Multiple-Valued Neutrosophic Uncertain Linguistic Sets with Dombi Normalized Weighted Bonferroni Mean Operator and Their Applications in Multiple Attribute Decision Making Problem

Abstract

In order to take into account quantitative and qualitative information in real complex decision making issue, a multiple-valued neutrosophic uncertain linguistic set (MVNULS) is initially proposed, which includes the uncertain linguistic part and the multiple-valued neutrosophic set (MVNS). Consequently, it has the advantages of them in expressing evaluation information. In the article, we initially define some concepts containing a multiple-valued neutrosophic uncertain linguistic set (MVNULS) and a multiple-valued neutrosophic uncertain linguistic element (MVNULE). Next, we present some basic operational rules regarding Dombi t-conorm and t-norm, which is more flexibility with a general parameter, and introduce a comparison method for multiple-valued neutrosophic uncertain linguistic numbers (MVNULNs). Since the aggregating operator of normalized weighted Bonferroni mean (NWBM) cannot only capture the interrelationship among multiple arguments, but also consider weight vector on each criterion and has the reducibility property, the NWBM operator has gained many attentions of scholars. Hence, in order to deal with the aggregation of MVNULEs, we put forward the multiple-valued neutrosophic uncertain linguistic Dombi normalized weighted Bonferroni mean (MVNULDNWBM) operator on account of Dombi t-conorm and t-norm, and discuss the desirable properties of the MVNULDNWBM operator. Furthermore, we investigate a multiple attribute decision making (MADM) approach in view of the aggregating operator to handle the MADM problem with multiple-valued neutrosophic uncertain linguistic information. Eventually, we conduct a concrete instance to validate the effectiveness and application of the developed approach.