Symmetry

Research

22 pages, 2516 KiB

Open AccessArticle

Novel Fuzzy Clustering Methods for Test Case Prioritization in Software Projects

by A. D. Shrivathsan, K. S. Ravichandran, R. Krishankumar, V. Sangeetha, Samarjit Kar, Pawel Ziemba and Jaroslaw Jankowski

Symmetry 2019, 11(11), 1400; https://doi.org/10.3390/sym11111400 - 12 Nov 2019

Cited by 10 | Viewed by 3704

Abstract

Systematic Regression Testing is essential for maintaining software quality, but the cost of regression testing is high. Test case prioritization (TCP) is a widely used approach to reduce this cost. Many researchers have proposed regression test case prioritization techniques, and clustering is one [...] Read more.

Systematic Regression Testing is essential for maintaining software quality, but the cost of regression testing is high. Test case prioritization (TCP) is a widely used approach to reduce this cost. Many researchers have proposed regression test case prioritization techniques, and clustering is one of the popular methods for prioritization. The task of selecting appropriate test cases and identifying faulty functions involves ambiguities and uncertainties. To alleviate the issue, in this paper, two fuzzy-based clustering techniques are proposed for TCP using newly derived similarity coefficient and dominancy measure. Proposed techniques adopt grouping technology for clustering and the Weighted Arithmetic Sum Product Assessment (WASPAS) method for ranking. Initially, test cases are clustered using similarity//dominancy measures, which are later prioritized using the WASPAS method under both inter- and intra-perspectives. The proposed algorithms are evaluated using real-time data obtained from Software-artifact Infrastructure Repository (SIR). On evaluation, it is inferred that the proposed algorithms increase the likelihood of selecting more relevant test cases when compared to the recent state-of-the-art techniques. Finally, the strengths of the proposed algorithms are discussed in comparison with state-of-the-art techniques. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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21 pages, 1717 KiB

Open AccessArticle

A Rough Hybrid Multicriteria Decision-Making Model for Improving the Quality of a Research Information System

by Qi-Gan Shao, James J. H. Liou, Sung-Shun Weng and Yen-Ching Chuang

Symmetry 2019, 11(10), 1248; https://doi.org/10.3390/sym11101248 - 7 Oct 2019

Cited by 4 | Viewed by 2509

Abstract

Improving the quality of research information systems is an important goal in the process of improving the performance of research management in Chinese universities. Since the evaluation of information system (IS) quality is a multicriteria decision problem, it is critical to identify the [...] Read more.

Improving the quality of research information systems is an important goal in the process of improving the performance of research management in Chinese universities. Since the evaluation of information system (IS) quality is a multicriteria decision problem, it is critical to identify the interrelationships among the dimensions and criteria, and decide on the important criteria for proposed improvement strategies. This paper suggests a hybrid multicriteria decision-making (MCDM) model for improving the quality of a research information system. First, a rough method combined with the decision-making trial and evaluation laboratory and analytical network process (rough DANP) model is used to improve the objectivity of expert judgements. Additionally, the rough DANP can be used to construct an influential network relationship map (INRM) between research information system components to derive the criterion weights. The complex proportional assessment of alternatives with rough numbers (COPRAS-R) is applied to evaluate the performance of the research information system. A Chinese university research information system is chosen to illustrate the usefulness of the proposed model. The results show that efficiency, effectiveness, and user frequency have the highest priorities for improvement. Selected management implications based on the actual case study are supplied. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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23 pages, 793 KiB

Open AccessArticle

Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method

by Krzysztof Piasecki, Ewa Roszkowska and Anna Łyczkowska-Hanćkowiak

Symmetry 2019, 11(9), 1104; https://doi.org/10.3390/sym11091104 - 2 Sep 2019

Cited by 10 | Viewed by 2237

Abstract

We examine some aspects of the use of Simple Additive Weighting method to evaluate decision alternatives. Decision alternative attributes may be evaluated by verbal assessments which by their nature are imprecise. This means that for the purposes of Simple Additive Weighting method, any [...] Read more.

We examine some aspects of the use of Simple Additive Weighting method to evaluate decision alternatives. Decision alternative attributes may be evaluated by verbal assessments which by their nature are imprecise. This means that for the purposes of Simple Additive Weighting method, any verbal assessment is represented by a fuzzy number being an imprecise approximation of a number. In this paper, all verbal assessments are represented by ordered fuzzy numbers. This approach is justified in the way that any ordered fuzzy number is additionally equipped with orientation, i.e., information about the location of the approximated number. The family of all ordered fuzzy numbers is divided into centrally symmetric families of positively oriented fuzzy numbers and of negatively oriented fuzzy numbers. The main purpose of this paper is to examine the consequences of omitting orientation of criterion ratings. We restrict all considerations to the case of trapezoidal oriented fuzzy numbers. We prove the mathematical theorem that an orientation omission can result in an increase in risk when choosing the right decision alternative. We study an empirical example of the Simple Additive Weighting method application to rank some negotiation offers. From the discussion, it follows that an orientation omission results in an increase in risk. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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24 pages, 1585 KiB

Open AccessArticle

An Adaptive Routing-Forwarding Control Scheme Based on an Intelligent Fuzzy Decision-Making System for Opportunistic Social Networks

by Yian Zhu, Lin Zhang, Haobin Shi, Kao-Shing Hwang, Xianchen Shi and Shuyan Luo

Symmetry 2019, 11(9), 1095; https://doi.org/10.3390/sym11091095 - 2 Sep 2019

Cited by 3 | Viewed by 2583

Abstract

Routing selection in opportunistic social networks is a complex and challenging issue due to intermittent communication connections among mobile devices and dynamic network topologies. The structural characteristics of opportunistic social networks indicate that the social attributes of mobile nodes play a significant role [...] Read more.

