNs. Let $e_k=\left({\mu }_k,{\nu }_k\right),k=1,2,\dots ,l$ be an IFN, and then the weighted value is given as the normalized IF-score $\left({\lambda }_k\right)$ degree of each DME, which is estimated as

$${\lambda }_k=\frac{{\mu }_k+{\pi }_k\left({\mu }_k/\left({\mu }_k+{\nu }_k\right)\right)}{{\displaystyle {\sum }_{k=1}^l\left({\mu }_k+{\pi }_k\left({\mu }_k/\left({\mu }_k+{\nu }_k\right)\right)\right)}},k=1,2,\dots ,l,$$

(5)

where ${\lambda }_k\ge 0$ and ${\displaystyle \sum _{k=1}^l{\lambda }_k=1.}$

Step 3: Create the “aggregated IFDM” (AIFDM).

The IFWA (or IFWG) operator is applied to define the AIFDM $A={\left({\xi }_{ij}\right)}_{s\times t},$ where

$${\xi }_{ij}=\left({\mu }_{ij},{\nu }_{ij}\right)=IFW{A}_{{\lambda }_k}\left({\xi }_{ij}^{\left(1\right)},{\xi }_{ij}^{\left(2\right)},\dots ,{\xi }_{ij}^{\left(l\right)}\right)\mathrm{or}IFW{G}_{{\lambda }_k}\left({\xi }_{ij}^{\left(1\right)},{\xi }_{ij}^{\left(2\right)},\dots ,{\xi }_{ij}^{\left(l\right)}\right).$$

(6)

Step 4: Find the normalized AIFDM (N-AIFDM).

The N-AIFDM $\mathbb{N}={\left({\delta }_{ij}\right)}_{s\times t}$ is calculated from the AIFDM $A={\left({\xi }_{ij}\right)}_{s\times t}$, where

$${\delta }_{ij}=\left({\tilde{\mu }}_{ij},{\tilde{\nu }}_{ij}\right)=\{\begin{array}{ll}{y}_{ij}=\left({\mu }_{ij},{\nu }_{ij}\right),& j\in n_b,\\ {\left(y_{ij}\right)}^c=\left({\nu }_{ij},{\mu }_{ij}\right),& j\in n_n,\end{array}$$

(7)

and where $n_b$ and $n_n$ symbolize the benefit and cost type indicators, respectively.

Step 5: Compute the weights of the criteria with the IF-SPC model.

Let $w={\left(w_1,w_2,\dots ,w_t\right)}^T$ be the weight of the indicator set, where $w_j\in \left[0,1\right]$ and ${\displaystyle \sum _{j=1}^t{w}_j}=1.$ In the following, we present the procedure for deriving the numerical weights of the criteria.

Step 5.1: Obtain the IF score rating of the N-AIFDM.

We estimate the IF score rating of each N-AIFDM grade using Equation (2), as

$${\alpha }_{ij}=\frac{1}{2}\left(\mathbb{S}\left({\delta }_{ij}\right)+1\right),i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(8)

Step 5.2: Estimate the symmetry value of each indicator.

Let ${\left({\alpha }_{11},{\alpha }_{21},\dots ,{\alpha }_{i1}\right)}^T,i=1,2,\dots ,s$ be IF score value of n₁ indicator over a set of options. If the minimum and maximum grades of an interval $\left[a,b\right]$ are described as $a=\min {\left({\alpha }_{11},{\alpha }_{21},\dots ,{\alpha }_{i1}\right)}^T$ and $b=\max {\left({\alpha }_{11},{\alpha }_{21},\dots ,{\alpha }_{i1}\right)}^T,$ respectively, then the symmetry point $\left({\beta }_j\right)$ is defined by

$${\beta }_j=\frac{\min \left\{{\alpha }_{ij}\right\}+\max \left\{{\alpha }_{ij}\right\}}{2},i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(9)

Step 5.3: Calculate the matrix of the absolute distances.

The matrix of the absolute distances is computed in the following form:

$$D={\left(\left|d_{ij}\right|\right)}_{s\times t}=\left|{\alpha }_{ij}-{\beta }_j\right|,i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(10)

Step 5.4: Create the matrix of the moduli of symmetry.

Let $D_{i1}=\left\{d_{11},d_{21},\dots ,d_{i1}\right\},i=1,2,\dots ,s$ be the column value of the absolute distances for indicator n₁. Therefore, the matrix of the moduli of symmetry is in the following form:

$$M={\left(\left|{\overline{m}}_{ij}\right|\right)}_{s\times t}={\left(\begin{array}{cccc}\frac{{\displaystyle \sum _{i=1}^s{d}_{i1}}}{s.{\alpha }_{11}}& \frac{{\displaystyle \sum _{i=1}^s{d}_{i2}}}{s.{\alpha }_{12}}& \dots & \frac{{\displaystyle \sum _{i=1}^s{d}_{it}}}{s{\alpha }_{1t}}\\ \frac{{\displaystyle \sum _{i=1}^s{d}_{i1}}}{s.{\alpha }_{21}}& \frac{{\displaystyle \sum _{i=1}^s{d}_{i2}}}{s.{\alpha }_{22}}& \dots & \frac{{\displaystyle \sum _{i=1}^s{d}_{it}}}{s.{\alpha }_{2t}}\\ ⋮& ⋮& \ddots & ⋮\\ \frac{{\displaystyle \sum _{i=1}^s{d}_{i1}}}{s.{\alpha }_{s1}}& \frac{{\displaystyle \sum _{i=1}^s{d}_{i2}}}{s.{\alpha }_{s2}}& \dots & \frac{{\displaystyle \sum _{i=1}^s{d}_{it}}}{s.{\alpha }_{st}}\end{array}\right)}_{s\times t}.$$

(11)

Step 5.5: Determine the modulus of symmetry of the criterion.

We find the mean value (Q) of matrix M, where each value q_j signifies the modulus of symmetry of the j^th indicator as

$$Q=\left(q_j\right)=\left(\frac{{\displaystyle \sum _{i=1}^s{\overline{m}}_{i1}}}{s}\frac{{\displaystyle \sum _{i=1}^s{\overline{m}}_{i2}}}{s}\dots .\frac{{\displaystyle \sum _{i=1}^s{\overline{m}}_{it}}}{s}\right),j=1,2,\dots ,t.$$

(12)

Step 5.6: Find the objective weight of the indicator.

In this step, each objective criterion weight is computed using the vector of the moduli of symmetry. The following equation is used for assessing the weight of criteria:

$$w_j^o=\frac{q_j}{{\displaystyle {\sum }_{j=1}^t{q}_j}},j=1,2,\dots ,t.$$

(13)

Case II: Computation of the subjective weight using the IF-RS tool.

Step 5f: Estimate the rating of each indicator with the LR grades provided by the DMEs from the IFWA operator, obtained as

$$N={\left({\xi }_j\right)}_{1\times t}=IFW{A}_{{\lambda }_k}\left({\xi }_j^{\left(1\right)},{\xi }_j^{\left(2\right)},\dots ,{\xi }_j^{\left(l\right)}\right)=\left({\mu }_j,{\nu }_j\right),j=1,2,\dots ,t.$$

(14)

Step 5g: Find the IF-SM.

