scholarly journals Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 170 ◽  
Author(s):  
Mohuya B. Kar ◽  
Bikashkoli Roy ◽  
Samarjit Kar ◽  
Saibal Majumder ◽  
and Dragan Pamucar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imperfect Information ◽  
Real Life ◽  
Distance Measures ◽  
Expert Assessment ◽  
Decision Making Problem ◽  
Medical Diagnosis System

In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions or feedback of several experts. Usually, the feedback of these experts are heterogeneous imperfect information collected from various more or less reliable sources. In this paper, we introduce the concept of multi-sets over type-2 fuzzy sets. We have tried to propose an extension of type-1 multi-fuzzy sets into a type-2 multi-fuzzy set (T2MFS). After defining T2MFS, we discuss the algebraic properties of these sets including set-theoretic operations such as complement, union, intersection, and others with examples. Subsequently, we define two distance measures over these sets and illustrate a decision-making problem which uses the idea of type-2 multi-fuzzy sets. Furthermore, an application of a medical diagnosis system based on multi-criteria decision making of T2MFS is illustrated with a real-life case study.

Extension of TOPSIS for Multiple Attribute Decision Making Using Intuitionistic Fuzzy Sets

2012 ◽  
Vol 433-440 ◽  
pp. 4053-4058 ◽  
Author(s):  
Yuan Yuan ◽  
Li Yang He
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quantitative Estimation ◽  
Ideal Point ◽  
Real Life ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

This electronic document is a “live” template. The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. Due to the nature of vagueness inherent to real-life situations, some fuzzy data are deemed to suitable enough to describe the qualitative and/or quantitative estimation for decision making problems. Therefore, a new method for multiple attribute decision making under fuzzy environment is discussed, in which the attribute values take the form of intuitionistic fuzzy numbers. To overcome some disadvantages of existing distance measures like indiscrimination, counterintuitive results and difficulty of interpretation, we introduce a new class of distance for describing the deviation degrees between intuitionistic fuzzy sets. Furthermore, the measure of similarity degree for each alternative to ideal point is calculated through using the new proposed fuzzy distance. A model of TOPSIS is designed with the introduction of the particular closeness coefficient composed of similarity degrees. Then, we extend the TOPSIS method to aggregate the fuzzy information corresponding to each alternative, and rank the alternatives according to their closeness coefficients. Finally, an illustrative example is given to demonstrate the proposed approach practicality and effectiveness.

Evaluation of Renewable Energy Alternatives using Hesitant Fuzzy TOPSIS and Interval Type-2 Fuzzy AHP

2015 ◽  
pp. 191-224 ◽  
Author(s):  
Başar Öztayşi ◽  
Cengiz Kahraman
Keyword(s):  
Decision Making ◽  
Renewable Energy ◽  
Fuzzy Sets ◽  
Fuzzy Ahp ◽  
Fuzzy Topsis ◽  
Decision Makers ◽  
Priority Weights ◽  
Interval Type

The selection among renewable energy alternatives is a fuzzy multicriteria problem with many conflicting criteria under uncertainty. In many decision-making problems, the Decision Makers (DM) define their preference in linguistic form since it is relatively difficult to provide exact numerical values during the evaluation of alternatives. Therefore, in many studies, fuzzy logic is successfully used to model this kind of uncertainty. In this chapter, the authors try to capture this uncertainty by using interval type-2 fuzzy sets and hesitant fuzzy sets. They propose a fuzzy multicriteria method for the evaluation of renewable energy alternatives, in which the priority weights of the criteria are determined by interval type-2 fuzzy AHP, and the alternatives are ranked using hesitant fuzzy TOPSIS. A case study is also given.

scholarly journals An Approach for Achieving Consistency for Symmetric Trapezoidal Interval Type-2 Fuzzy Sets

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Jiuping Xu ◽  
Kang Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Preference Relation ◽  
Mapping Method ◽  
Linguistic Terms ◽  
Actual Case ◽  
Preference Relations ◽  
Interval Type

Interval type-2 fuzzy sets (IT2 FSs) are powerful tools for dealing with linguistic information in decision making. However, there is a dearth of research regarding the consistency of preference relations based on IT2 FSs. In this paper, symmetric IT2 FSs and IT2 additive preference relations are defined, whilst at the same time a mapping method is proposed to convert IT2 numbers into the corresponding linguistic terms based on the ranking values for IT2 FSs, and some properties for symmetric IT2 FSs are proved. Then, we discuss the process for achieving consistency for IT2 additive preference relations. An algorithm is developed for the IT2 additive preference relation process for achieving consistency, and some desired algorithmic properties are proved. Finally, an actual case study is used in order to demonstrate the effectiveness of the proposed approach.

scholarly journals EXTENDED HESITANT FUZZY SETS

2017 ◽  
Vol 22 (1) ◽  
pp. 100-121 ◽  
Author(s):  
Bin ZHU ◽  
Zeshui XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Close Relationships ◽  
Information Loss ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets ◽  
Information Loss Problem

Hesitant fuzzy sets (HFSs) are a useful tool to manage situations in which the decision makers (DMs) hesitate about several possible values for the membership to assess a variable, alternative, etc. However, HFSs have the information loss problem and cannot identify different DMs, which interferes with the application of HFSs in decision making. To overcome these limitations, we develop the extended hesitant fuzzy sets (EHFSs) in this paper. As an extension of HFSs, EHFSs have close relationships with existing fuzzy sets including intuitionistic fuzzy sets (IFSs), fuzzy multisets (FMSs), type-2 fuzzy sets (T2FSs), dual hesitant fuzzy sets (DHFSs), and especially HFSs. We propose a concept of extended hesitant fuzzy elements (EHFEs), then study the basic operations and the desirable properties of EHFEs in detail. Some extended hesitant distance measures are developed to illustrate their advantages comparing with the existing hesitant distance measures. To extend EHFSs to decision making, we combine the proposed distance measures with the Dempster-Shafer belief structure.

Evaluation of Renewable Energy Alternatives Using Hesitant Fuzzy TOPSIS and Interval Type-2 Fuzzy AHP

2017 ◽  
pp. 1378-1412 ◽  
Author(s):  
Başar Öztayşi ◽  
Cengiz Kahraman
Keyword(s):  
Decision Making ◽  
Renewable Energy ◽  
Fuzzy Sets ◽  
Fuzzy Ahp ◽  
Fuzzy Topsis ◽  
Decision Makers ◽  
Priority Weights ◽  
Interval Type

The selection among renewable energy alternatives is a fuzzy multicriteria problem with many conflicting criteria under uncertainty. In many decision-making problems, the Decision Makers (DM) define their preference in linguistic form since it is relatively difficult to provide exact numerical values during the evaluation of alternatives. Therefore, in many studies, fuzzy logic is successfully used to model this kind of uncertainty. In this chapter, the authors try to capture this uncertainty by using interval type-2 fuzzy sets and hesitant fuzzy sets. They propose a fuzzy multicriteria method for the evaluation of renewable energy alternatives, in which the priority weights of the criteria are determined by interval type-2 fuzzy AHP, and the alternatives are ranked using hesitant fuzzy TOPSIS. A case study is also given.

scholarly journals Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1012
Author(s):  
Subhadip Roy ◽  
Jeong-Gon Lee ◽  
Anita Pal ◽  
Syamal Kumar Samanta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Decision Making Problem ◽  
Definition Of ◽  
Bipolar Fuzzy Sets

In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

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