Routing selection in opportunistic social networks is a complex and challenging issue due to intermittent communication connections among mobile devices and dynamic network topologies. The structural characteristics of opportunistic social networks indicate that the social attributes of mobile nodes play a significant role on data dissemination. To this end, in this paper, we propose an adaptive routing-forwarding control scheme (FPRDM) based on an intelligent fuzzy decision-making system. On the foundation of the conception of fuzzy inference logic, two techniques are used in the proposed routing algorithm. Information fusion of social characteristics of message users and node identification are implemented based on the fuzzy recognition strategy, and the fuzzy decision-making mechanism is applied to control message replication and optimize data transmission. Simulation results demonstrate that, in the best case, the proposed scheme presents an average delivery ratio of 0.8, reduces the average end-to-end delay by nearly 45% as compared with the Epidemic routing protocol, and lowers the network overhead by about 75% as compared to the Spray and Wait routing algorithm. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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23 pages, 3085 KiB

Open AccessArticle

Application of Fuzzy Sets to the Expert Estimation of Scrum-Based Projects

by Paweł Rola and Dorota Kuchta

Symmetry 2019, 11(8), 1032; https://doi.org/10.3390/sym11081032 - 9 Aug 2019

Cited by 11 | Viewed by 3024

Abstract

The paper is basically dedicated to the problem of effort estimation for the Product Backlog items of IT projects led accordingly to the Scrum framework. The effort estimation issue is important, because low quality estimation decreases the efficiency of project implementation. The paper [...] Read more.

The paper is basically dedicated to the problem of effort estimation for the Product Backlog items of IT projects led accordingly to the Scrum framework. The effort estimation issue is important, because low quality estimation decreases the efficiency of project implementation. The paper proposes an estimation method for the Product Backlog items of Scrum-based IT projects (which can be adapted also to other projects), which has two original elements with respect to the state of art in Scrum estimation: the usage of fuzzy numbers and strict rules for consensus forming, combined with a space for human interaction. The assumptions of the method should be complied with and were formulated on the basis of literature and authors experience. Two case studies were used for an initial method validation. The case studies confirmed a high potential of the method to increase estimation quality in Scrum-based projects, as well as in other project types. The case studies were conducted using research methods fulfilling the symmetry principle. The paper is thus an example of symmetry in management research. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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20 pages, 3803 KiB

Open AccessArticle

Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems

by Avishek Chakraborty, Sankar Prasad Mondal, Shariful Alam, Ali Ahmadian, Norazak Senu, Debashis De and Soheil Salahshour

Symmetry 2019, 11(7), 932; https://doi.org/10.3390/sym11070932 - 16 Jul 2019

Cited by 53 | Viewed by 4278

Abstract

This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and [...] Read more.

This research paper adds to the theory of the generalized neutrosophic number from a distinctive frame of reference. It is universally known that the concept of a neutrosophic number is generally associated with and strongly related to the concept of positive, indeterminacy and non-belongingness membership functions. Currently, all membership functions always lie within the range of 0 to 1. However, we have generated bipolar concept in this paper where the membership contains both positive and negative parts within the range −1 to 0 and 0 to 1. We describe different structures of generalized triangular bipolar neutrosophic numbers, such as category-1, category-2, and category-3, in relation to the membership functions containing dependency or independency with each other. Researchers from different fields always want to observe the co-relationship and interdependence between fuzzy numbers and crisp numbers. In this platform, we also created the perception of de-bipolarization for a triangular bipolar rneutrosophic number with the help of well-known techniques so that any bipolar neutrosophic fuzzy number of any type can be smoothly converted into a real number instantly. Creating a problem using bipolar neutrosophic perception is a more reliable, accurate, and trustworthy method than others. In this paper, we have also taken into account a multi-criteria decision-making problem (MCDM) for different users in the bipolar neutrosophic domain. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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14 pages, 693 KiB

Open AccessArticle

A New Method for MAGDM Based on Improved TOPSIS and a Novel Pythagorean Fuzzy Soft Entropy

by Qi Han, Weimin Li, Yafei Song, Tao Zhang and Rugen Wang

Symmetry 2019, 11(7), 905; https://doi.org/10.3390/sym11070905 - 11 Jul 2019

Cited by 31 | Viewed by 2742

Abstract

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the [...] Read more.

