Goodness-of-fit test for membership functions with fuzzy data

Pei Chun Lin*, Berlin Wu, Junzo Watada

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)


    Conventionally, we use a chi-square test of homogeneity to determine whether the cell probabilities of a multinomial are equal. However, this process of testing hypotheses is based on the assumption of two-valued logic. If we collect questionnaire data using fuzzy logic, i.e., we record the category data with memberships instead of with a 0-1 type, then the conventional test of goodness-of-fit will not work. In this paper, we present a new method, the fuzzy chi-square test, which will enable us to analyze those fuzzy sample data. The new testing process will efficiently solve the problem for which the category data are not integers. Some related properties of the fuzzy multinomial distribution are also described.

    Original languageEnglish
    Pages (from-to)7437-7450
    Number of pages14
    JournalInternational Journal of Innovative Computing, Information and Control
    Issue number10 B
    Publication statusPublished - 2012 Oct


    • Chi-square test for goodness-of-fit
    • Fuzzy numbers
    • Fuzzy set theory
    • Membership functions
    • Sampling survey

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Information Systems
    • Software
    • Theoretical Computer Science


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