Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

• Published in: International journal of computational intelligence systems Vol. 8; no. 2; pp. 345 - 363
• Main Authors: Peng, Juan-juan, Wang, Jian-qiang, Wu, Xiao-hui, Wang, Jing, Chen, Xiao-hong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2015; Springer Nature B.V; Springer
• Subjects: Agglomeration; Decision making; Fuzzy sets; Multi-criteria group decision-making; multi-valued neutrosophic sets; Multiple criterion; Operators; power aggregation operators; Research Article; Multi-criteria group decision-making; multi-valued neutrosophic sets; power aggregation operators
• ISSN: 1875-6891; 1875-6883; 1875-6883
• DOI: 10.1080/18756891.2015.1001957

In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy-membership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov’s intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggregation operators, and an example is provided to illustrate the application of the proposed method, together with a comparison analysis.