scholarly journals New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 3-18
Author(s):  
Melda Kokoç ◽  
Süleyman Ersöz
Keyword(s):  
Decision Making ◽  
High Performance ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Score Function ◽  
Multi Criteria Decision Making ◽  
Ranking Functions ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

Multi-Criteria Decision-Making Approach Based on Moderator Intuitionistic Fuzzy Hybrid Aggregation Operators

2019 ◽  
pp. 237-251
Author(s):  
Bhagawati Prasad Joshi ◽  
Akhilesh Singh
Keyword(s):  
Decision Making ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Uncertainty Index ◽  
Geometric Point ◽  
Membership Grade

It has been seen in literature that the notion of intuitionistic fuzzy sets (IFSs) is very powerful tool to deal with real life problems under the environment of uncertainty. This notion of IFSs favours the intermingling of the uncertainty index in membership functions. The uncertainty index is basically generated from a lot of parameters such as lack of awareness, historical information, situation, short of standard terminologies, etc. Hence, the uncertainty index appended finding the membership grade under IFSs needs additional enhancement. Then, the concept of a moderator intuitionistic fuzzy set (MIFS) is defined by adding a parameter in the IFSs environment to make the uncertain behaviour more accurate. In this chapter, some new moderator intuitionistic fuzzy hybrid aggregation operators are presented on the basis of averaging and geometric point of views to aggregate moderator intuitionistic fuzzy information. Then, a multi-criteria decision-making (MCDM) approach is provided and successfully implemented to real-life problems of candidate selection.

A New Ranking Approach for Interval Valued Intuitionistic Fuzzy Sets and its Application in Decision Making

2019 ◽  
Vol 8 (2) ◽  
pp. 110-125 ◽  
Author(s):  
Pranjal Talukdar ◽  
Palash Dutta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Ranking of interval valued intuitionistic fuzzy sets (IVIFSs) plays an important role because of its attraction and applicability to model uncertainty in real life problems. In this article, an attempt has been made to devise a new method for ranking of IVIFSs based on exponential function. The significance of the method is illustrated with the help of some numerical examples and the results are compared with other existing methods. Furthermore, a multi criteria decision making method is presented here to evaluate the final ranking of the alternatives using the proposed ranking method and discussed the consistency of so obtained results.

ELECTRE Method Based on Interval-Valued Intuitionistic Fuzzy Number

2012 ◽  
Vol 220-223 ◽  
pp. 2308-2312 ◽  
Author(s):  
Jun Li ◽  
Min Lin ◽  
Jian Hua Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Preference Relation ◽  
Intuitionistic Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy ◽  
Electre Method ◽  
Deviation Degree ◽  
Interval Valued

A new multi-criteria decision-making method for interval-valued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and ELECTRE method. Firstly, the possibility-degree and deviation-degree of interval number are used to establish the preference relation of interval-valued intuitionistic fuzzy number. Then, we exposit the decision theory and the steps of this method. Finally, a numerical example is given to illustrate the application of the method. The numerical results show that it is feasible and effective.

scholarly journals Group Decision Making using Interval-Valued Intuitionistic Fuzzy Soft Matrix and Confident Weight of Experts

2014 ◽  
Vol 4 (1) ◽  
pp. 57-77 ◽  
Author(s):  
Sujit Das ◽  
Samarjit Kar ◽  
Tandra Pal
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Soft Sets ◽  
Soft Matrix ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Interval Valued

Abstract This article proposes an algorithmic approach for multiple attribute group decision making (MAGDM) problems using interval-valued intuitionistic fuzzy soft matrix (IVIFSM) and confident weight of experts. We propose a novel concept for assigning confident weights to the experts based on cardinals of interval-valued intuitionistic fuzzy soft sets (IVIFSSs). The confident weight is assigned to each of the experts based on their preferred attributes and opinions, which reduces the chances of biasness. Instead of using medical knowledgebase, the proposed algorithm mainly relies on the set of attributes preferred by the group of experts. To make the set of preferred attributes more important, we use combined choice matrix, which is combined with the individual IVIFSM to produce the corresponding product IVIFSM. This article uses IVIFSMs for representing the experts’ opinions. IVIFSM is the matrix representation of IVIFSS and IVIFSS is a natural combination of interval-valued intuitionistic fuzzy set (IVIFS) and soft set. Finally, the performance of the proposed algorithm is validated using a case study from real life

An improved fuzzy TODIM method based on entropy measure under Intuitionistic Fuzzy Information

2021 ◽  
Vol 23 (05) ◽  
pp. 464-470
Author(s):  
Sunit Kumar ◽  
◽  
Satish Kumar ◽  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Fuzzy Information ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Todim Method

Intuitionistic fuzzy set (IFS) is one of the most extensive and important tool to accommodate more uncertainties than existing fuzzy set structures. In the present paper, we describe an improved entropy based on TODIM procedure for handling multi-criteria decision-making (MCDM) under IF setting and also the weight information is partially known. First, we study the basic notions and operating laws of IFSs, also the accuracy and score function of it. The new entropy has been proposed. Secondly, the IF information-based decision-making technique for MCDM is presented. Lastly, a numerical example is given related, to demonstrate that their results are credible and feasible.

Interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making method based on Prospect theory

Kybernetes ◽  
2015 ◽  
Vol 44 (1) ◽  
pp. 25-42 ◽  
Author(s):  
Jianwei Gao ◽  
Huihui Liu
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Decision Maker ◽  
Score Function ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making ◽  
Content Type ◽  
Intuitionistic Fuzzy ◽  
New Criteria ◽  
Interval Valued

Purpose – The purpose of this paper is to provide a new approach to solving the interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making (MCDM) problems. Design/methodology/approach – To transform the interval-valued intuitionistic fuzzy number (IVIFN) into a computational numerical value, a new precision score (P-score) function is developed based on the degrees of membership, non-membership and hesitation. The prospect decision-making matrix is derived by applying P-score function and Prospect theory. A new criteria weighting model is put forward based on the least square method, the maximizing deviation method and Prospect theory. Consequently, combined criteria weighting model with the prospect decision-making matrix, the integrated prospect value is derived which presents a measurement scale for ranking the order of alternatives. Findings – As a result, the method of the interval-valued intuitionistic fuzzy stochastic MCDM is suggested. In this method, the new P-score function responses the comprehensive information of the criteria. The prospect decision-making matrix can reflect the risk attitude of the decision maker. The new criteria weighting model can express both the subjective considerations of the decision maker and the objective information meaning. Research limitations/implications – The research results may lack generalizability for other fuzzy decision making because of the chosen research approach for IVIFN decision making. Therefore, researchers are encouraged to test the proposed propositions further. Practical implications – The developed approach can be applied in many decision-making fields such as selection of renewable energy alternatives, assessment of flexible manufacturing system alternatives and human resource alternatives performance evaluation, etc. where the evaluation values are IVIFNs. Originality/value – This paper succeeds in studying the interval-valued intuitionistic fuzzy MCDM based on Prospect theory, which has not been reported in the existing academic literature.

Interval-Valued Intuitionistic Fuzzy Sets based Method for Multiple Criteria Decision-Making

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.

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