T-norm-based limit theorems for fuzzy random variables

S. Wang*, J. Watada

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    The objective of this paper is to derive some limit theorems of fuzzy random variables under the extension principle associated with continuous Archimedean triangular norms (t-norms). First of all, some convergence theorems for the sum of fuzzy random variables in chance measure and expected value are proved respectively based on the arithmetics of continuous Archimedean triangular norms. Then, a law of large numbers for fuzzy random variables is established by using the obtained convergence theorems. The results of the derived law of large numbers can degenerate to the strong laws of large numbers for random variables and fuzzy variables, respectively.

    Original languageEnglish
    Pages (from-to)233-242
    Number of pages10
    JournalJournal of Intelligent and Fuzzy Systems
    Issue number4
    Publication statusPublished - 2010


    • Archimedean t-norm
    • Fuzzy random variable
    • Law of large numbers
    • Limit theorem

    ASJC Scopus subject areas

    • Artificial Intelligence
    • Engineering(all)
    • Statistics and Probability


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