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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12 pages, 298 KiB

Open AccessArticle

The Three-Way Decisions Method Based on Theory of Reliability with SV-Triangular Neutrosophic Numbers

by Xiang Li and Xianjiu Huang

Symmetry 2019, 11(7), 888; https://doi.org/10.3390/sym11070888 - 8 Jul 2019

Cited by 3 | Viewed by 2251

Abstract

Three-way decisions, as a decision-making mode which is consistent with human cognition, have been widely used in various fields. In this paper, we fuse the theory of reliability into the three-way decisions method, replace the conditional probability in the three-way decisions method with [...] Read more.

Three-way decisions, as a decision-making mode which is consistent with human cognition, have been widely used in various fields. In this paper, we fuse the theory of reliability into the three-way decisions method, replace the conditional probability in the three-way decisions method with reliability, and then propose a novel three-way decisions method. We also describe the loss functions with single-valued triangular neutrosophic numbers (SVTNNs) and propose an operator to calculate the score function of triangular neutrosophic numbers. Then, the result of decision is attained according to the principle of minimizing loss. Finally, we apply this method to the overhaul of machines in a factory, which proves the practicability and effectiveness of the proposed methods. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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26 pages, 627 KiB

Open AccessArticle

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

by Ping Wang, Guiwu Wei, Jie Wang, Rui Lin and Yu Wei

Symmetry 2019, 11(6), 771; https://doi.org/10.3390/sym11060771 - 6 Jun 2019

Cited by 35 | Viewed by 3123

Abstract

The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment [...] Read more.

The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker’s (DM’s) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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20 pages, 329 KiB

Open AccessArticle

Group Decision-Making Based on m-Polar Fuzzy Linguistic TOPSIS Method

by Arooj Adeel, Muhammad Akram and Ali N. A. Koam

Symmetry 2019, 11(6), 735; https://doi.org/10.3390/sym11060735 - 29 May 2019

Cited by 67 | Viewed by 3333

Abstract

The fuzzy linguistic approach provides favorable outputs in several areas, whose description is relatively qualitative. The encouragement for the utilization of sentences or words instead of numbers is that linguistic characterizations or classifications are usually less absolute than algebraic or arithmetical ones. In [...] Read more.

The fuzzy linguistic approach provides favorable outputs in several areas, whose description is relatively qualitative. The encouragement for the utilization of sentences or words instead of numbers is that linguistic characterizations or classifications are usually less absolute than algebraic or arithmetical ones. In this research article, we animate the m-polar fuzzy (mF) linguistic approach and elaborate it with real life examples and tabular representation to develop the affluence of linguistic variables based on mF approach. As an extension of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, we develop an m-polar fuzzy linguistic TOPSIS approach for multi-criteria group decision-making (MCGDM). It is used to evaluate the best alternative, to get more authentic and comparable results and to handle the real life problems of having multi-polar information in terms of linguistic variables and values. In this approach decision-makers contribute their estimations in the form of linguistic term sets. To show the efficiency and compatibility of the proposed approach, we compare it with the m-polar fuzzy linguistic ELECTRE-I (Elimination and Choice Translating Reality) approach. Finally, we draw a flow chart of our proposed approach as an algorithm and generate a computer programming code. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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16 pages, 1335 KiB

Open AccessArticle

Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection

by Dušan Polomčić, Zoran Gligorić, Dragoljub Bajić, Miloš Gligorić and Milanka Negovanović

Symmetry 2019, 11(5), 705; https://doi.org/10.3390/sym11050705 - 23 May 2019

Cited by 5 | Viewed by 2607

Abstract

When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic [...] Read more.

When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic approach and the use of fuzzy logic are required. In this way, decision-making criteria relating to an optimal groundwater control system do not always have a numerical value. Groundwater control scenarios (alternatives) are identified through hydrodynamic modeling of the aquifer, providing an indication of their effectiveness. The paper develops a fuzzy-stochastic multi-criteria decision-making model to deal with a topical problem: selection of the most suitable groundwater control system for an open-cast mine. Both real numerical and linguistic variables are used to express the values of all criteria that affect the final decision. In particular, it should be pointed out that the values of the criteria are varied over a predefined time horizon. For mathematical calculations, fuzzy dynamic TOPSIS and the stochastic diffusion process—geometric Brownian motion—were used. The proposed method is tested in a case study: the selection of an optimal groundwater control system for an open-cast mine. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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26 pages, 632 KiB

Open AccessArticle

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

by M. G. Brikaa, Zhoushun Zheng and El-Saeed Ammar

Symmetry 2019, 11(5), 702; https://doi.org/10.3390/sym11050702 - 22 May 2019

Cited by 24 | Viewed by 3115

Abstract

Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs [...] Read more.

Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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14 pages, 255 KiB

Open AccessArticle

Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets

by Hui-Chin Tang and Kuan-Sheng Cheng

Symmetry 2019, 11(5), 612; https://doi.org/10.3390/sym11050612 - 2 May 2019

Cited by 1 | Viewed by 2318

Abstract

This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity [...] Read more.

This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

19 pages, 820 KiB

Open AccessArticle

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

by Shouzhen Zeng, Azmat Hussain, Tahir Mahmood, Muhammad Irfan Ali, Shahzaib Ashraf and Muhammad Munir

Symmetry 2019, 11(4), 547; https://doi.org/10.3390/sym11040547 - 16 Apr 2019

Cited by 89 | Viewed by 4406

Abstract

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy [...] Read more.

