Frank Choquet Bonferroni Mean Operators of Bipolar Neutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems

Comprehensive multi-criteria decision-making (MCDM) methods are investigated under bipolar neutrosophic environment and the proposed operators simultaneously consider the interactions and interrelationships among the criteria by combining the Choquet integral operator and Bonferroni mean operators.

Abstract

In this study, comprehensive multi-criteria decision-making (MCDM) methods are investigated under bipolar neutrosophic environment. First, the operations of BNNs are redefined based on the Frank operations considering the extant operations of bipolar neutrosophic numbers (BNNs) lack flexibility and robustness. Subsequently, the Frank bipolar neutrosophic Choquet weighted Bonferroni mean operator and the Frank bipolar neutrosophic Choquet geometric Bonferroni mean operator are proposed based on the Frank operations of BNNs. The proposed operators simultaneously consider the interactions and interrelationships among the criteria by combining the Choquet integral operator and Bonferroni mean operators. Furthermore, MCDM methods are developed based on the proposed aggregation operators. A numerical example of plant location selection is conducted to explain the application of the proposed methods, and the influences of parameters are also discussed. Finally, the proposed methods are compared with several extant methods to verify their feasibility.