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A model of three-way approximation of intuitionistic fuzzy sets

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Abstract

A three-way approximation of a fuzzy set, as a generalization of the core and the support of the fuzzy set, provides a generalized qualitatively interpretation of a fuzzy set. An intuitionistic fuzzy set (IFS) generalizes a fuzzy set by using jointly a membership function and a nonmembership function. In this paper, we present a model for constructing a three-way approximation of an IFS according to the TAO (trisecting-acting-outcome) framework of three-way decision (3WD). Given an IFS, we use its membership and nonmembership functions as a pair of evaluations to trisect a universe of objects to produce a three-way approximation of the IFS. We present a general optimization model for determining the required parameters according to the principle of the minimum cost with respect to a distance function and costs of three actions. We use Manhattan distance to illustrate the basic ideas of the optimization model.

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Acknowledgements

The authors thank reviewers for their valuable comments and constructive suggestions. This work was supported in part by the China Scholarship Council (No. 201808515107), the National Natural Science Foundation of China (No. 61673285), Sichuan Science and Technology program of China (2021YJ0085, 2019YJ0529), and a Discovery Grant from NSERC, Canada.

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Authors and Affiliations

  1. Department of Computer Science, Sichuan Normal University, Chengdu, 610101, China

    Jilin Yang

  2. Department of Computer Science, University of Regina, Regina, S4S 0A2, Canada

    Yiyu Yao

  3. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, China

    Xianyong Zhang

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  1. Jilin Yang
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  2. Yiyu Yao
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  3. Xianyong Zhang
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Correspondence to Jilin Yang.

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Yang, J., Yao, Y. & Zhang, X. A model of three-way approximation of intuitionistic fuzzy sets. Int. J. Mach. Learn. & Cyber. 13, 163–174 (2022). https://doi.org/10.1007/s13042-021-01380-y

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