Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making
International Journal of Intelligent SystemsPublished 16 July 2012
Zeshui Xu, Meimei Xia
Citations307
SJR quartileQ1
SJR score1.14
SNIP1.40
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TL;DR
Two multiattribute decision‐making methods are developed in which the attribute values are given in the form of hesitant fuzzy sets reflecting humans' hesitant thinking comprehensively, and it is found that three measures are interchangeable under certain conditions.
Abstract
We introduce the concepts of entropy and cross-entropy for hesitant fuzzy information, and discuss their desirable properties. Several measure formulas are further developed, and the relationships among the proposed entropy, cross-entropy, and similarity measures are analyzed, from which we can find that three measures are interchangeable under certain conditions. Then we develop two multiattribute decision-making methods in which the attribute values are given in the form of hesitant fuzzy sets reflecting humans' hesitant thinking comprehensively. In one method, the weight vector is determined by the hesitant fuzzy entropy measure, and the optimal alternative is obtained by comparing the hesitant fuzzy cross-entropies between the alternatives and the ideal solutions; in another method, the weight vector is derived from the maximizing deviation method and the optimal alternative is obtained by using the TOPSIS method. An actual example is provided to compare our methods with the existing ones. © 2012 Wiley Periodicals, Inc.
Keywords
Computer ScienceDecision SciencesMathematics
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