Applying Equation (2), the IF-SM $\overline{\Omega }={\left({\overline{\eta }}_j\right)}_{1\times t}$ of each IFN ${\xi }_j$ is computed as

$${\eta }_j=\frac{1}{2}\left(\left({\mu }_j-{\nu }_j\right)+1\right),j=1,2,\dots ,t.$$

(15)

Step 5h: Obtain the indicator weight $\left(t-r_j+1\right)$, where $r_j$ is the preference of each indicator. Now, the normalized weight of the indicator is described as

$$w_j^s=\frac{t-r_j+1}{{\displaystyle \sum _{j=1}^t\left(t-r_j+1\right)}},$$

(16)

where t represents the total criteria, j = 1, 2, 3,…, t.

Case III: Determine the combined weight of the criteria.

To obtain the combined weight of the criteria, we merge both the subjective and objective weighting models. The procedure for integrating the weight of the criteria is given by:

$$w_j=\gamma w_j^o+\left(1-\gamma \right)w_j^s,j=1,2,\dots ,t,$$

(17)

where $\gamma \in [0,1]$ is a decision precision parameter.

Step 6: Derive the distances of each indicator from the IF-PIS and IF-NIS.

Initially, an IFN has an IF-PIS and an IF-NIS, which take values ${\varphi }^{+}$ = (1, 0, 0) and ${\varphi }^{-}$ = (0, 1, 0), respectively. To find the distances, a normalized IF-Euclidean distance is implemented. Let $p_{ij}^{+}$ and $p_{ij}^{-}$ be the distances of $A={\left({\xi }_{ij}\right)}_{s\times t}$ from IF-PIS and IF-NIS using Equation (18) and Equation (19), respectively.

$$p_{ij}^{+}=\frac{1}{2}\left(\left|{\mu }_{ij}-{\mu }_{{\varphi }^{+}}\right|+\left|{\nu }_{ij}^2-{\nu }_{{\varphi }_j^{+}}^2\right|+\left|{\pi }_{ij}^2-{\pi }_{{\varphi }_j^{+}}^2\right|\right),$$

(18)

$$p_{ij}^{-}=\frac{1}{2}\left(\left|{\mu }_{ij}-{\mu }_{{\varphi }^{-}}\right|+\left|{\nu }_{ij}^2-{\nu }_{{\varphi }_j^{-}}^2\right|+\left|{\pi }_{ij}^2-{\pi }_{{\varphi }_j^{-}}^2\right|\right).$$

(19)

Step 7: Estimate the relative closeness decision matrix (RC-DM).

$$r{c}_{ij}=\frac{p_{ij}^{-}}{p_{ij}^{-}+p_{ij}^{+}},i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(20)

Step 8: Make the normalized RC-DM.

Each assessment indicator is normalized using the linear max–min normalization procedure and the normalized RC-DM $Z={\left(z_{ij}\right)}_{s\times t}$ is obtained as follows:

$$z_{ij}=\{\begin{array}{l}\frac{r{c}_{ij}-{\left(r{c}_{ij}\right)}_{\min }}{{\left(r{c}_{ij}\right)}_{\max }-{\left(r{c}_{ij}\right)}_{\min }},\mathrm{if}j\in n_b,\\ \frac{{\left(r{c}_{ij}\right)}_{\max }-r{c}_{ij}}{{\left(r{c}_{ij}\right)}_{\max }-{\left(r{c}_{ij}\right)}_{\min }},\mathrm{if}j\in n_n.\end{array}$$

(21)

Step 9: Obtain the theoretical IF decision matrix (TDM).

Initially, the preference of each possible option is computed as

$$P_{A_i}=1/s,\mathrm{where}{\displaystyle {\sum }_{i=1}^s{P}_{A_i}=1.}$$

(22)

Afterwards, ratings for the selection of options are multiplied with indicator weights, thus the TDM $T={\left(t_{ij}\right)}_{s\times t}$ is estimated as

$$t_{ij}=P_{A_i}{w}_j,i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(23)

Step 10: Develop the real IF assessment matrix.

To create a real assessment matrix $R={\left(r_{ij}\right)}_{s\times t}$, the ratings of the normalized RC-DM are multiplied by rating each TDM as

$$r_{ij}=t_{ij}.z_{ij},i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(24)

Step 11: Build the IF discrimination matrix.

The IF discrimination matrix $G={\left(g_{ij}\right)}_{s\times t}$ is obtained by subtracting the real IF assessment matrix from the TDM as

$$g_{ij}=t_{ij}-r_{ij},i=1,2,\dots ,s,j=1,2,\dots ,t.$$

(25)

Step 12: Determine the utility degrees (UDs) of the alternatives.

The UDs of options can be computed by adding the ratings of the IF discrimination-matrix using Equation (26), as

$$u_i={\displaystyle {\sum }_{j=1}^t{g}_{ij}},i=1,2,\dots ,s.$$

(26)

Step 13: Prioritize the options and select the optimal one.

We determine the preferences of the options using the UDs, from the smallest to largest ratings. The option with the smallest UD is the optimal one among the others because it is near to the ideal best option.

5. Case Study: Selection of Biomass Resources for Biofuel Production

India has significant prospects for the further use of bioenergy, mainly via the substitution of coal with solid biomass in extant assets, substitution of conventional bioenergy with more modern (and less-polluting) bioenergy practices, or an increase in utilizing transport biofuels created with domestically accessible agricultural residues. There are various prospects for RES from MSW as portion of the development of waste management structures. As an agricultural and forestry region, northeast India has encouraging prospects for biofuel production from first-, second-, and third-generation biomass resources. Thus, northeast India has been used as the case study for the assessment. Northeast India primarily depends on an agricultural zone which comprises 2.2% (in mountainous regions such as Arunachal Pradesh) and 35.4% (in Assam) of the cultivated region to the whole geographical region of India. Rapid increases in urban population alongside the modernization of markets and industries have produced a huge quantity of solid waste in the northeast region. Consequently, agricultural residues and MSW have become other sources for biofuel production in the northeastern states [10].

In this study, a vivid model in which data were collected with a questionnaire is presented. To handle MADA questions, an indicator to assess the options was required. The questionnaire was prepared after a detailed review of appropriate literature and conferring with academic researchers/scholars in northeast India. It contains thirteen indicators or decision parameters, as shown in

Table 1. Influential criteria for biofuel production from biomass resources and source references.

Dimension	Criteria	Meaning	Types	References
Technical	Safety and reliability (T-1)	A parameter for quantifying the risk and structure reliability of the procedure for biofuel generation.	B	[50]
	Conversion efficiency (T-2)	The quantity of the product (biofuels) used as feedstock input.	B	[51]
	Maturity (T-3)	A parameter for estimating the degree of maturity of the technology.	B	[50]
Economic	Investment cost (EC-1)	All of the costs associated with buying mechanical tools, technological installations, and related manufacturing services.	C	[50]
	Cost of biomass conversion process (EC-2)	The cost for the operation and maintenance of the entire procedure of biodiesel production.	C	[50]
	Cost of biomass supply (EC-3)	The costs associated with the production of biodiesel.	C	[2]
	Biomass reusability (EC-4)	The competitiveness of feedstock and biofuel production and of related biofuels on the fuel trade market.	B	[2]
Environment	Reduction of GHG emissions (EN-1)	The effect of a biofuel on mitigating global warming through its entire life cycle of as compared to fossil fuels.	B	[52]
	Environmental impacts of biomass accumulation (EN-2)	The unified performance of land usage reform and impacts on biodiversity caused by all actions taken for biodiesel production.	B	[2]
	Soil quality (EN-3)	The percentage of land for which soil’s organic carbon is preserved or enhanced out of the total land.	B	[53]
Social-political	Local acceptability (SP-1)	The outline of the views associated with the biodiesel production structures of locals concerning the hypothesized recognition of the projects in an assessment from a consumer viewpoint.	B	[50]
	Security for food supply (SP-2)	The reduction of supplied food and stimulus of the security of the food supply caused by the production of crop-based biodiesel.	B	[54,55]
	Employment (SP-3)	The total job creation in the local sector caused by the growth of biofuel firms.	B	[51,52]

Note: B—benefit, C—cost, criteria.

