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

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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
    School of Accounting, 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)

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.

Suggested Citation

  • Juan-juan Peng & Chao Tian & Zhi-qiang Zhang & Hai-yu Song & Jian-qiang Wang, 2019. "Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1081-:d:285255
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    References listed on IDEAS

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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    2. Juan-juan Peng & Jian-qiang Wang & Jing Wang & Hong-yu Zhang & Xiao-hong Chen, 2016. "Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2342-2358, July.
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