scholarly journals INTUITIONISTIC FUZZY ENTROPY AND ITS APPLICATIONS TO MULTICRITERIA DECISION MAKING WITH IF-TODIM

2021 ◽  
Vol 16 (7) ◽  
Author(s):  
Sahar Abbas
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Daily Life ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Numerical Comparison ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures

The intuitionistic fuzzy entropy (IFE) is being used to measure the degree of uncertainty of a fuzzy set (FS) with alarming accuracy and precision more accurately than the fuzzy set theory. Entropy plays a very important role in managing the complex issues efficiently which we often face in our daily life. In this paper, we first review several existing entropy measures of intuitionistic fuzzy sets (IFSs) and then suggest two new entropies of IFSs better than the existing ones. To show the efficiency of proposed entropy measures over existing ones, we conduct a numerical comparison analysis. Our entropy methods are not only showing better performance but also handle those IFSs amicably which the existing method fails to manage. To show the practical applicability and reliability, we utilize our methods to build intuitionistic fuzzy Portuguese of interactive and multicriteria decision making (IF-TODIM) method. The numerical results show that the suggested entropies are convenient and reasonable in handling vague and ambiguous information close to daily life matters.

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.

NOVEL ENTROPY MEASURE OF A FUZZY SET AND ITS APPLICATION TO MULTICRITERIA DECISION MAKING WITH FUZZY TOPSIS

2021 ◽  
Vol 16 (7) ◽  
Author(s):  
Manzoor Hussain
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Daily Life ◽  
Multicriteria Decision Making ◽  
Fuzzy Topsis ◽  
Vital Role ◽  
Entropy Measure ◽  
Numerical Comparison ◽  
Uncertain Information ◽  
Multicriteria Decision

Fuzzy entropy is being used to measure the uncertainty with high precision and accuracy than classical crisp set theory. It plays a vital role in handling complex daily life problems involving uncertainty. In this manuscript, we first review several existing entropy measures and then propose novel entropy to measure the uncertainty of a fuzzy set. We also construct an axiomatic definition based on the proposed entropy measure. Numerical comparison analysis is carried out with existing entropies to show the reliability and practical applicability of our proposed entropy measure. Numerical results show that our suggested entropy is reasonable and appropriate in dealing with vague and uncertain information. Finally, we utilize our proposed entropy measure to construct fuzzy TOPSIS (Technique for Ordering Preference by Similarity to Ideal Solution) method to manage Multicriteria decision-making problems related to daily life settings. The final results demonstrate the practical effectiveness and applicability of our proposed entropy measure

On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making

2021 ◽  
Vol 40 (1) ◽  
pp. 1191-1217
Author(s):  
Rajkumar Verma
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Entropy ◽  
Information Measures ◽  
Divergence Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures

The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work develops and studies some parametric information measures under the intuitionistic fuzzy environment. First, the paper reviews the existing intuitionistic fuzzy divergence measures in detail with their shortcomings and then proposes four new order-α divergence measures between two IFSs. It is worth mentioning that the developed divergence measures satisfy several elegant mathematical properties. Second, we define four new entropy measures called order-α intuitionistic fuzzy entropy measures in order to quantify the fuzziness associated with an IFS. We prove basic and advanced properties of the order-α intuitionistic fuzzy entropy measures for justifying their validity. The paper shows that the introduced measures include various existing fuzzy and intuitionistic fuzzy information measures as their special cases. Further, utilizing the conventional multi-attributive border approximation area comparison (MABAC) model, we develop an intuitionistic fuzzy MABAC method to solve real-life multiple attribute group decision-making problems. Finally, the proposed method is demonstrated by using a practical application of personnel selection.

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).

scholarly journals Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

2015 ◽  
Vol 15 (4) ◽  
pp. 13-26 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Cross Entropy ◽  
Entropy Measure ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Entropy Measures ◽  
The Cross ◽  
Ranking Order ◽  
Interval Neutrosophic Sets

Abstract Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.

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.

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