Generalized Intuitionistic Fuzzy Entropy Measure of Order α and Degree β and Its Applications to Multi-Criteria Decision Making Problem

2017 ◽  
Vol 6 (1) ◽  
pp. 86-107 ◽  
Author(s):  
Harish Garg ◽  
Nikunj Agarwal ◽  
Alka Tripathi
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Decision Maker ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Decision Making Process ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Decision Making Problem

The objective of this manuscript is divided into two fold. Firstly, a more generalized intuitionistic fuzzy entropy measure of order and degree has been presented for measuring the degree of fuzziness of the set with a proof of its validity. A structured linguistic variable has been taken as an illustrative example to show its validity and superiority than the existing measures. Furthermore, based on this measure, an approach to deal with multi-criteria decision making (MCDM) problem is developed. Finally, a practical example is provided to illustrate the decision making process. A computed result is compared with the help of existing results. A sensitivity analysis on the different values of the parameters will make a decision maker more choice for accessing their results.

Multi-Criteria Decision-Making Model using Intuitionistic Fuzzy Entropy and Variable Weight Theory

Mekatronika ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 18-25
Author(s):  
Omar Ayasrah ◽  
Faiz Mohd Turan
Keyword(s):  
Decision Making ◽  
Fuzzy Entropy ◽  
Decision Makers ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Variable Weight ◽  
Intuitionistic Fuzzy Entropy ◽  
Perform Sensitivity Analysis ◽  
Almost All

The aim of this research is to develop a new multi-criteria decision-making method that integrates an intuitionistic fuzzy entropy measure and variable weight theory to be implemented in different fields to provide a solution for MCDM problems when the available information is incomplete. A limited number of studies have considered determining decision maker’s weights by performing objective techniques, and almost all of these researches detected a constant weights for the decision makers. In addition, most of the MCDM studies were not formulated to perform sensitivity analysis. The new method is based on the TOPSIS model with an intuitionistic fuzzy entropy measure in the exponential-related function form and the engagement of the variable weight theory to determine weights for the decision-makers that vary as per attibutes. Lastly, a mathematical model was developed in this research to be as an input for developing the mobile-aplication based method in future for virtual use of the new MCDM method.

scholarly journals On Some Knowledge Measures of Intuitionistic Fuzzy Sets of Type Two with Application to MCDM

2020 ◽  
Vol 20 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Surender Singh ◽  
Sumita Lalotra ◽  
Abdul Haseeb Ganie
Keyword(s):  
Decision Making ◽  
Comparative Study ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Knowledge Measure ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures

AbstractTo overcome the certain limitations of Intuitionistic Fuzzy Sets (IFSs), the notion of Intuitionistic Fuzzy Sets of Second Type (IFSST) was introduced. IFSST is a modified version of IFS for handling some problems in a reasonable manner. Type two Intuitionistic Fuzzy entropy (IFSST-entropy) measures the amount of ambiguity/uncertainty present in an IFSST. In the present paper, we introduce the concept of dual measure of IFSST-entropy, i.e., IFSST-knowledge measure. We develop some IFSST-knowledge measures and prove some of their properties. We also show the superiority of the proposed IFSST-knowledge measures through comparative study. Further, we demonstrate the application of the proposed knowledge measures in Multi-Criteria Decision-Making (MCDM).

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

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.

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