Abstract
Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively.
Highlights
Research background Since Zadeh (1965) first proposed fuzzy set (FS) theory, it has been widely investigated and applied to a variety of fields
In order to simplify the complexity of solving a fuzzy measure, we further define the GBIVIFGC operator w.r.t. 2-adttitive measure, which is expressed as the GABIVIFGC operator
When we deal with the real decision making problems, it is unreasonable to use the additive measures because the independence among elements in a set usually violates
Summary
Technological and Economic Development of Economy, 2015, 21(2): 186–215 which is characterized by a degree of membership and a degree of non-membership. In 1989, Atanassov and Gargov (1989) introduced the concept of interval-valued intuitionistic fuzzy sets, which are characterized by an interval membership function and an interval non-membership function. Such a generalization further facilitates effectively representing inherent imprecision and uncertainty in the human decision making process. Many aggregation operators have been developed under intuitionistic fuzzy environment, there are some problems that should be pointed out: (1) The existing aggregation operators based on the Choquet integral do not consider the interaction among elements globally; (2) How to obtain the fuzzy measure on a set is not studied; (3) The complexity of solving a fuzzy measure is not taken into account.
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