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.
Highlights
Neutrosophic Sets (NSs) as a generalization of intuitionistic fuzzy sets (IFSs) is initially proposed by Smarandache [1]
The Hamacher operational rules are generalization of the Algebraic operations and Einstein operations, the method proposed by Li is flexible, whereas Li’s method can only handle multiplevalued neutrosophic linguistic elements, and our method proposed in this paper can handle more complex multiple-valued neutrosophic uncertain linguistic information
The key characteristics of the proposed approach are summarized as below: (1) an multiple-valued neutrosophic uncertain linguistic set (MVNULS) is more suitable for expressing the indeterminate, inconsistent information in practical multiple attribute decision making (MADM) or MAGDM problems, the reason is that it combined the multiple-valued neutrosophic set and uncertain linguistic variables takes into account both quantitative and qualitative information. (2) the proposed MVNULNWBM operator is more general and flexible in the aggregating process, the reason is that it is based on the operations of Dombi with a general parameter ρ. (3) the proposed approach is more effective and practical in solving MADM problem, the reason is that it utilizing normalized weighted Bonferroni mean (NWBM) operator can capture the interrelationships among attributes, and the parameters p and q can be determined by decision makers according to the actual situation
Summary
Neutrosophic Sets (NSs) as a generalization of intuitionistic fuzzy sets (IFSs) is initially proposed by Smarandache [1]. Dombi operations are more flexibility in the aggregating process because of a general parameter, some scholars presented a few aggregating operators in view of dombi operation, for example Zhang [42] proposed Heronian mean aggregating operator on the basis of dombi operational rules to manage picture fuzzy numbers, Liu [43] developed dombi Bonferroni mean operators to fuse intuitionistic fuzzy elements in MAGDM problem, He [44] defined dombi aggregating operators with hesitant information, He [45] established a group decision making approach utilizing dombi operations to aggregate interval-valued intuitionistic fuzzy elements and applied it to personnel evaluation, Li [46] investigated dombi prioritized weighted aggregation operators for MAGDM problem under intuitionistic fuzzy environment, Chen [47] studied dombi weighted aggregating operator under singlevalued neutrosophic environment.
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