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Intuitionistic fuzzy reducible weighted Maclaurin symmetric means and their application in multiple-attribute decision making

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Abstract

As an important information aggregation tool, the Maclaurin symmetric mean (MSM) can capture the correlation between multiple input values and has recently become a hot topic in the field of academic research. Due to the importance of the fact that attribute variables are often different, many weighted MSMs have been designed to deal with various fuzzy information aggregation problems. However, these weighted form operators do not have the properties of idempotency, i.e., the weighted average value of equivalent fuzzy numbers varies with their weights. In addition, when their weights are equal, the weighted MSMs cannot reduce to the MSM, which means they do not have reducibility. To solve these problems, in this paper, we introduce the reducible weighted MSM (RWMSM) and the reducible weighted dual MSM (RWDMSM), and we extend them to aggregate intuitionistic fuzzy information. In order to better analyze and understand the operation mechanism of the proposed weighted MSMs, we discuss several advantageous properties and special related cases of the proposed weighted MSMs. The other objective of this paper is to investigate the practice application of the proposed weighted MSMs in decision making under conditions of an intuitionistic fuzzy environment. A case study shows that the decision-making method based on the intuitionistic fuzzy RWMSM and RWDMSM can flexibly capture the correlation and reflect the decision maker’s risk preference.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11171221), the Major Project of Anhui Educational Committee (Grant Nos. KJ2016A742, SK2016A0971, the Natural Science Foundation of Anhui Province (Grant No. 1808085MG224), Key discipline construction projects of West Anhui University (Grant No. 0060201131406), Professional degree key construction projects of West Anhui University (Grant No. 0044617001).

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Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, Shanghai, China

    Minghua Shi & Qingxian Xiao

  2. College of Finance and Mathematics, West Anhui University, Lu’an, Anhui, China

    Minghua Shi

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  1. Minghua Shi
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  2. Qingxian Xiao
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Correspondence to Minghua Shi.

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Shi, M., Xiao, Q. Intuitionistic fuzzy reducible weighted Maclaurin symmetric means and their application in multiple-attribute decision making. Soft Comput 23, 10029–10043 (2019). https://doi.org/10.1007/s00500-018-3558-2

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