Building confidence-interval-based fuzzy random regression models

Junzo Watada, Shuming Wang, Witold Pedrycz

    Research output: Contribution to journalArticle

    73 Citations (Scopus)

    Abstract

    In real-world regression analysis, statistical data may be linguistically imprecise or vague. Given the co-existence of stochastic and fuzzy uncertainty, real data cannot be characterized by using only the formalism of random variables. In order to address regression problems in the presence of such hybrid uncertain data, fuzzy random variables are introduced in this study to serve as an integral component of regression models. A new class of fuzzy regression models that is based on fuzzy random data is built, and is called the confidence-interval-based fuzzy random regression model (CI-FRRM). First, a general fuzzy regression model for fuzzy random data is introduced. Then, using expectations and variances of fuzzy random variables, σ-confidence intervals are constructed for fuzzy random inputoutput data. The CI-FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers. Since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process, the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming. Therefore, we resort to some heuristics. Finally, an illustrative example is provided.

    Original languageEnglish
    Article number5173567
    Pages (from-to)1273-1283
    Number of pages11
    JournalIEEE Transactions on Fuzzy Systems
    Volume17
    Issue number6
    DOIs
    Publication statusPublished - 2009 Dec

    Keywords

    • Confidence interval
    • Expected value
    • Fuzzy random variable
    • Fuzzy regression model
    • Variance

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Artificial Intelligence
    • Computational Theory and Mathematics
    • Applied Mathematics

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