scholarly journals An Entropy-Based Knowledge Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application to Multiple Attribute Decision Making

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 981 ◽  
Author(s):  
Gang Wang ◽  
Jie Zhang ◽  
Yafei Song ◽  
Qiang Li
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Knowledge Measure ◽  
Multiple Attribute ◽  
New Knowledge ◽  
Atanassov’S Intuitionistic Fuzzy Sets

As the complementary concept of intuitionistic fuzzy entropy, the knowledge measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) has attracted more attention and is still an open topic. The amount of knowledge is important to evaluate intuitionistic fuzzy information. An entropy-based knowledge measure for AIFSs is defined in this paper to quantify the knowledge amount conveyed by AIFSs. An intuitive analysis on the properties of the knowledge amount in AIFSs is put forward to facilitate the introduction of axiomatic definition of the knowledge measure. Then we propose a new knowledge measure based on the entropy-based divergence measure with respect for the difference between the membership degree, the non-membership degree, and the hesitancy degree. The properties of the new knowledge measure are investigated in a mathematical viewpoint. Several examples are applied to illustrate the performance of the new knowledge measure. Comparison with several existing entropy and knowledge measures indicates that the proposed knowledge has a greater ability in discriminating different AIFSs and it is robust in quantifying the knowledge amount of different AIFSs. Lastly, the new knowledge measure is applied to the problem of multiple attribute decision making (MADM) in an intuitionistic fuzzy environment. Two models are presented to determine attribute weights in the cases that information on attribute weights is partially known and completely unknown. After obtaining attribute weights, we develop a new method to solve intuitionistic fuzzy MADM problems. An example is employed to show the effectiveness of the new MADM method.

Extension of TOPSIS for Multiple Attribute Decision Making Using Intuitionistic Fuzzy Sets

2012 ◽  
Vol 433-440 ◽  
pp. 4053-4058 ◽  
Author(s):  
Yuan Yuan ◽  
Li Yang He
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quantitative Estimation ◽  
Ideal Point ◽  
Real Life ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

This electronic document is a “live” template. The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. Due to the nature of vagueness inherent to real-life situations, some fuzzy data are deemed to suitable enough to describe the qualitative and/or quantitative estimation for decision making problems. Therefore, a new method for multiple attribute decision making under fuzzy environment is discussed, in which the attribute values take the form of intuitionistic fuzzy numbers. To overcome some disadvantages of existing distance measures like indiscrimination, counterintuitive results and difficulty of interpretation, we introduce a new class of distance for describing the deviation degrees between intuitionistic fuzzy sets. Furthermore, the measure of similarity degree for each alternative to ideal point is calculated through using the new proposed fuzzy distance. A model of TOPSIS is designed with the introduction of the particular closeness coefficient composed of similarity degrees. Then, we extend the TOPSIS method to aggregate the fuzzy information corresponding to each alternative, and rank the alternatives according to their closeness coefficients. Finally, an illustrative example is given to demonstrate the proposed approach practicality and effectiveness.

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.

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