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Membership functions and operational law of uncertain sets

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Abstract

Uncertain set is a set-valued function on an uncertainty space, and attempts to model “unsharp concepts” that are essentially sets but their boundaries are not sharply described. This paper will propose a concept of membership function and define the independence of uncertain sets. This paper will also present an operational law of uncertain sets via membership functions or inverse membership functions. Finally, the linearity of expected value operator is verified.

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Authors and Affiliations

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

    Baoding Liu

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  1. Baoding Liu
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Correspondence to Baoding Liu.

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Liu, B. Membership functions and operational law of uncertain sets. Fuzzy Optim Decis Making 11, 387–410 (2012). https://doi.org/10.1007/s10700-012-9128-7

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  • DOI: https://doi.org/10.1007/s10700-012-9128-7

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