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.

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.

Entropy Analysis on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and its Applications in Mode Assessment on Open Communities

2018 ◽  
Vol 22 (1) ◽  
pp. 147-155 ◽  
Author(s):  
Hang Tian ◽  
Jiaru Li ◽  
Fangwei Zhang ◽  
Yujuan Xu ◽  
Caihong Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Entropy Measures ◽  
Interval Valued

This paper identifies four variables to reveal the internal mechanisms of the entropy measures on intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). First, four variables are used to propose a pair of generalized entropy measures on IFSs and IVIFSs. Second, three specific entropy measures are put forward to illustrate the effectiveness of the generalized entropy measure functions. Third, a novel multiple attribute decision-making approach under an intuitionistic fuzzy environment is proposed. The superiority of the decision-making approach is that the weight values of the attributes are obtained by their related entropy measures. Finally, the performance of the proposed entropy regulations on IFSs and IVIFSs is illustrated through a mode assessment example on open communities.

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 A New Type of Compositive Information Entropy for IvIFS and Its Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Junjun Mao ◽  
Yuan Zhao ◽  
Chuang Ma
Keyword(s):  
Intuitionistic Fuzzy Set ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures ◽  
New Type ◽  
Definition Of ◽  
Multiple Attributes Decision Making ◽  
Interval Valued

We first show the interval-valued intuitionistic fuzzy entropy which reflects intuitionism and fuzziness of interval-valued intuitionistic fuzzy set (IvIFS) based on interval-valued intuitionistic fuzzy cross-entropy. As for intuitionism and fuzziness of IvIFS, we propose interval-valued intuitionistic entropy and interval-valued fuzzy entropy, respectively. Furthermore, we establish the interval-valued span entropy describing the uncertainty of membership degree and nonmembership degree and show some concrete measure formulas. Combining intuitionistic factor, fuzzy factor, and span factor, we ultimately put forward the axiomatic definition of the compositive entropy and give a measure formula of compositive entropy. In addition, the effectiveness of the compositive entropy measure is illuminated by comparison with other entropy measures. Furthermore, the compositive entropy is applied to multiple attributes’ decision-making by using the weighted correlation coefficient between IvIFSs and pattern recognition by a similarity measure transformed from the compositive entropy.

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 A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chong Wu ◽  
Peng Luo ◽  
Yongli Li ◽  
Xuekun Ren
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Ideal Point ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

As an important content in fuzzy mathematics, similarity measure is used to measure the similarity degree between two fuzzy sets. Considering the existing similarity measures, most of them do not consider the hesitancy degree and some methods considering the hesitancy degree are based on the intuitionistic fuzzy sets, intuitionistic fuzzy values. It may cause some counterintuitive results in some cases. In order to make up for the drawback, we present a new approach to construct the similarity measure between two interval-valued intuitionistic fuzzy sets using the entropy measure and considering the hesitancy degree. In particular, the proposed measure was demonstrated to yield a similarity measure. Besides, some examples are given to prove the practicality and effectiveness of the new measure. We also apply the similarity measure to expert system to solve the problems on pattern recognition and the multicriteria group decision making. In these examples, we also compare it with existing methods such as other similarity measures and the ideal point method.

scholarly journals Dynamic Air Target Threat Assessment Based on Interval-Valued Intuitionistic Fuzzy Sets, Game Theory, and Evidential Reasoning Methodology

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Ruojing Zhao ◽  
Fengbao Yang ◽  
Linna Ji ◽  
Yongqiang Bai
Keyword(s):  
Game Theory ◽  
Fuzzy Sets ◽  
Threat Assessment ◽  
Intuitionistic Fuzzy Sets ◽  
Evidential Reasoning ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Combat Environment ◽  
Interval Valued ◽  
Assessment Results

In order to reduce the uncertainty of target threat assessment results and improve exact target assessment in the complicated and changeable air combat environment, a novel method based on the combination of interval-valued intuitionistic fuzzy sets (IVIFSs), game theory, and evidential reasoning methodology is proposed in this paper. First, the imprecise and fuzzy information of battlefield air target is expressed by IVIFS. Second, the optimal index weight is determined by the interval intuitionistic fuzzy entropy and game theory. And the time series weight is calculated by the inverse Poisson distribution method. Then, the target evaluation information at different times is dynamically fused through an evidential reasoning algorithm. Finally, the accuracy function is applied to obtain the threat ranking of all the targets. A case of the threat assessment of air targets is provided to demonstrate the implementation process of the method proposed in this paper. Simulation experiments show that in a rapidly evolving combat environment, this algorithm can effectively reduce the uncertainty of target threat assessment results. It provides us with a useful way for target threat assessment based on interval-valued intuitionistic fuzzy sets, game theory, and evidential reasoning methodology.

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.

scholarly journals On Intuitionistic Fuzzy Entropy of Order-α

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rajkumar Verma ◽  
BhuDev Sharma
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Fuzzy Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Renyi’S Entropy ◽  
Sets Theory

Using the idea of Rènyi’s entropy, intuitionistic fuzzy entropy of order-α is proposed in the setting of intuitionistic fuzzy sets theory. This measure is a generalized version of fuzzy entropy of order-α proposed by Bhandari and Pal and intuitionistic fuzzy entropy defined by Vlachos and Sergiadis. Our study of the four essential and some other properties of the proposed measure clearly establishes the validity of the measure as intuitionistic fuzzy entropy. Finally, a numerical example is given to show that the proposed entropy measure for intuitionistic fuzzy set is reasonable by comparing it with other existing entropies.

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