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 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.

A Novel Entropy Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Application to Failure Mode and Effect Analysis

2021 ◽  
pp. 115-134
Author(s):  
Kamal Kumar ◽  
Naveen Mani ◽  
Amit Sharma ◽  
Reeta Bhardwaj
Keyword(s):  
Failure Mode ◽  
Fuzzy Set ◽  
Failure Modes ◽  
Intuitionistic Fuzzy Set ◽  
Entropy Measure ◽  
Effect Analysis ◽  
Intuitionistic Fuzzy ◽  
Safety And Reliability ◽  
Definition Of ◽  
Interval Valued

The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.

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.

An Improved Axiomatic Definition and Structural Formula of Interval-Valued Intuitionistic Fuzzy Entropy

2014 ◽  
Vol 644-650 ◽  
pp. 1556-1559
Author(s):  
Ming Mei Gao ◽  
Tao Sun ◽  
Rui Ping Xu ◽  
Li Song ◽  
Hui Qun Zhang
Keyword(s):  
Structural Formula ◽  
Fuzzy Entropy ◽  
Axiomatic System ◽  
Computational Formula ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Entropy ◽  
Axiomatic Definition ◽  
Definition Of ◽  
New Formula ◽  
Interval Valued

In view of the defects of existing axiomatic definitions of interval-valued intuitionistic fuzzy entropy, an improved axiomatic definition of the interval-valued intuitionistic fuzzy entropy is presented and the corresponding formula is structured in the paper. Firstly, defects in three kinds of the axiomatic system of entropy of IVIFS are analyzed in detail respectively. New axiomatic entropy definition is proposed for the sake of more reasonable depiction of the fuzziness of IVIFS. Based on the new axiomatic entropy definition, a new computational formula is mentioned. Finally, an example is showed to illustrate the effectiveness of this new formula. Overall, the results indicate that the improved axiomatic definition and the new proposed formula are reasonable and effective.

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.

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 Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1119
Author(s):  
Xuan Wu ◽  
Yafei Song ◽  
Yifei Wang
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Malicious Code ◽  
General Level ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Knowledge Measure ◽  
Intuitionistic Fuzzy Entropy ◽  
Definition Of

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

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.

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