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Three-Way Decisions with Intuitionistic Uncertain Linguistic Decision-Theoretic Rough Sets Based on Generalized Maclaurin Symmetric Mean Operators

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Abstract

As a typical model of three-way decisions (3WDs), decision-theoretic rough set (DTRS) has received extensive attention from researchers in the decision-making fields. Intuitionistic uncertain linguistic variables (IULVs) combine the advantages of intuitionistic fuzzy sets (IFSs) and uncertain linguistic variables (ULVs), IULV is more flexible in dealing with uncertain information in decision-making process, and provides a novel means for obtaining loss function (LF) of DTRSs. To get more comprehensive results, a new 3WD model is proposed to solve the multi-attribute group decision-making (MAGDM) problem. First, we gave the LF of DTRSs with IULVs, combined the IULVs and the generalized Maclaurin symmetric mean (GMSM), and proposed the IULGMSM and WIULGMSM operators to aggregate decision information; further, we proposed an intuitionistic uncertain linguistic DTRS model. Then, a method for deducing a new DTRS model is constructed, which can give the corresponding semantic interpretation of the decision results of each alternative. Finally, an example is applied to elaborate the proposed method in detail, and the effects of different conditional probabilities on decision results are discussed.

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), and Shandong Provincial Social Science Planning Project (Nos. 17BGLJ04, 16CGLJ31 and 16CKJJ27).

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Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu & Hongyu Yang

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  1. Peide Liu
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  2. Hongyu Yang
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Correspondence to Peide Liu.

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We declare that we do not have any commercial or associative interests that represent conflicts of interest in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

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Liu, P., Yang, H. Three-Way Decisions with Intuitionistic Uncertain Linguistic Decision-Theoretic Rough Sets Based on Generalized Maclaurin Symmetric Mean Operators. Int. J. Fuzzy Syst. 22, 653–667 (2020). https://doi.org/10.1007/s40815-019-00718-7

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