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

Pei Chun Lin, Berlin Wu, Junzo Watada

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    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
    Volume8
    Issue number10 B
    Publication statusPublished - 2012 Oct

    Fingerprint

    Fuzzy Data
    Goodness of Fit Test
    Membership functions
    Membership Function
    Chi-squared test
    Testing
    Fuzzy logic
    Test of Homogeneity
    Multinomial Distribution
    Testing Hypotheses
    Goodness of fit
    Questionnaire
    Fuzzy Logic
    Logic
    Integer
    Cell

    Keywords

    • 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

    Cite this

    Goodness-of-fit test for membership functions with fuzzy data. / Lin, Pei Chun; Wu, Berlin; Watada, Junzo.

    In: International Journal of Innovative Computing, Information and Control, Vol. 8, No. 10 B, 10.2012, p. 7437-7450.

    Research output: Contribution to journalArticle

    Lin, Pei Chun ; Wu, Berlin ; Watada, Junzo. / Goodness-of-fit test for membership functions with fuzzy data. In: International Journal of Innovative Computing, Information and Control. 2012 ; Vol. 8, No. 10 B. pp. 7437-7450.
    @article{480205cd315e4035bd5c0c80f0610b2a,
    title = "Goodness-of-fit test for membership functions with fuzzy data",
    abstract = "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.",
    keywords = "Chi-square test for goodness-of-fit, Fuzzy numbers, Fuzzy set theory, Membership functions, Sampling survey",
    author = "Lin, {Pei Chun} and Berlin Wu and Junzo Watada",
    year = "2012",
    month = "10",
    language = "English",
    volume = "8",
    pages = "7437--7450",
    journal = "International Journal of Innovative Computing, Information and Control",
    issn = "1349-4198",
    publisher = "IJICIC Editorial Office",
    number = "10 B",

    }

    TY - JOUR

    T1 - Goodness-of-fit test for membership functions with fuzzy data

    AU - Lin, Pei Chun

    AU - Wu, Berlin

    AU - Watada, Junzo

    PY - 2012/10

    Y1 - 2012/10

    N2 - 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.

    AB - 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.

    KW - Chi-square test for goodness-of-fit

    KW - Fuzzy numbers

    KW - Fuzzy set theory

    KW - Membership functions

    KW - Sampling survey

    UR - http://www.scopus.com/inward/record.url?scp=84866037397&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84866037397&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:84866037397

    VL - 8

    SP - 7437

    EP - 7450

    JO - International Journal of Innovative Computing, Information and Control

    JF - International Journal of Innovative Computing, Information and Control

    SN - 1349-4198

    IS - 10 B

    ER -