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Open AccessArticle

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

by Gang Wang 1, Jie Zhang 1, Yafei Song 1,* and Qiang Li 2
1
Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
2
Aviation Maintenance NCO Academy, Air Force Engineering University, Xinyang 464000, China
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(12), 981; https://doi.org/10.3390/e20120981
Received: 22 November 2018 / Revised: 10 December 2018 / Accepted: 16 December 2018 / Published: 17 December 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
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. View Full-Text
Keywords: Atanassov’s intuitionistic fuzzy set; knowledge measure; entropy; multiple attribute decision-making Atanassov’s intuitionistic fuzzy set; knowledge measure; entropy; multiple attribute decision-making
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Wang, G.; Zhang, J.; Song, Y.; Li, Q. An Entropy-Based Knowledge Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application to Multiple Attribute Decision Making. Entropy 2018, 20, 981.

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