. Five sets of biomass resources were used, considering the available biomass resources in the northeast region: peanut waste (m₁), municipal solid waste and sewage (m₂), rice waste (m₃), livestock and poultry waste (m₄), and forest and wood farming waste (m₅). Of the biomass resources used in this study, rice and peanuts belong to the feedstock category of first-generation biofuels. A snowball sampling model was used to recognize the four DMEs. Snowball sampling, also known as chain-referral or network sampling, is a nonprobability sampling method where new units are recruited by other units to form part of the sample. Although specific steps can vary depending on the research subject or sampling method, all snowball sampling techniques follow a similar pattern. We considered these steps to apply snowball sampling to the research: (a) identify potential population subjects, (b) contact potential subjects, (c) ask subjects to participate in the research, (d) encourage referrals, (e) evaluate referrals if using discriminative sampling, and (f) repeat until the desired sample size is reached. To offer respondents a perfect understanding of the indicators, we provide a detailed description of each indicator. The respondents were examined to score the practicality of these options with thirteen considered indicators on an 11-point scale (from AB = absolutely bad to AG = absolutely good), which is depicted in

Table 2. LRs of options over indicators for biofuel production.

LRs	IFNs
Absolutely good (AG)	(0.95, 0.05)
Very very good (VVG)	(0.85, 0.10)
Very good (VG)	(0.80, 0.15)
Good (G)	(0.70, 0.20)
Slightly good (SG)	(0.60, 0.30)
Average (A)	(0.50, 0.40)
Slightly bad (SB)	(0.40, 0.50)
Bad (B)	(0.30, 0.60)
Very very bad (VB)	(0.20, 0.70)
Very bad (VVB)	(0.10, 0.80)
Absolutely bad (AB)	(0.05, 0.95)

.

Step 1: Table 2 defines the LRs for estimating the DMEs’ weights, indicators, and sub-criteria for prioritizing biomass resources for biofuel production, which are then transformed into IFNs. The decision matrix is in the form of LRs for ranking suitable biomass resources for biofuel production given by four DMEs is presented in

Table 3. The decision matrix in the form of LRs for biomass resources for biofuel production given by DMEs.

Indicators	m1	m2	m3	m4	m5
n1	(SG, VG, B, SB)	(G, VG, SB, VB)	(A, SB, VVG, B)	(G, SG, VB, B)	(G, G, VG, A)
n2	(SG, G, A, SG)	(VG, G, VG, A)	(SB, SG, A, SG)	(VG, SB, A, SG)	(A, G, SG, SG)
n3	(SB, SG, A, VG)	(A, VG, SB, SG)	(SG, A, VG, G)	(VG, G, A, SG)	(A, SG, VVG, SB)
n4	(B, SB, A, SB)	(B, B, VB, SB)	(VVB, SB, B, SB)	(B, SB, SB, B)	(SB, A, VVB, SG)
n5	(B, VB, SB, A)	(A, VB, B, VB)	(A, SB, VB, B)	(VB, SB, B, B)	(VVB, SB, VB, B)
n6	(VVB, SB, A, B)	(VB, B, SB, VB)	(SB, SB, VB, B)	(SB, B, VVB, A)	(SB, B, A, AB)
n7	(B, VG, SB, VG)	(VG, SB, SG, A)	(A, G, A, SG)	(SG, B, A, AG)	(VG, SB, A, VVG)
n8	(AG, SG, VG, A)	(SB, SG, A, G)	(G, VG, A, SG)	(A, SG, A, G)	(VG, VG, A, SG)
n9	(SG, AG, B, SB)	(G, SG, VG, SB)	(SG, G, G, SG)	(SB, AG, SB, A)	(VG, A, A, VG)
n10	(A, SG, SG, G)	(SG, AG, G, G)	(SG, G, A, VG)	(G, SB, SG, VVG)	(SG, A, SG, AG)
n11	(SG, A, G, SB)	(A, SB, AG, G)	(VG, A, G, VG)	(SG, G, A, VG)	(SB, SG, A, VG)
n12	(VVG, SB, A, SG)	(SG, AG, A, SG)	(VG, A, SG, SG)	(A, SG, VG, G)	(SG, G, VG, A)
n13	(AG, SG, VG, A)	(VG, VG, A, SG)	(SG, G, A, G)	(VG, G, SG, G)	(VG, A, SG, VVG)

. As it is difficult to find a conclusive agreement, the evaluation data investigated and provided by each DME are found in Table 3. The variables e₁, e₂, e_3, and e₄ represent the DMEs in different related disciplines, n₁–n₁₃ represent the eleven sustainability sub-criteria, and m₁–m₅ represent five biomass resources for biofuel production.

Step 2: Using the IFN scale in Table 1 and Equation (5), the weights of the DMEs are obtained and discussed in

Table 4. The weights of the DMEs for ranking suitable biomass resources for biofuel production.

DMEs	g1	g2	g3	g4
LRs	VGG (0.85, 0.10)	VG (0.80, 0.15)	G (0.70, 0.20)	SG (0.60, 0.30)
Weight	0.2812	0.2647	0.2445	0.2096

for ranking suitable biomass resources for biofuel production.

Step 3: Using Equation (6) and Table 2 and Table 3, the AIFDM $A={\left({\xi }_{ij}\right)}_{s\times t}$ which uses the IFWAO is constructed and is shown in

