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Interval‐Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral
Author(s) -
Meng Fanyong,
Tang Jie
Publication year - 2013
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.21624
Subject(s) - choquet integral , mathematics , fuzzy measure theory , operator (biology) , group decision making , measure (data warehouse) , entropy (arrow of time) , fuzzy logic , fuzzy set , fuzzy number , discrete mathematics , mathematical optimization , algebra over a field , computer science , artificial intelligence , pure mathematics , data mining , chemistry , physics , quantum mechanics , biochemistry , repressor , transcription factor , law , political science , gene
In this paper, a new operator called the arithmetic interval‐valued intuitionistic fuzzy Choquet aggregation (AIVIFCA) operator is defined. Since interactions between elements might exist in all their combinations, the generalized Shapley AIVIFCA (GSAIVIFCA) operator is introduced. Further, to simplify the complexity of solving a fuzzy measure, the 2‐additive generalized Shapley AIVIFCA (2AGSAIVIFCA) operator is presented. Moreover, a decision procedure to interval‐valued intuitionistic fuzzy multiattribute group decision making is developed. When the weight vectors on attribute set and expert set are not exactly known, the models for obtaining the optimal fuzzy measures are established by using the defined cross entropy measure and the Shapley function. Finally, a numerical example is provided to illustrate the developed procedure.