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Computation of generalized linguistic term sets based on fuzzy logical algebras for multi-attribute decision making

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Abstract

Computational models of various linguistic term sets whose evaluation scales are the identity functions have been extensively investigated. Among these models, although the virtual linguistic model is the most straightforward and convenient for the calculations, the operations are not closed on the given scales. In this paper, we develop the fuzzy logical algebras-based virtual linguistic model. We propose the generalized linguistic term sets based on general strictly increasing functions with the existing linguistic term sets as special cases, and define some novel operational laws and measures such as similarity measures, distance measures and entropy measures for them. Then we provide some linguistic aggregation operators for the generalized linguistic term sets in multi-attribute decision making. Particularly, when these operators are reduced to the existing ones, it is shown that the proposed operational laws can be considered as a modification of the existing ones in related literature. Based on the proposed operators, a multi-attribute decision-making model is built, and a method for determining the objective–subjective weight vector in generalized linguistic term sets are put forward. Finally, an illustrative example is presented for verifying our models and methods and a comparative analysis with the existing methods is made.

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Acknowledgements

The authors are very grateful to the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This research was supported by the Natural Science Foundation of Shandong Province (no. ZR2017MG027) and the AMEP (DYSP) of Linyi University (no. LYDX2014BS017).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276005, China

    Zhen Ming Ma

  2. Business School, Sichuan University, Chengdu, 610064, China

    Ze Shui Xu

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  1. Zhen Ming Ma
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  2. Ze Shui Xu
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Correspondence to Ze Shui Xu.

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Ma, Z.M., Xu, Z.S. Computation of generalized linguistic term sets based on fuzzy logical algebras for multi-attribute decision making. Granul. Comput. 5, 17–28 (2020). https://doi.org/10.1007/s41066-019-00199-x

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