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.

Group decision making method for residents to choose livable cities depicted by n-intuitionistic polygonal fuzzy sets1

2020 ◽  
Vol 39 (3) ◽  
pp. 3503-3518
Author(s):  
Guijun Wang ◽  
Jie Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Arithmetic Operation ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Information ◽  
Decision Matrix ◽  
Arithmetic Average

The polygonal fuzzy set is an effective tool to express a class of fuzzy information with the help of finite ordered real numbers. It can not only guarantee the closeness of arithmetic operation of the polygonal fuzzy sets, but also has good linearity and intuitiveness. Firstly, the concept of the n-intuitionistic polygonal fuzzy set (n-IPFS) is proposed based on the intuitionistic fuzzy set and the polygonal fuzzy set. The ordered representation and arithmetic operation of n-IPFS are given by an example. Secondly, a new aggregation method for multi attribute fuzzy information is given based on the n-IPFS operations and the weighted arithmetic average operator, and the ranking criteria of n-IPFS are obtained by using the score function and the accuracy function. Finally, a new group decision making method is proposed for urban residents to choose the livable city problem based on the decision matrix of the n-IPFS, and the effectiveness of the proposed method is explained by an actual example.

scholarly journals Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tabasam Rashid ◽  
Shahzad Faizi ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Fuzzy entropy means the measurement of fuzziness in a fuzzy set and therefore plays a vital role in solving the fuzzy multicriteria decision making (MCDM) and multicriteria group decision making (MCGDM) problems. In this study, the notion of the measure of distance based entropy for uncertain information in the context of interval-valued intuitionistic fuzzy set (IVIFS) is introduced. The arithmetic and geometric average operators are firstly used to aggregate the interval-valued intuitionistic fuzzy information provided by the decision makers (DMs) or experts corresponding to each alternative, and then the fuzzy entropy of each alternative is calculated based on proposed distance measure. Several numerical examples are solved to demonstrate the application to MCDM and MCGDM problems to show the effectiveness of the proposed approach.

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.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

2007 ◽  
Vol 15 (03) ◽  
pp. 285-297 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

scholarly journals A New Multiple Criteria Decision Making Method and its Application in Cloud Computing for Education

2015 ◽  
Vol 10 (8) ◽  
pp. 21
Author(s):  
Heng Sun
Keyword(s):  
Decision Making ◽  
Cloud Computing ◽  
Membership Function ◽  
Fuzzy Set ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Intuitionistic Fuzzy

Cloud computing can extend the traditional education framework. In education, cloud can provide students and teachers with tools to deploy computing resources on-demand for lectures and labs according to their learning needs. But how to select a perfect cloud server is a key point, which is considered as a multiple criteria decision making problem. So, in this paper, intuitionistic fuzzy set is first introduced to express the decision maker’s views. Intuitionistic fuzzy set (IFS) includes a membership function and a non-membership function. More importantly, a new operator with choquet integral is developed to deal with assessment of education using cloud computing. Meanwhile, score function and accuracy function are demonstrated to obtain the final result. Finally, we develop this method to apply in a case study to show its applicability.

scholarly journals Extended Fuzzy Sets and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 770
Author(s):  
Bahram Farhadinia ◽  
Francisco Chiclana
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Innovative Concept

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

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