Spherical Fuzzy Bonferroni Mean Aggregation Operators and Their Applications to Multiple-Attribute Decision Making

Abstract

The Bonferroni Mean (BM) which was introduced by Bonferroni has been extensively applied in Multi-Attribute Group Decision-Making (MAGDM) and support system problems because of its usefulness in the aggregation techniques. One of the most important and distinguishing characteristic of the BM is its capability to capture the interrelationship between arguments. Motivated by the applications of Spherical Fuzzy Sets (SFS) in recent studies and in order to consider the interrelationship between arguments, it seems necessary to develop novel aggregation operators to use in this kind of fuzzy sets in MAGDM problems. Therefore, in this paper we tried to adopt BM and spherical fuzzy sets operators in order to propose newfound aggregation operators such as: Spherical Fuzzy Bonferroni mean (SFBM) and Spherical Fuzzy Normalized Weighted Bonferroni mean (SFNWBM). Finally, based on the proposed aggregation operators (SFNWBM), we present an approach to multi-criteria group-decision making problems under the spherical fuzzy environment, and to illustrate the validity of the novel aggregation operator, a practical example is provided.