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy

β

-neighborhoods (SF

β

-neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF

β

-neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

19 pages, 856 KiB

Open AccessArticle

Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives

by Krzysztof Piasecki, Ewa Roszkowska and Anna Łyczkowska-Hanćkowiak

Symmetry 2019, 11(4), 482; https://doi.org/10.3390/sym11040482 - 3 Apr 2019

Cited by 24 | Viewed by 4953

Abstract

From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy [...] Read more.

From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy Simple Additive Weighting (OF-SAW) scoring function. The ranking of alternatives may be defined by means of a nonincreasing sequence of defuzzified values of a scoring function. Any defuzzification procedure distorts ordered fuzzy numbers in a way that information on imprecision and orientation is lost. This undermines the credibility of the determined alternatives’ ranking. The main purpose of this paper is to avoid the defuzzification stage in the OF-SAW method. Thus, the OF-SAW method is equipped with fuzzy scoring order. This OF-SAW method is described as a negotiation scoring system. We study an empirical example of the OF-SAW application and rank some negotiation offers. Here, we focus on the effects of replacing the defuzzified scoring function by a fuzzy one. The obtained conclusions are generalized for the case of any decision alternatives. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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26 pages, 390 KiB

Open AccessArticle

Novel m—Polar Fuzzy Linguistic ELECTRE-I Method for Group Decision-Making

by Arooj Adeel, Muhammad Akram, Imran Ahmed and Kashif Nazar

Symmetry 2019, 11(4), 471; https://doi.org/10.3390/sym11040471 - 2 Apr 2019

Cited by 38 | Viewed by 3819

Abstract

Linguistic variables play a vital role in several qualitative decision environments, in which decision-makers assume several feasible linguistic values or criteria instead of a single term for an alternative or variable. The motivation for the use of words or sentences instead of numbers [...] Read more.

Linguistic variables play a vital role in several qualitative decision environments, in which decision-makers assume several feasible linguistic values or criteria instead of a single term for an alternative or variable. The motivation for the use of words or sentences instead of numbers is that linguistic classification and characterizations are generally less precise than numerical ones. In this research article, we encourage the fuzzy linguistic approach and introduce the novel concept known as m-polar fuzzy linguistic variable (mFLV) to increase the affluence of linguistic variables based on m-polar fuzzy (mF) approach. An mF set is an effective concept for interpreting uncertainty and fuzziness. The concept of mFLV is more versatile and sensible for dealing with real-life problems, when data comes from qualitative and multipolar information. We also introduce an mF linguistic ELECTRE-I approach to solve multiple-criteria decision-making (MCDM) and multiple-criteria group decision-making (MCGDM) problems, where the evaluation of the alternatives under suitable linguistic values are determined by the decision-makers. Furthermore, we validate the efficiency of our proposed technique by applying it to real-life examples, such as the salary analysis of companies and by selecting a corrupt country. Finally, we develop an algorithm of our proposed approach, present its flow chart, and generate computer programming code. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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21 pages, 1366 KiB

Open AccessArticle

Use of the PVM Method Computed in Vector Space of Increments in Decision Aiding Related to Urban Development

by Marek Kannchen, Paweł Ziemba and Mariusz Borawski

Symmetry 2019, 11(4), 446; https://doi.org/10.3390/sym11040446 - 28 Mar 2019

Cited by 11 | Viewed by 3259

Abstract

The paper presents a possibility to use a new PVM-VSI (Preference Vector Method computed in Vector Space of Increments) method in making decisions that demand that different variants should be considered, while being evaluated with respect to different criteria. Hence, knowledge about them [...] Read more.

The paper presents a possibility to use a new PVM-VSI (Preference Vector Method computed in Vector Space of Increments) method in making decisions that demand that different variants should be considered, while being evaluated with respect to different criteria. Hence, knowledge about them is a must, and that knowledge is not necessarily available quantitatively, whereas the very evaluation should be relatively objective; that is, independent from the decision maker’s preferences or opinions. The paper presents the use of the PVM-VSI method in support decisions related to urban development—to rank projects submitted for implementation within the framework of a citizen budget. The ranking will make it feasible to determine which of the submitted projects will have the dominant influence on the town’s sustainable development, and, subsequently, which ones should be presented to citizens as the better ones out of the projects submitted, and to compare the method mentioned with methods used in similar decision-making problems in the past: Fuzzy AHP (Analytic Hierarchy Process), Fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), and Fuzzy PROMETHEE (Preference Ranking Organization METHod for Enrichment of Evaluation). Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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21 pages, 531 KiB

Open AccessArticle

A New Fuzzy Multiple Attribute Decision Making Method Based on the Utility Transformation Functions

by Yuting Zuo and Chunfang Chen

Symmetry 2019, 11(3), 418; https://doi.org/10.3390/sym11030418 - 21 Mar 2019

Viewed by 2544

Abstract

The 2-tuple linguistic information model (2TLIM) is a useful tool to avoid the loss of information, which has been widely adapted in the study of the multiple attribute decision making (MADM) problem. However, there is a limitation, the limitation is that the difference [...] Read more.