Table 5. AIFDM for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	(0.584, 0.329, 0.086)	(0.608, 0.302, 0.091)	(0.581, 0.329, 0.090)	(0.509, 0.381, 0.111)	(0.698, 0.216, 0.087)
n2	(0.609, 0.289, 0.102)	(0.730, 0.199, 0.071)	(0.527, 0.372, 0.102)	(0.613, 0.303, 0.084)	(0.605, 0.292, 0.103)
n3	(0.591, 0.321, 0.088)	(0.609, 0.314, 0.077)	(0.663, 0.251, 0.086)	(0.678, 0.238, 0.084)	(0.635, 0.277, 0.088)
n4	(0.401, 0.498, 0.101)	(0.300, 0.600, 0.101)	(0.302, 0.597, 0.102)	(0.353, 0.547, 0.100)	(0.420, 0.475, 0.105)
n5	(0.349, 0.549, 0.102)	(0.340, 0.558, 0.102)	(0.368, 0.530, 0.102)	(0.302, 0.597, 0.101)	(0.255, 0.644, 0.101)
n6	(0.336, 0.561, 0.103)	(0.280, 0.619, 0.101)	(0.335, 0.543, 0.122)	(0.336, 0.562, 0.103)	(0.342, 0.568, 0.090)
n7	(0.628, 0.297, 0.075)	(0.616, 0.300, 0.084)	(0.583, 0.313, 0.103)	(0.683, 0.266, 0.051)	(0.685, 0.241, 0.074)
n8	(0.803, 0.163, 0.035)	(0.554, 0.341, 0.104)	(0.676, 0.239, 0.085)	(0.577, 0.321, 0.103)	(0.711, 0.220, 0.069)
n9	(0.712, 0.246, 0.042)	(0.661, 0.251, 0.088)	(0.655, 0.244, 0.101)	(0.701, 0.259, 0.040)	(0.681, 0.247, 0.072)
n10	(0.599, 0.299, 0.102)	(0.798, 0.155, 0.047)	(0.661, 0.250, 0.089)	(0.666, 0.243, 0.091)	(0.726, 0.222, 0.052)
n11	(0.569, 0.326, 0.104)	(0.732, 0.221, 0.048)	(0.719, 0.209, 0.073)	(0.661, 0.250, 0.089)	(0.591, 0.321, 0.088)
n12	(0.643, 0.271, 0.086)	(0.756, 0.200, 0.043)	(0.651, 0.266, 0.083)	(0.662, 0.252, 0.086)	(0.672, 0.242, 0.086)
n13	(0.817, 0.146, 0.037)	(0.711, 0.220, 0.069)	(0.631, 0.266, 0.103)	(0.713, 0.204, 0.083)	(0.716, 0.212, 0.073)

.

Step 4: Since n₄, n₅, and n₆ are cost indicators and others are benefits, we are thus required to create a normalized AIFDM $\mathbb{N}={\left({\delta }_{ij}\right)}_{s\times t}$ using Equation (7), which is given in

Table 6. Normalized AIFDM for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	(0.584, 0.329, 0.086)	(0.608, 0.302, 0.091)	(0.581, 0.329, 0.090)	(0.509, 0.381, 0.111)	(0.698, 0.216, 0.087)
n2	(0.609, 0.289, 0.102)	(0.730, 0.199, 0.071)	(0.527, 0.372, 0.102)	(0.613, 0.303, 0.084)	(0.605, 0.292, 0.103)
n3	(0.591, 0.321, 0.088)	(0.609, 0.314, 0.077)	(0.663, 0.251, 0.086)	(0.678, 0.238, 0.084)	(0.635, 0.277, 0.088)
n4	(0.498, 0.401, 0.101)	(0.600, 0.300, 0.101)	(0.597, 0.302, 0.102)	(0.547, 0.353, 0.100)	(0.475, 0.420, 0.105)
n5	(0.549, 0.349, 0.102)	(0.558, 0.340, 0.102)	(0.530, 0.368, 0.102)	(0.597, 0.302, 0.101)	(0.644, 0.255, 0.101)
n6	(0.561, 0.336, 0.103)	(0.619, 0.280, 0.101)	(0.543, 0.335, 0.122)	(0.562, 0.336, 0.103)	(0.568, 0.342, 0.090)
n7	(0.628, 0.297, 0.075)	(0.616, 0.300, 0.084)	(0.583, 0.313, 0.103)	(0.683, 0.266, 0.051)	(0.685, 0.241, 0.074)
n8	(0.803, 0.163, 0.035)	(0.554, 0.341, 0.104)	(0.676, 0.239, 0.085)	(0.577, 0.321, 0.103)	(0.711, 0.220, 0.069)
n9	(0.712, 0.246, 0.042)	(0.661, 0.251, 0.088)	(0.655, 0.244, 0.101)	(0.701, 0.259, 0.040)	(0.681, 0.247, 0.072)
n10	(0.599, 0.299, 0.102)	(0.798, 0.155, 0.047)	(0.661, 0.250, 0.089)	(0.666, 0.243, 0.091)	(0.726, 0.222, 0.052)
n11	(0.569, 0.326, 0.104)	(0.732, 0.221, 0.048)	(0.719, 0.209, 0.073)	(0.661, 0.250, 0.089)	(0.591, 0.321, 0.088)
n12	(0.643, 0.271, 0.086)	(0.756, 0.200, 0.043)	(0.651, 0.266, 0.083)	(0.662, 0.252, 0.086)	(0.672, 0.242, 0.086)
n13	(0.817, 0.146, 0.037)	(0.711, 0.220, 0.069)	(0.631, 0.266, 0.103)	(0.713, 0.204, 0.083)	(0.716, 0.212, 0.073)

.

Step 5: From Equations (8) and (9), we find the IF score matrix with the AIFDM and the symmetry point of each indicator, presented in

Table 7. IF score matrix and symmetric point of each indicator.

	m1	m2	m3	m4	m5	$\mathbf{min}\left\{{\mathit{\alpha }}_{\mathit{i}\mathit{j}}\right\}$	$\mathbf{max}\left\{{\mathit{\alpha }}_{\mathit{i}\mathit{j}}\right\}$	${\mathit{\beta }}_{\mathit{j}}$
n1	0.628	0.653	0.626	0.564	0.741	0.564	0.741	0.652
n2	0.660	0.766	0.577	0.655	0.657	0.577	0.766	0.672
n3	0.635	0.647	0.706	0.720	0.679	0.635	0.720	0.677
n4	0.549	0.650	0.647	0.597	0.527	0.527	0.650	0.589
n5	0.600	0.609	0.581	0.647	0.694	0.581	0.694	0.638
n6	0.613	0.669	0.604	0.613	0.613	0.604	0.669	0.637
n7	0.665	0.658	0.635	0.709	0.722	0.635	0.722	0.678
n8	0.820	0.606	0.718	0.628	0.745	0.606	0.820	0.713
n9	0.733	0.705	0.705	0.721	0.717	0.705	0.733	0.719
n10	0.650	0.821	0.706	0.711	0.752	0.650	0.821	0.736
n11	0.622	0.755	0.755	0.706	0.635	0.622	0.755	0.688
n12	0.686	0.778	0.692	0.705	0.715	0.686	0.778	0.732
n13	0.836	0.745	0.683	0.755	0.752	0.683	0.836	0.759

. Applying Equation (10), we determine absolute distances, presented in

Table 8. Resulting matrix of absolute distances.

Indicators	m1	m2	m3	m4	m5
n1	0.025	0.001	0.027	0.089	0.089
n2	0.012	0.094	0.094	0.017	0.015
n3	0.043	0.030	0.029	0.043	0.002
n4	0.040	0.061	0.059	0.008	0.061
n5	0.038	0.029	0.057	0.010	0.057
n6	0.024	0.033	0.033	0.024	0.023
n7	0.013	0.021	0.044	0.030	0.044
n8	0.107	0.107	0.005	0.085	0.032
n9	0.014	0.014	0.014	0.002	0.002
n10	0.086	0.086	0.030	0.025	0.016
n11	0.067	0.067	0.066	0.017	0.054
n12	0.046	0.046	0.040	0.027	0.017
n13	0.076	0.014	0.076	0.005	0.007

. Following this, we generate the moduli matrix and the modulus of the symmetry point of the criterion with Equations (11) and (12), presented in

Table 9. Matrix of moduli and criteria weight.

