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Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making
Author(s) -
Xu Zeshui,
Xia Meimei
Publication year - 2012
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21548
Subject(s) - topsis , entropy (arrow of time) , ideal solution , mathematics , fuzzy logic , computer science , mathematical optimization , data mining , artificial intelligence , mathematical economics , thermodynamics , physics
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.