The 2-tuple linguistic information model (2TLIM) is a useful tool to avoid the loss of information, which has been widely adapted in the study of the multiple attribute decision making (MADM) problem. However, there is a limitation, the limitation is that the difference between the neighboring 2-tuple linguistic information is fixed regardless of the decision-makers’ attitude. In this paper, we define the utility transformation functions based on the 2-tuple linguistic utility to overcome the drawback. Firstly, by introducing the economic utility theory, the 2-tuple linguistic utility is defined, the 2-tuple linguistic utility parameter (2TLUP) and the 2-tuple linguistic marginal utility (2TLMU) are constructed to achieve the measurement of the decision-makers’ attitude. The utility transformation functions are developed on the decision-makers’ attitude. Secondly, the 2-tuple linguistic operational laws are presented with the extended Hamacher T-norm (TN) and T-conorm (TC). Subsequently, we propose the 2-tuple linguistic utility weighted average (2TLUWA) operator and the method of MADM. Lastly, the application and the comparison with the existing methods are summarized to verify the practicality and advantages of the proposed method of MADM. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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23 pages, 5517 KiB

Open AccessArticle

Dynamic Service Selection Based on Adaptive Global QoS Constraints Decomposition

by Yuan Yuan, Weishi Zhang, Xiuguo Zhang and Huawei Zhai

Symmetry 2019, 11(3), 403; https://doi.org/10.3390/sym11030403 - 19 Mar 2019

Cited by 13 | Viewed by 2975

Abstract

As there are more and more available Web services with the same or similar functionalities but different Quality of Service (QoS), the challenge of QoS-aware service composition is to efficiently select appropriate component services to achieve maximum utility and meet the global QoS [...] Read more.

As there are more and more available Web services with the same or similar functionalities but different Quality of Service (QoS), the challenge of QoS-aware service composition is to efficiently select appropriate component services to achieve maximum utility and meet the global QoS constraints with low time cost. In this paper, we propose a dynamic service selection approach based on adaptive global QoS constraints decomposition. Fuzzy logic technology and Cultural Genetic Algorithm are used to adaptively decompose global QoS constraints into near-optimal local constraints. According to the near-optimal local constraints, the optimal service is selected for each service class during the running time efficiently. Experimental results show that the proposed approach not only achieves the near-optimal solution, but also significantly reduces the computation time, and has good adaptability and scalability. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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19 pages, 804 KiB

Open AccessArticle

Pythagorean Fuzzy Dombi Aggregation Operators and Their Application in Decision Support System

by Arshad Ahmad Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Qiyas, Jianchao Luo and Sufyan Ullah Khan

Symmetry 2019, 11(3), 383; https://doi.org/10.3390/sym11030383 - 15 Mar 2019

Cited by 122 | Viewed by 4997

Abstract

Keeping in mind the importance and well growing Pythagorean fuzzy sets, in this paper, some novel operators for Pythagorean fuzzy sets and their properties are demonstrated. In this paper, we develop a comprehensive model to tackle decision-making problems where strong points of view [...] Read more.

Keeping in mind the importance and well growing Pythagorean fuzzy sets, in this paper, some novel operators for Pythagorean fuzzy sets and their properties are demonstrated. In this paper, we develop a comprehensive model to tackle decision-making problems where strong points of view are in the favour and against the some projects, entities or plans. Therefore, a new approach, based on Pythagorean fuzzy set models by means of Pythagorean fuzzy Dombi aggregation operators is proposed. An approach to deal with decision-making problems using Pythagorean Dombi averaging and Dombi geometric aggregation operators is established. This model has a stronger capability than existing averaging, geometric, Einstein, logarithmic averaging and logarithmic geometric aggregation operators for Pythagorean fuzzy information. Finally, the proposed method is demonstrated through an example of how the proposed method helps us and is effective in decision-making problems. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

19 pages, 855 KiB

Open AccessArticle

Fuzzy Parameterized Complex Multi-Fuzzy Soft Expert Set Theory and Its Application in Decision-Making

by Yousef Al-Qudah, Mazlan Hassan and Nasruddin Hassan

Symmetry 2019, 11(3), 358; https://doi.org/10.3390/sym11030358 - 9 Mar 2019

Cited by 26 | Viewed by 3077

Abstract

Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis [...] Read more.

Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set (

F P

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CMFSES

), and investigate part of its fundamental properties. This

F P

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CMFSES

model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among

F P

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CMFSES

and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

27 pages, 383 KiB

Open AccessArticle

Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

by Kifayat Ullah, Nasruddin Hassan, Tahir Mahmood, Naeem Jan and Mazlan Hassan

Symmetry 2019, 11(3), 357; https://doi.org/10.3390/sym11030357 - 9 Mar 2019

Cited by 98 | Viewed by 4904

Abstract

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The [...] Read more.