Indicators	m1	m2	m3	m4	m5	qj	${\mathit{w}}_{\mathit{j}}^{\mathit{o}}$
n1	0.188	0.184	0.183	0.135	0.113	0.161	0.0809
n2	0.179	0.157	0.198	0.116	0.127	0.156	0.0784
n3	0.186	0.186	0.162	0.106	0.123	0.153	0.0769
n4	0.215	0.185	0.177	0.128	0.159	0.173	0.0870
n5	0.197	0.198	0.197	0.118	0.120	0.166	0.0836
n6	0.192	0.180	0.190	0.124	0.136	0.165	0.0829
n7	0.177	0.183	0.180	0.108	0.116	0.153	0.0770
n8	0.144	0.198	0.159	0.121	0.112	0.147	0.0741
n9	0.161	0.171	0.162	0.106	0.117	0.143	0.0722
n10	0.181	0.147	0.162	0.107	0.111	0.142	0.0714
n11	0.190	0.159	0.152	0.108	0.132	0.148	0.0746
n12	0.172	0.155	0.165	0.108	0.117	0.143	0.0723
n13	0.141	0.162	0.168	0.101	0.111	0.137	0.0688

. As a final step, we find the objective weight of the indicator from Equation (13) in Table 9, depicted in Figure 1.

From Equations (14)–(16), the subjective weights of the indicators and sub-criteria are calculated for ranking suitable biomass resources for biofuel production, which is presented in

Table 10. The subjective weights of the indicators using the IF-RS model.

Indicators	e1	e2	e3	e4	AIFNs	${\mathit{\eta }}_{\mathit{j}}$	rj	Weight	${\mathit{w}}_{\mathit{j}}^{\mathit{s}}$
n1	G	SG	B	SG	(0.577, 0.317, 0.106)	0.630	8	6	0.0659
n2	A	G	A	SB	(0.546, 0.349, 0.105)	0.599	12	2	0.0220
n3	SG	G	SG	A	(0.612, 0.286, 0.102)	0.663	2	12	0.1319
n4	G	SB	SB	A	(0.525, 0.369, 0.106)	0.578	13	1	0.0110
n5	A	SG	VG	SB	(0.609, 0.306, 0.086)	0.652	4	10	0.1099
n6	VG	SG	SG	A	(0.655, 0.262, 0.083)	0.696	1	13	0.1429
n7	SG	A	G	A	(0.586, 0.311, 0.103)	0.637	6	8	0.0879
n8	SG	A	SB	VG	(0.595, 0.317, 0.088)	0.639	5	9	0.0989
n9	A	SB	SG	G	(0.554, 0.342, 0.104)	0.606	11	3	0.0330
n10	VG	SB	A	A	(0.594, 0.322, 0.083)	0.636	7	7	0.0769
n11	VG	A	SG	SB	(0.620, 0.297, 0.084)	0.662	3	11	0.1209
n12	SB	SG	G	A	(0.562, 0.333, 0.105)	0.614	10	4	0.0440
n13	G	A	SG	SB	(0.574, 0.321, 0.105)	0.626	9	5	0.0549

and Figure 1.

From Equation (17), we integrate the IF-SPC and the IF-RS models. The integrated weight for $\tau =0.5$ for ranking suitable biomass resources for biofuel production is depicted in the Figure 1 and is given by:

w_j = (0.0734, 0.0502, 0.1044, 0.0490, 0.0968, 0.1129, 0.0824, 0.0865, 0.0526, 0.0742, 0.0978, 0.0581, 0.0618).

Figure 1 presents the variation of the weights of the diverse indicators for ranking suitable biomass resources for biofuel production. The cost of biomass supply (EC-3), with a weight of 0.1129, turned out to be the best indicator for ranking suitable biomass resources for biofuel production. Maturity (T-3), with a weight of 0.1044, is the second-best indicator for ranking suitable biomass resources for biofuel production. Local acceptability (SP-1) is third, with a significance value of 0.0978, and cost of biomass conversion process (EC-2), with a weight value of 0.0968, is the fourth most important criterion for ranking suitable biomass resources for biofuel production. The others are considered crucial criteria for ranking suitable biomass resources for biofuel production.

Steps 6–7: From Equations (20)–(28), we find the RC-DM $R={\left(r{c}_{ij}\right)}_{s\times t}$, which is given in

Table 11. RC-DM for ranking suitable biomass resources for biofuel production.

Indicators	m1	m2	m3	m4	m5
n1	0.617	0.640	0.615	0.558	0.722
n2	0.645	0.748	0.570	0.643	0.642
n3	0.624	0.637	0.690	0.703	0.665
n4	0.456	0.364	0.366	0.412	0.475
n5	0.409	0.401	0.427	0.366	0.323
n6	0.398	0.346	0.407	0.398	0.396
n7	0.654	0.646	0.622	0.699	0.707
n8	0.809	0.596	0.701	0.616	0.729
n9	0.724	0.688	0.686	0.712	0.702
n10	0.636	0.807	0.689	0.693	0.739
n11	0.610	0.744	0.738	0.689	0.624
n12	0.671	0.766	0.678	0.688	0.698
n13	0.824	0.729	0.666	0.735	0.735

.

Step 8: Using Equation (21), we obtain the normalized RC-DM $R_N={\left(r{c}_{ij}^{(N)}\right)}_{s\times t},$ which is computed and presented in

Table 12. Normalized RC-DM for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	0.365	0.505	0.352	0.000	1.000
n2	0.419	1.000	0.000	0.408	0.403
n3	0.000	0.164	0.831	1.000	0.518
n4	0.175	1.000	0.979	0.568	0.000
n5	0.169	0.246	0.000	0.588	1.000
n6	0.159	1.000	0.000	0.162	0.186
n7	0.374	0.278	0.000	0.904	1.000
n8	1.000	0.000	0.492	0.092	0.624
n9	1.000	0.052	0.000	0.697	0.432
n10	0.000	1.000	0.310	0.336	0.604
n11	0.000	1.000	0.954	0.590	0.102
n12	0.000	1.000	0.064	0.178	0.281
n13	1.000	0.402	0.000	0.438	0.438

.

Step 9: From Equations (22) and (23), we estimate the TDM $T={\left(t_{ij}\right)}_{s\times t},$ which is calculated and presented in

Table 13. The TDM for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	0.015	0.015	0.015	0.015	0.015
n2	0.010	0.010	0.010	0.010	0.010
n3	0.021	0.021	0.021	0.021	0.021
n4	0.010	0.010	0.010	0.010	0.010
n5	0.019	0.019	0.019	0.019	0.019
n6	0.023	0.023	0.023	0.023	0.023
n7	0.016	0.016	0.016	0.016	0.016
n8	0.017	0.017	0.017	0.017	0.017
n9	0.011	0.011	0.011	0.011	0.011
n10	0.015	0.015	0.015	0.015	0.015
n11	0.020	0.020	0.020	0.020	0.020
n12	0.012	0.012	0.012	0.012	0.012
n13	0.012	0.012	0.012	0.012	0.012

.

