scholarly journals A New Entropy and Its Properties Based on the Improved Axiomatic Definition of Intuitionistic Fuzzy Entropy

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Dengying Jiang ◽  
Yaxiong Wang
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Constraint Condition ◽  
Entropy Formula ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Axiomatic Definition ◽  
Definition Of

Regarding the problem of the existing intuitionistic fuzzy entropy formulas in ordering the partial entropy, the constraint condition that is consistent with the intuitionistic facts is proposed in this paper, the axiomatic definition of entropy which fully reflects the intuition and fuzziness of intuitionistic fuzzy sets is given, and the improved intuitionistic fuzzy entropy formula is constructed according to the entropy axiomatic definition and its properties are studied. Finally, we compare the improved formula with the existing intuitionistic fuzzy entropy formulas, and the result turns out that the improved formula can solve the problem in the entropy ordering theoretically and practically.

scholarly journals An Effective Interval-Valued Intuitionistic Fuzzy Entropy to Evaluate Entrepreneurship Orientation of Online P2P Lending Platforms

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaohong Chen ◽  
Li Yang ◽  
Pei Wang ◽  
Wei Yue
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Evaluation Procedure ◽  
Entropy Measure ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Essential Properties ◽  
P2p Lending ◽  
Interval Valued

This paper describes an approach to measure the entrepreneurship orientation of online P2P lending platforms. The limitations of existing methods for calculating entropy of interval-valued intuitionistic fuzzy sets (IVIFSs) are significantly improved by a new entropy measure of IVIFS considered in this paper, and then the essential properties of the proposed entropy are introduced. Moreover, an evaluation procedure is proposed to measure entrepreneurship orientation of online P2P lending platforms. Finally, a case is used to demonstrate the effectiveness of this method.

A NOTE ON ENTROPY OF INTUITIONISTIC FUZZY SETS

2003 ◽  
Vol 11 (05) ◽  
pp. 627-633 ◽  
Author(s):  
WEN-LIANG HUNG
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Intuitionistic Fuzzy ◽  
Entropy Measures

In this paper, two new formulas of fuzzy entropy induced by distances between two intuitionistic fuzzy sets are given. These entropy measures can be computed easily and give reliable results. Some examples are illustrated for the comparison with Burillo and Bustince (1996) and Szmidt and Kacprzyk (2001).

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 New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1600
Author(s):  
Neeraj Gandotra ◽  
Bartłomiej Kizielewicz ◽  
Abhimanyu Anand ◽  
Aleksandra Bączkiewicz ◽  
Andrii Shekhovtsov ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Pythagorean Fuzzy Set ◽  
Additional Advantage ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

Generalized Exponential Entropy on Intuitionistic Fuzzy Sets

2014 ◽  
Vol 556-562 ◽  
pp. 4097-4102 ◽  
Author(s):  
Lan Zhen Yang ◽  
Xiao Ying Gong ◽  
Xian Jie Wang ◽  
Sheng Qiao An
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Exponential Entropy

Based on the concept of intuitionistic fuzzy entropy, this paper proposes a generalized parametric exponential intuitionistic fuzzy entropy measure. This measure is a generalized version of exponential intuitionistic fuzzy entropy proposed by Verma and Sharma, and its validity as an intuitionistic fuzzy entropy is verified. Further, some interesting properties of this measure are also analyzed, and an example shows that this measure is nonmonotone.

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