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

13 pages, 731 KiB

Open AccessArticle

Dimensional Analysis under Pythagorean Fuzzy Approach for Supplier Selection

by Aldo Joel Villa Silva, Luis Asunción Pérez Dominguez, Erwin Martínez Gómez, Alejandro Alvarado-Iniesta and Iván Juan Carlos Pérez Olguín

Symmetry 2019, 11(3), 336; https://doi.org/10.3390/sym11030336 - 6 Mar 2019

Cited by 18 | Viewed by 3225

Abstract

The supplier appraisal process is one of the most important decision problems for companies focused on improving supply chain costs. Supplier selection is typically a multi-criteria decision making (MCDM) issue, as there is a lot of uncertain information. In order to overcome this [...] Read more.

The supplier appraisal process is one of the most important decision problems for companies focused on improving supply chain costs. Supplier selection is typically a multi-criteria decision making (MCDM) issue, as there is a lot of uncertain information. In order to overcome this issue, The Pythagorean Fuzzy Set is applied to handle the uncertainties involved in comparing the alternatives, criteria and opinions of decision makers. At the same time, a potential of Dimensional Analysis is a technique which deploys an association of the criteria capturing the interrelationship normally present in MCDM. In this sense, the purpose of this paper is to evaluate the suppliers in a supply chain cycle using Pythagorean Fuzzy Set and Dimensional Analysis. Finally, the applicability of the proposed method is illustrated through numerical examples, and a validation via Spearman correlation and Cronbach’s alpha. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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21 pages, 1564 KiB

Open AccessArticle

Grey Regulatory Focus Theory Weighting Method for the Multi-Criteria Decision-Making Problem in Evaluating University Reputation

by Moses Olabhele Esangbedo and Sijun Bai

Symmetry 2019, 11(2), 230; https://doi.org/10.3390/sym11020230 - 14 Feb 2019

Cited by 15 | Viewed by 4308

Abstract

Evaluating the reputation of higher institutions is important as a benchmark for the continuous development of universities. In multi-criteria decision-making (MCDM), the estimation of the criteria weight is significant in improving the accuracy of the evaluation results. However, criteria weights assigned by decision [...] Read more.

Evaluating the reputation of higher institutions is important as a benchmark for the continuous development of universities. In multi-criteria decision-making (MCDM), the estimation of the criteria weight is significant in improving the accuracy of the evaluation results. However, criteria weights assigned by decision makers (DMs) can be inaccurate when not measured from the orientations from which the DMs pursue their decision goals. This paper combines the grey system theory (GST) and regulatory focus theory (RFT) in estimating the weights of criteria by measuring the promotional and prevention focus orientations of the DMs and representing it as grey numbers. In this paper, we showed not all weight measurements from the DMs are symmetrical. In essence, to improve the accuracy of the MCDM weights, the grey regulatory focus theory (GRFT) weighting method is proposed to estimate the weights of an MCDM problem as well as aggregating the weights of the group DMs, thereby overcoming the limitation of a single orientation measurement. Furthermore, the GRFT weighting method is applied in ranking four universities in Xi’an city of China from a sample data from 1200 students. The most reputable university is consistent with the other ranking indexes in the literature. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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34 pages, 2916 KiB

Open AccessEditor’s ChoiceArticle

Analysis of the Digital Divide Using Fuzzy Forecasting

by Paweł Ziemba and Jarosław Becker

Symmetry 2019, 11(2), 166; https://doi.org/10.3390/sym11020166 - 1 Feb 2019

Cited by 37 | Viewed by 5045

Abstract

In the countries of the former Eastern Bloc (Central and Eastern Europe) belonging to the European Union, a gradual elimination of the technological gap, greater expenditures, competitiveness and productivity can be noticed. In this context, analysis and forecast of the level of accessibility [...] Read more.

In the countries of the former Eastern Bloc (Central and Eastern Europe) belonging to the European Union, a gradual elimination of the technological gap, greater expenditures, competitiveness and productivity can be noticed. In this context, analysis and forecast of the level of accessibility and use of ICT (information and communication technologies) by households in these countries has become interesting. It allows for the selection of digitally excluded regions, or those threatened with this phenomenon in the coming years (2018–2020). To carry out the analysis, a framework based on fuzzy numbers and the NEAT F-PROMETHEE (New Easy Approach To Fuzzy-PROMETHEE) method was developed. The potential of the fuzzy outranking approach taking into account the uncertainty of input data (criteria and preferences) has been demonstrated as an alternative to the IDI (ICT Development Index) methodology widely used in research on regional ICT development based on composite indices. Research has shown that Estonia is the leader in the area of ICT expansion among households, and in the next three years will definitely maintain its dominant position. Slovenia follows shortly after, followed by Latvia. At the end of the ranking were the countries with the largest percentage in Central and Eastern Europe of population excluded digitally or threatened with this phenomenon; these are: Poland, Slovakia, Bulgaria and, in last place, Romania. Within this framework, the robustness of the obtained rankings to change in the degree of uncertainty of preferences was also examined. It turned out that eliminating the uncertainty of preferences resulted in an increase in the uncertainty of the aggregate, fuzzy grades obtained at the output. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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20 pages, 1698 KiB

Open AccessArticle

A MAGDM Algorithm with Multi-Granular Probabilistic Linguistic Information

by Ju-Xiang Wang

Symmetry 2019, 11(2), 127; https://doi.org/10.3390/sym11020127 - 22 Jan 2019

Cited by 14 | Viewed by 3045

Abstract

The traditional multi-attribute group decision making (MAGDM) method needs to be improved to the integration of assessment information under multi-granular probabilistic linguistic environments. Some novel distance measures between two multi-granular probabilistic linguistic term sets (PLTSs) are proposed, and distance measures are proved to [...] Read more.