Step 10: Based on Equation (24), we obtain the real IF assessment matrix $R={\left(r_{ij}\right)}_{s\times t},$ which is determined and presented in

Table 14. Real IF assessment matrix for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	0.005	0.007	0.005	0.000	0.015
n2	0.004	0.010	0.000	0.004	0.004
n3	0.000	0.003	0.017	0.021	0.011
n4	0.002	0.010	0.010	0.006	0.000
n5	0.003	0.005	0.000	0.011	0.019
n6	0.004	0.023	0.000	0.004	0.004
n7	0.006	0.005	0.000	0.015	0.016
n8	0.017	0.000	0.009	0.002	0.011
n9	0.011	0.001	0.000	0.007	0.005
n10	0.000	0.015	0.005	0.005	0.009
n11	0.000	0.020	0.019	0.012	0.002
n12	0.000	0.012	0.001	0.002	0.003
n13	0.012	0.005	0.000	0.005	0.005

.

Step 11: Based on Equation (25), we obtain the IF discrimination matrix $G={\left(g_{ij}\right)}_{s\times t},$ which is determined and discussed in

Table 15. The IF discrimination matrix for ranking suitable biomass resources for biofuel production.

	m1	m2	m3	m4	m5
n1	0.009	0.007	0.010	0.015	0.000
n2	0.006	0.000	0.010	0.006	0.006
n3	0.021	0.017	0.004	0.000	0.010
n4	0.008	0.000	0.000	0.004	0.010
n5	0.016	0.015	0.019	0.008	0.000
n6	0.019	0.000	0.023	0.019	0.018
n7	0.010	0.012	0.016	0.002	0.000
n8	0.000	0.017	0.009	0.016	0.007
n9	0.000	0.010	0.011	0.003	0.006
n10	0.015	0.000	0.010	0.010	0.006
n11	0.020	0.000	0.001	0.008	0.018
n12	0.012	0.000	0.011	0.010	0.008
n13	0.000	0.007	0.012	0.007	0.007

.

Step 12: Using Equation (26), we compute the UDs u_i of biomass resources for biofuel production m_i, where i =1, 2, 3, 4, 5; u₁ $=$ 0.136; u₂ $=$ 0.086; u₃ $=$ 0.135; u₄ = 0.107; and u₅ = 0.095. The preference order is u₂ > u₅ > u₄ > u₃ > u₁.

Step 13: The RO of the biomass resources for biofuel production m₁, m₂, m₃, m₄ and m₅ is: $m_2\succ m_5\succ m_4\succ m_3\succ m_1.$ Thus, municipal solid waste and sewage (m₂) is the best biomass resource for biofuel production.

5.1. Sensitivity Analysis

We have varied and analyzed the significance of the objective to subjective weights for the considered indicators in the proposed weight-finding technique over the parameter γ = 0.0 to γ = 1.0 of the IF-SPC-RS-MAIRCA method to show the performance of the utility scores of biomass resources for biofuel production selection. We show the sensitivity investigation associated with the parameter γ.

Table 16. The UDs of the options over diverse values of γ.

γ	m1	m2	m3	m4	m5
γ = 0.0 (Subjective weight IF-RS model)	0.141	0.090	0.133	0.105	0.092
γ = 0.1	0.140	0.090	0.134	0.105	0.093
γ = 0.2	0.139	0.089	0.134	0.106	0.094
γ = 0.3	0.138	0.088	0.135	0.106	0.094
γ = 0.4	0.137	0.087	0.135	0.106	0.095
γ = 0.5 (Integrated weight)	0.136	0.086	0.135	0.107	0.095
γ = 0.6	0.134	0.085	0.136	0.107	0.096
γ = 0.7	0.133	0.084	0.136	0.107	0.097
γ = 0.8	0.132	0.083	0.137	0.108	0.097
γ = 0.9	0.131	0.082	0.137	0.108	0.098
γ = 1.0 (Objective weight IF-SPC model)	0.130	0.081	0.138	0.108	0.099

and Figure 2 signify the sensitivity of biomass resources for biofuel production selection with different values of parameter γ. According to the assessments, we find the preference order to be $m_2\succ m_5\succ m_4\succ m_3\succ m_1$ for γ = 0.0 to γ = 0.5 and $m_2\succ m_5\succ m_4\succ m_1\succ m_3$ for ϑ = 0.6 to ϑ = 1.0, which implies that municipal solid waste and sewage (m₂) is the top biomass resource for biofuel production for ϑ = 0.0 to ϑ = 1.0, while peanut waste (m₁) is ranked last for ϑ = 0.0 to ϑ = 0.5 and rice waste (m₃) is ranked last for ϑ = 0.6 to ϑ = 1.0. Consequently, it is found that the IF-SPC-RS-MAIRCA model holds ample steadiness with parameter γ values. From Table 16, is can be seen that the proposed IF-SPC-RS-MAIRCA model is proficient at creating stable, and, simultaneously, flexible prioritization outcomes for diverse parameter values.

5.2. Comparison and Discussion

To show the effectiveness of the IF-SPC-RS-MAIRCA model, we relate the results of the proposed model using various extant tools, namely the “IF-COPRAS” [56], “IF-WASPAS” [57], “IF-TOPSIS” [58], and “IF-CoCoSo” [59] models.

5.2.1. IF-TOPSIS Model

The steps of the IF-TOPSIS model are as follows:

Steps 1–5: Similar to the above-mentioned model.

Step 6: Calculate the IF-PIS and IF-NIS.

Let $n_b$ and $n_n$ be the benefit and cost indicators, respectively. Let ${\mathrm{N}}_j^{+}$ and ${\mathrm{N}}_j^{-}$ be the IF-PIS and IF-NIS, which are given as

$${\mathrm{N}}_j^{+}=\left({\mu }_j^{+},{\nu }_j^{+}\right)=\{\begin{array}{l}\max \mathbb{S}\left(y_{ij}\right),\mathrm{for}\mathrm{benefit}\mathrm{criterion}\\ \min \mathbb{S}\left(y_{ij}\right),\mathrm{for}\cos \mathrm{t}\mathrm{criterion}\end{array}$$

(27)

$${\mathrm{N}}^{-}=\left({\mu }_j^{-},{\nu }_j^{-}\right)=\{\begin{array}{l}\min \mathbb{S}\left(y_{ij}\right),\mathrm{for}\mathrm{benefit}\mathrm{criterion}\\ \max \mathbb{S}\left(y_{ij}\right),\mathrm{for}\cos \mathrm{t}\mathrm{criterion}\end{array},i=1,2,\dots ,s.$$

(28)

where $j=1,2,\dots ,t.$

Step 7: Assess the distances from IF-PIS and IF-NIS.

The weighted distance of option $m_i\left(i=1,2,\dots ,s\right)$ from IF-PIS ${\mathrm{N}}_j^{+}$ is estimated as

$$D\left(y_{ij},{\mathrm{N}}_j^{+}\right)=\sqrt{\frac{1}{2}{\displaystyle \sum _{j=1}^t{w}_j\left[{\left({\mu }_{ij}-{\mu }_j^{+}\right)}^2+{\left({\nu }_{ij}-{\nu }_j^{+}\right)}^2+{\left({\pi }_{ij}-{\pi }_j^{+}\right)}^2\right]}},$$

(29)

and the distance of options $m_i\left(i=1,2,\dots ,s\right)$ from IF-NIS ${\mathrm{N}}_j^{-}$ is calculated as

$$D\left(y_{ij},{\mathrm{N}}_j^{-}\right)=\sqrt{\frac{1}{2}{\displaystyle \sum _{j=1}^t{w}_j\left[{\left({\mu }_{ij}-{\mu }_j^{-}\right)}^2+{\left({\nu }_{ij}-{\nu }_j^{-}\right)}^2+{\left({\pi }_{ij}-{\pi }_j^{-}\right)}^2\right]}},$$

(30)

Step 8: Estimate the “closeness coefficient” (CC) as

$$C{C}_i=\frac{D\left(y_{ij},{\mathrm{N}}_j^{-}\right)}{D\left(y_{ij},{\mathrm{N}}_j^{-}\right)+D\left(y_{ij},{\mathrm{N}}_j^{+}\right)},i=1,2,\dots ,s.$$

(31)

Step 9: Select the optimal option with the highest CC degree.

