Intuitionistic Fuzzy Interaction Bonferroni Means and Its Application to Multiple Attribute Decision Making

The Bonferroni mean (BM) was originally presented by Bonferroni and had been generalized by many researchers for its capacity to capture the interrelationship between input arguments. Nevertheless, the existing intuitionistic fuzzy BMs only consider the effects of membership function or nonmembership function of different intuitionistic fuzzy sets (IFSs). As complements to the existing generalizations of BM under intuitionistic fuzzy environment, this paper also considers the interactions between the membership function and nonmembership function of different IFSs and develops the intuitionistic fuzzy interaction BM and the weighted intuitionistic fuzzy interaction BM. We investigate the properties of these new extensions of BM and discuss their special cases. Furthermore, the detailed steps of multiple attribute decision making with the presented operators under intuitionistic fuzzy environment are investigated and an example is illustrated to show the validity and feasibility of the new approach.