Some intuitionistic fuzzy power Bonferroni mean operators in the framework of Dempster–Shafer theory and their application to multicriteria decision making

Abstract

There is a strong link between intuitionistic fuzzy set (IFS) and the Dempster–Shafer Theory (DST). It is easy to use this link to provide evident and productive semantics for IFS in terms of DST. It is widely known that there are a few limitations and shortcomings in the ordinary operational laws of intuitionistic fuzzy numbers (IFNs). In the environment of DST, an IFN can be transformed into a basic probability assignment (BPA), and operations on IFNs are represented as operations on belief interval (BI), which are free of the revealed limitations and shortcomings of ordinary operational laws of IFNs. Additionally, although many operators exist to aggregate IFNs, there is a paucity of operators to aggregate BPAs. For example, the Bonferroni mean (BM) operator exhibits the advantage of considering interrelationships between criteria, and Power average (PA) operator eliminates the effects of biased criteria values. In this study, based on the DST, the intuitionistic fuzzy power BM (IFPBMDST) operator, intuitionistic fuzzy weighted power BM (IFWPBMDST) operator, intuitionistic fuzzy geometric power BM (IFGPBMDST) operator, and intuitionistic fuzzy weighted geometric power BM (IFWGPBMDST) operator are proposed, and their desirable properties are developed. Subsequently, a novel method based on IFWPBMDST operator and IFWGPBMDST operator is proposed to solve multicriteria decision making (MCDM) problems without intermediate defuzzification when criteria and their weights correspond to IFNs. Finally, a few real cases are used to illustrate the following advantages of the proposed method: (1) it is free of the limitations of ordinary IFS; (2) it eliminates the effects of biased values; (3) it considers the interrelationships between criteria; and (4) criteria weights can be denoted by IFNs.