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

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School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, China
2
School of Accounting, Zhejiang University of Finance & Economics, Hangzhou 310018, China
3
School of Business, Central South University, Changsha 410083, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1081; https://doi.org/10.3390/math7111081
Received: 12 October 2019 / Revised: 1 November 2019 / Accepted: 6 November 2019 / Published: 9 November 2019
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 multi-criteria decision-making; single-valued neutrosophic sets; Shapley fuzzy measure; aggregation operators
MDPI and ACS Style

Peng, J.-J.; Tian, C.; Zhang, Z.-Q.; Song, H.-Y.; Wang, J.-Q. Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making. Mathematics 2019, 7, 1081.

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