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Multi-Granularity Probabilistic Rough Fuzzy Sets for Interval-Valued Fuzzy Decision Systems

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Abstract

The probabilistic rough set (PRS) model, through the incorporation of error levels, represents a quantitative extension of the classical rough set model. It serves as a fundamental expansion that enables robust fault tolerance capabilities by employing relative quantitative description. However, when confronted with interval-valued fuzzy data, the PRS model is rendered ineffective. The primary reason for this lies in the absence of a unique equivalence relation in interval-valued decision systems. This paper presents a novel approach to address this limitation. In this paper, we first propose a fuzzy similarity relation based on diversity function, which establishes a viable foundation for constricting models of probabilistic rough fuzzy set and multi-granularity probabilistic rough set models for interval-valued fuzzy decision systems. Then the decision rules are derived from the presented three kinds of multi-granularity probabilistic rough fuzzy sets, respectively. In order to elucidate the concepts of interval-valued probabilistic rough fuzzy sets and multi-granularity probabilistic rough fuzzy sets, a case study is considered, which is helpful for applying these theories to deal with practical issues.

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Acknowledgements

The authors would like to thank the Associate Editor and the reviewers for their insightful comments and suggestions.

Funding

This paper is supported by the National Natural Science Foundation of China (No. 12201518), the China Postdoctoral Science Foundation (No. 2023T160401), the Natural Science Foundation of Chongqing (No. CSTB2023NSCQ-MSX0152), the Science and Technology Research Program of Chongqing Education Commission (Nos. KJQN202300202, KJQN202100205, KJQN202100206).

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Authors and Affiliations

  1. College of Artificial Intelligence, Southwest University, Chongqing, 400715, People’s Republic of China

    Wentao Li

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Tao Zhan

  3. The School of Automation, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Tao Zhan

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  1. Wentao Li
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Correspondence to Tao Zhan.

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Li, W., Zhan, T. Multi-Granularity Probabilistic Rough Fuzzy Sets for Interval-Valued Fuzzy Decision Systems. Int. J. Fuzzy Syst. 25, 3061–3073 (2023). https://doi.org/10.1007/s40815-023-01577-z

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  • DOI: https://doi.org/10.1007/s40815-023-01577-z

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