The traditional multi-attribute group decision making (MAGDM) method needs to be improved to the integration of assessment information under multi-granular probabilistic linguistic environments. Some novel distance measures between two multi-granular probabilistic linguistic term sets (PLTSs) are proposed, and distance measures are proved to be reasonable. To calculate the weights of the alternative attributes, the extended cross-entropy method for multi-granular probabilistic linguistic term sets is proposed. Then, a novel extended MAGDM algorithm based on prospect theory (PT) is proposed. Two case studies of decision making (DM) on purchasing a car is provided to illustrate the application of the extended MAGDM algorithm. The case analyses are proposed to illustrate the novelty, feasibility, and application of the proposed MAGDM algorithm by comparing the other three algorithms based on TOPSIS, VIKOR, and Pang Qi et al.’s method. The analyses results demonstrate that the proposed algorithm based on PT is superior. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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20 pages, 319 KiB

Open AccessArticle

Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

by Rui Wang, Jie Wang, Hui Gao and Guiwu Wei

Symmetry 2019, 11(1), 6; https://doi.org/10.3390/sym11010006 - 21 Dec 2018

Cited by 121 | Viewed by 4846

Abstract

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some [...] Read more.

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

18 pages, 300 KiB

Open AccessArticle

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

by Donghai Liu, Xiaohong Chen and Dan Peng

Symmetry 2018, 10(11), 602; https://doi.org/10.3390/sym10110602 - 7 Nov 2018

Cited by 18 | Viewed by 3213

Abstract

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of [...] Read more.

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

27 pages, 5889 KiB

Open AccessArticle

Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

by Hongran Zhang, Runtong Zhang, Huiqun Huang and Jun Wang

Symmetry 2018, 10(11), 593; https://doi.org/10.3390/sym10110593 - 4 Nov 2018

Cited by 64 | Viewed by 4259

Abstract

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy [...] Read more.

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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25 pages, 2402 KiB

Open AccessArticle

Combining an Extended SMAA-2 Method with Integer Linear Programming for Task Assignment of Multi-UCAV under Multiple Uncertainties

by Jun Wang, Pengcheng Luo, Xinwu Hu and Xiaonan Zhang

Symmetry 2018, 10(11), 587; https://doi.org/10.3390/sym10110587 - 2 Nov 2018

Cited by 10 | Viewed by 3152

Abstract

Uncertainty should be taken into account when establishing multiobjective task assignment models for multiple unmanned combat aerial vehicles (UCAVs) due to errors in the target information acquired by sensors, implicit preferences of the commander for operational objectives, and partially known weights of sensors. [...] Read more.

Uncertainty should be taken into account when establishing multiobjective task assignment models for multiple unmanned combat aerial vehicles (UCAVs) due to errors in the target information acquired by sensors, implicit preferences of the commander for operational objectives, and partially known weights of sensors. In this paper, we extend the stochastic multicriteria acceptability analysis-2 (SMAA-2) method and combine it with integer linear programming to achieve multiobjective task assignment for multi-UCAV under multiple uncertainties. We first represent the uncertain target information as normal distribution interval numbers so that the values of criteria (operational objectives) concerned can be computed based on the weighted arithmetic averaging operator. Thus, we obtain multiple criteria value matrices for each UCAV. Then, we propose a novel aggregation method to generate the final criteria value matrix based on which the holistic acceptability indices are computed by the extended SMAA-2 method. On this basis, we convert the task assignment model with uncertain parameters into an integer linear programming model without uncertainty so as to implement task assignment using the integer linear programming method. Finally, we conduct a case study and demonstrate the feasibility of the proposed method in solving the multiobjective task assignment problem multi-UCAV under multiple uncertainties. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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28 pages, 566 KiB

Open AccessArticle

Assessment of Conditions for Implementing Information Technology in a Warehouse System: A Novel Fuzzy PIPRECIA Method

by Željko Stević, Željko Stjepanović, Zdravko Božičković, Dillip Kumar Das and Dragiša Stanujkić

Symmetry 2018, 10(11), 586; https://doi.org/10.3390/sym10110586 - 2 Nov 2018

Cited by 76 | Viewed by 7669

Abstract

The application of information technology in all areas represents a significant facilitation of all business processes and activities. A competitive business system is hardly imaginable without adequate information technology. Therefore, this paper evaluates the conditions for the implementation of barcode technology in a [...] Read more.

