Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Juan-juan Peng, Chao Tian, Zhi-qiang Zhang, Hai-yu Song and Jian-qiang Wang
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Juan-juan Peng: School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, China
Chao Tian: School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, China
Zhi-qiang Zhang: School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, China
Hai-yu Song: School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, China
Jian-qiang Wang: School of Business, Central South University, Changsha 410083, China

Mathematics, 2019, vol. 7, issue 11, 1-27

Abstract: Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

Keywords: multi-criteria decision-making; single-valued neutrosophic sets; Shapley fuzzy measure; aggregation operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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