Analytical properties of credibilistic expectation functions

Shuming Wang*, Bo Wang, Junzo Watada

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained.

    Original languageEnglish
    Article number294183
    JournalThe Scientific World Journal
    Publication statusPublished - 2014

    ASJC Scopus subject areas

    • Biochemistry, Genetics and Molecular Biology(all)
    • Environmental Science(all)
    • Medicine(all)


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