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Inequalities and Convergence Concepts of Fuzzy and Rough Variables

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Abstract

It is well-known that Markov inequality, Chebyshev inequality, Hölder's inequality, and Minkowski inequality are important and useful results in probability theory. This paper presents the analogous inequalities in fuzzy set theory and rough set theory. In addition, sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper presents four types of convergence concept of fuzzy/rough sequence: convergence almost surely, convergence in credibility/trust, convergence in mean, and convergence in distribution. Some mathematical properties of those new convergence concepts are also given.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Baoding Liu

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  1. Baoding Liu
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Liu, B. Inequalities and Convergence Concepts of Fuzzy and Rough Variables. Fuzzy Optimization and Decision Making 2, 87–100 (2003). https://doi.org/10.1023/A:1023491000011

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  • DOI: https://doi.org/10.1023/A:1023491000011

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