Using Table 5 and Equations (27) and (28), the IF-PIS and IF-NIS are determined as

${\mathrm{N}}_j^{+}=$ {(0.698, 0.216, 0.087), (0.730, 0.199, 0.071), (0.678, 0.238, 0.084), (0.300, 0.600, 0.101), (0.255, 0.644, 0.101), (0.280, 0.619, 0.101), (0.685, 0.241, 0.074), (0.803, 0.163, 0.035), (0.712, 0.246, 0.042), (0.798, 0.155, 0.047), (0.732, 0.221, 0.048), (0.756, 0.200, 0.043), (0.817, 0.146, 0.037)},

${\mathrm{N}}_j^{-}=$ {(0.509, 0.381, 0.111), (0.527, 0.372, 0.102), (0.591, 0.321, 0.088), (0.420, 0.475, 0.105), (0.368, 0.530, 0.102), (0.335, 0.543, 0.122), (0.583, 0.313, 0.103), (0.554, 0.341, 0.104), (0.661, 0.251, 0.088), (0.599, 0.299, 0.102), (0.569, 0.326, 0.104), (0.643, 0.271, 0.086), (0.631, 0.266, 0.103)}.

Using Equations (29)–(31), the results of the IF-TOPSIS model are presented in

Table 17. The CC of the options for ranking suitable biomass resources for biofuel production.

Alternative	$\mathit{D}\left({\mathit{y}}_{\mathit{i}\mathit{j}},{\mathbf{N}}_{\mathit{j}}^{+}\right)$	$\mathit{D}\left({\mathit{y}}_{\mathit{i}\mathit{j}},{\mathbf{N}}_{\mathit{j}}^{-}\right)$	CCi	Ranks
m1	0.086	0.054	0.3866	4
m2	0.059	0.082	0.5783	1
m3	0.093	0.050	0.3487	5
m4	0.084	0.058	0.4092	3
m5	0.064	0.078	0.5515	2

.

Therefore, the ranking of biomass resources for biofuel production is $m_2\succ m_5\succ m_4\succ m_1\succ m_3$, indicating that municipal solid waste and sewage (m₂) has the highest degree of RCC.

5.2.2. IF-COPRAS Model

The steps of the IF-COPRAS tool are as follows:

Steps 1–5: Follow the proposed tool in Section 4.

Step 6: Create the ratings of benefit and cost indicators as

$${\alpha }_i=\underset{j=1}{\overset{l}{\oplus }}{w}_j{\xi }_{ij},$$

(32)

$${\beta }_i=\underset{j=l+1}{\overset{t}{\oplus }}{w}_j{\xi }_{ij},i=1,2,\dots ,s.$$

(33)

Step 7: Define the “relative degree” (RD) of each choice as

$${\gamma }_i=\vartheta \mathbb{S}\left({\alpha }_i\right)+\left(1-\vartheta \right)\frac{{\displaystyle \sum _{i=1}^s\mathbb{S}\left({\beta }_i\right)}}{\mathbb{S}\left({\beta }_i\right){\displaystyle \sum _{i=1}^s\frac{1}{\mathbb{S}\left({\beta }_i\right)}}},i=1,2,\dots ,s.$$

(34)

Step 8: Compute the UD of each choice as

$${\delta }_i=\frac{{\gamma }_i}{{\gamma }_{\max }}\times 100\%,i=1,2,\dots ,s.$$

(35)

Applying Equations (32)–(35), the outcomes are given in

Table 18. The UD of the options for ranking suitable biomass resources for biofuel production.

Options	${\mathit{\alpha }}_{\mathit{i}}$	$\mathbb{S}\left({\mathit{\alpha }}_{\mathit{i}}\right)$	${\mathit{\beta }}_{\mathit{i}}$	$\mathbb{S}\left({\mathit{\beta }}_{\mathit{i}}\right)$	${\mathit{\gamma }}_{\mathit{i}}$	${\mathit{\delta }}_{\mathit{i}}$
m1	(0.554, 0.373, 0.073)	0.591	(0.107, 0.854, 0.039)	0.126	0.4464	96.53
m2	(0.570, 0.358, 0.072)	0.606	(0.090, 0.873, 0.036)	0.109	0.4625	100.00
m3	(0.536, 0.374, 0.090)	0.581	(0.102, 0.856, 0.042)	0.123	0.4404	95.22
m4	(0.541, 0.376, 0.083)	0.582	(0.097, 0.865, 0.037)	0.116	0.4435	95.89
m5	(0.563, 0.357, 0.080)	0.603	(0.097, 0.867, 0.036)	0.115	0.4584	99.11

. Consequently, municipal solid waste and sewage (m₂) was obtained as the most suitable biomass resource for biofuel production with a maximum RD (0.4625).

5.2.3. The IF-CoCoSo Model

Steps 1–5: Follow the proposed tool in Section 4.

Step 6: Find the WSM and WPM degrees by using Equation (36) and Equation (37), respectively,

$$S_i^{(1)}=\underset{j=1}{\overset{t}{\oplus }}{w}_j{\varsigma }_{ij},$$

(36)

$$S_i^{(2)}=\underset{j=1}{\overset{t}{\otimes }}{w}_j{\varsigma }_{ij},i=1,2,\dots ,s.$$

(37)

Step 7: Estimate the “balanced compromise degrees” (BCDs) of choice as

$$Q_i^{\left(1\right)}=\frac{\mathbb{S}\left(S_i^{(1)}\right)+\mathbb{S}\left(S_i^{(2)}\right)}{{\displaystyle \sum _{i=1}^s\left(\mathbb{S}\left(S_i^{(1)}\right)+\mathbb{S}\left(S_i^{(2)}\right)\right)}},$$

(38)

$$Q_i^{\left(2\right)}=\frac{\mathbb{S}\left(S_i^{(1)}\right)}{\underset{i}{\min }\mathbb{S}\left(S_i^{(1)}\right)}+\frac{\mathbb{S}\left(S_i^{(2)}\right)}{\underset{i}{\min }\mathbb{S}\left(S_i^{(2)}\right)},$$

(39)

$$Q_i^{\left(3\right)}=\frac{\vartheta \mathbb{S}\left(S_i^{(1)}\right)+\left(1-\vartheta \right)\mathbb{S}\left(S_i^{(2)}\right)}{\underset{i}{\vartheta \max }\mathbb{S}\left(S_i^{(1)}\right)+\left(1-\vartheta \right)\underset{i}{\max }\mathbb{S}\left(S_i^{(2)}\right)},$$

(40)

Step 8: The “overall compromise degree” (OCD) of choice is determined as

$$Q_i={\left(Q_i^{\left(1\right)}{Q}_i^{\left(2\right)}{Q}_i^{\left(3\right)}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+\frac{1}{3}\left(Q_i^{\left(1\right)}+Q_i^{\left(2\right)}+Q_i^{\left(3\right)}\right).$$

(41)

Step 9: Rank the alternatives with the OCD $\left(Q_i\right).$

Applying Equations (37)–(41), the OCDs are given in

Table 19. The OCD for ranking suitable biomass resources for biofuel production.