The application of information technology in all areas represents a significant facilitation of all business processes and activities. A competitive business system is hardly imaginable without adequate information technology. Therefore, this paper evaluates the conditions for the implementation of barcode technology in a warehouse system of a company for the manufacture of brown paper. SWOT (Strengths, Weaknesses, Opportunities, Threats) matrix was formed with a total of 27 elements based on which the benefits of the implementation of barcode technology in the warehouse system need to be analysed. For this purpose, a new fuzzy PIPRECIA (PIvot Pairwise RElative Criteria Importance Assessment) method has been developed to evaluate all elements in SWOT matrix. In addition, a part of the new developed approach includes new fuzzy scales for criterion assessment that are adapted to the methodology required by the fuzzy PIPRECIA method. To determine the consistency of the method, Spearman and Pearson correlation coefficients are applied. The results obtained in this study show that weaknesses are most noticeable in the current system. By implementing barcode technology, it is possible to create opportunities defined in SWOT matrix, which, in a very efficient way, allow elimination of the current weaknesses of the system. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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39 pages, 440 KiB

Open AccessArticle

Methods for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Dombi Hamy Mean Operators

by Zengxian Li, Hui Gao and Guiwu Wei

Symmetry 2018, 10(11), 574; https://doi.org/10.3390/sym10110574 - 1 Nov 2018

Cited by 105 | Viewed by 3510

Abstract

In this paper, we extended the Hamy mean (HM) operator, the Dombi Hamy mean (DHM) operator, the Dombi dual Hamy mean (DDHM), with the intuitionistic fuzzy numbers (IFNs) to propose the intuitionistic fuzzy Dombi Hamy mean (IFDHM) operator, intuitionistic fuzzy weighted Dombi Hamy [...] Read more.

In this paper, we extended the Hamy mean (HM) operator, the Dombi Hamy mean (DHM) operator, the Dombi dual Hamy mean (DDHM), with the intuitionistic fuzzy numbers (IFNs) to propose the intuitionistic fuzzy Dombi Hamy mean (IFDHM) operator, intuitionistic fuzzy weighted Dombi Hamy mean (IFWDHM) operator, intuitionistic fuzzy Dombi dual Hamy mean (IFDDHM) operator, and intuitionistic fuzzy weighted Dombi dual Hamy mean (IFWDDHM) operator. Following this, the multiple attribute group decision-making (MAGDM) methods are proposed with these operators. To conclude, we utilized an applicable example for the selection of a car supplier to prove the proposed methods. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

16 pages, 1107 KiB

Open AccessArticle

Nuclear Power Plant Location Selection in Vietnam under Fuzzy Environment Conditions

by Chia-Nan Wang, Chih-Chiang Su and Van Thanh Nguyen

Symmetry 2018, 10(11), 548; https://doi.org/10.3390/sym10110548 - 26 Oct 2018

Cited by 31 | Viewed by 4127

Abstract

The demands for energy in general and electrical power in particular in the process of industrialization–modernization in Vietnam are increasing. Although other renewable energy sources such as wind and solar power have been prioritized, they cannot compensate for the shortages of electricity in [...] Read more.

The demands for energy in general and electrical power in particular in the process of industrialization–modernization in Vietnam are increasing. Although other renewable energy sources such as wind and solar power have been prioritized, they cannot compensate for the shortages of electricity in Vietnam; moreover, traditional energy sources in Vietnam are not endless and will soon reach exhaustion. Nowadays, the government has chosen a solution to maximize domestic energy resources, i.e., develop renewable energy combined with importing coal and gas in appropriate proportions with the construction of nuclear power plants (NPP), which may be the optimal solution to ensure energy security, environmental protection, and sustainable development. However, site selection for construction of a nuclear power plant is one of the most difficult decisions that management faces. Thus, the authors proposed multicriteria decision-making (MCDM), including a fuzzy analytic network process (FANP) and technique for order preference by similarity of an ideal solution (TOPSIS) for NPP location selection in Vietnam. In the first stages of this research, the weight of all criteria and subcriteria will be calculated by an ANP model using fuzzy logic. A TOPSIS model is proposed for ranking all potential locations in the final stage. The results reveal that Binh Thuan is the best place for building an NPP in Vietnam. The contributions of this research include a fuzzy multicriteria decision-making (F-MCDM) approach for NPP site selection in Vietnam. This research also utilizes the evolution of a new approach that is flexible and practical for the decision-maker and provides useful guidelines for NPP site selection in countries around the world. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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34 pages, 406 KiB

Open AccessArticle

Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Group Decision Making and Their Application to Supplier Selection

by Zengxian Li, Guiwu Wei and Mao Lu

Symmetry 2018, 10(10), 505; https://doi.org/10.3390/sym10100505 - 15 Oct 2018

Cited by 105 | Viewed by 4072

Abstract

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, [...] Read more.

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, weighted Pythagorean fuzzy dual Hamy mean (WPFDHM) operator. Then the multiple attribute group decision making (MAGDM) methods are proposed with these operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

32 pages, 821 KiB

Open AccessArticle

Some Partitioned Maclaurin Symmetric Mean Based on q-Rung Orthopair Fuzzy Information for Dealing with Multi-Attribute Group Decision Making

by Kaiyuan Bai, Xiaomin Zhu, Jun Wang and Runtong Zhang

Symmetry 2018, 10(9), 383; https://doi.org/10.3390/sym10090383 - 5 Sep 2018

Cited by 78 | Viewed by 3956

Abstract

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, [...] Read more.

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

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