Options	${\mathit{S}}_{\mathit{i}}^{(1)}$	${\mathit{S}}_{\mathit{i}}^{(2)}$	$\mathbb{S}\left({\mathit{S}}_{\mathit{i}}^{(1)}\right)$	$\mathbb{S}\left({\mathit{S}}_{\mathit{i}}^{(2)}\right)$	${\mathit{Q}}_{\mathit{i}}^{\left(1\right)}$	${\mathit{Q}}_{\mathit{i}}^{\left(2\right)}$	${\mathit{Q}}_{\mathit{i}}^{\left(3\right)}$	${\mathit{Q}}_{\mathit{i}}$	Ranking
m1	(0.636, 0.284, 0.079)	(0.617, 0.297, 0.086)	0.676	0.660	0.1972	2.0093	0.9662	1.7837	4
m2	(0.659, 0.263, 0.077)	(0.646, 0.272, 0.082)	0.698	0.687	0.2044	2.0828	1.0000	1.8480	1
m3	(0.622, 0.283, 0.095)	(0.614, 0.289, 0.097)	0.670	0.662	0.1966	2.0034	0.9609	1.7770	5
m4	(0.631, 0.281, 0.087)	(0.623, 0.287, 0.090)	0.675	0.668	0.1983	2.0201	0.9687	1.7917	3
m5	(0.652, 0.265, 0.083)	(0.643, 0.272, 0.085)	0.693	0.685	0.2035	2.0733	0.9945	1.8391	2

. From Table 19, municipal solid waste and sewage (m₂) was shown to be the best choice of biomass resource for biofuel production.

The comparative results are presented in Table 17, Table 18 and Table 19 and Figure 3. From Table 17, Table 18 and Table 19, it can be found that the best biomass resource for biofuel production is municipal solid waste and sewage (m₂) when ranking suitable biomass resources for biofuel production with each MADA tool. The benefits of the IF-SPC-RS-MAIRCA tool are thus:

• The developed model employs the linear normalization process and symmetric point criterion, while the IF-COPRAS tool applies a vector normalization process [60]; the IF-TOPSIS and IF-CoCoSo models also utilize linear normalization process [61]. Thus, the proposed method avoids the information loss associated with other methods and provides more accurate decision results by means of different criteria.
• The IF-CoCoSo model considers WSM and WPM to find the OCDs of options. In the IF-COPRAS model, the IFWAO and IF score value are used to determine the UDs of each option. In the IF-TOPSIS model, the CCs are found using the distances of each option from the reference points, while the IF-SPC-RS-MAIRCA model proposes the gap between the ideal ratings and empirical ratings [44]. For each option, the sum of the gaps for all attributes offers the overall gap, and the option with the lowest utility score is taken as the appropriate option. The MAIRCA approach is more stable than the IF-TOPSIS or IF-VIKOR models because it uses a diverse linear normalization procedure characterized by simple mathematical computations and result permanence [45].
• The proposed tool defines the indicator’s objective weight using the IF-SPC (symmetric point criterion) and the IF-rank sum-based model. In contrast, in the IF-CoCoSo model, the indicator’s weight is estimated using the IF divergence measure and an IF score value-based tool, and in the IF-COPRAS and IF-TOPSIS models, the indicator’s weight is determined randomly.

Next,

Table 20. Ranking suitable biomass resources for biofuel production with diverse extant models.

Options	Proposed Method	IF-TOPSIS [58]	IF-COPRAS [56]	IF-WASPAS [57]	IF-CoCoSo [59]
m1	5	4	3	5	4
m2	1	1	1	1	1
m3	4	5	5	4	5
m4	3	3	4	3	3
m5	2	2	2	2	2
SRCC	-	0.90	0.70	1.00	0.90
WS-Coefficient	1	0.9714	0.901	1.00	0.9714

specifies the ranks the five models assigned to various biomass resources for biofuel production; a definite degree of deviation can be examined. The outcomes of the new method introduced in this paper and those of the existing methods are depicted in Table 20. From Table 20, the Spearman rank correlation coefficients (SRCCs) are greater than 0.7, with the exception of the IVFF-TOPSIS model results [58]. Also, the WS coefficients are greater than 0.901, with the exception of the IVFF-TOPSIS method [62], which are presented in Figure 4. The properties of the WS coefficient [63] indicate that it is a suitable procedure for comparing the similarity of priorities, which means the similarity of the ranking order of biomass resources for biofuel production options is high. As a result, it can be said that there is a strong relationship between ranking outcomes. Thus, it can be concluded that the results from the proposed tool are consistent with the extant models.

6. Conclusions

Biofuel production from biomass resources can support moving towards a sustainable energy production structure [64,65,66,67]. Therefore, it is very important to select a suitable biomass resource with accessible biomass while considering multiple criteria together [2]. This paper presents a hybrid MADA framework for choosing suitable biomass resources for biofuel production over several considered indicators which can be applied at the macro (country-based) and micro (local-based) levels. Towards this end, an IF-SPC-RS-MAIRCA model has been presented within the context of IFSs to incorporate the final rankings of the options. In this method, the objective weights of the indicators were estimated with an IF-SPC model which considers the symmetry of the indicators and the subjective weight of the indicators as determined using the IF-RS tool. Further, a case study of biofuel production from biomass resources was implemented, which supports the practicability of the developed model. Thirteen indicators and five alternatives were considered in this study. The outcomes specified second-generation biomass resources, namely “municipal solid waste and sewage,” “forest and wood farming waste,” and “livestock and poultry waste,” as being suitable for utilization as feedstock for biofuel production in the considered region. Furthermore, a sensitivity analysis was performed over diverse values of parameters to demonstrate the robustness of the obtained results. Based on a comparison with extant tools, the proposed IF-SPC-RS-MAIRCA tool offers a simple computation with precise and well-organized outcomes for dealing with MADA problems in an IFS environment.

Some limitations of the model could be determined while deducing the outcomes. The first limitation of the work is the number of DMEs who contributed in the study. The other limitation is the number of the indicators, sub-criteria, and options. The procedure of the assessment of biomass resources for biofuel production is intrinsically complex because of the various indicators and sub-criteria that must be estimated and assessed. These indicators and sub-criteria are described in both objective and subjective terms. Alternatively, it is challenging to quantify qualitative indicators and sub-criteria due to the presence of vagueness and uncertainty in the procedure related to the qualitative indicators and sub-criteria.

In the future, it would be exciting to consider the interdependencies and correlations between selection criteria. The proposed framework could be applied with different MADA models, namely the GLDS [60,61] model, DNMA [22] model, and others. In addition, other weighting models, namely MEREC [68] and FUCOM, may be applied with the presented framework to advance MCDM problems in the context of IFSs.