An objective approach for constructing a membership function based on fuzzy Harvda-Charvat entropy and mathematical programming

Takashi Hasuike, Hideki Katagiri

    Research output: Contribution to journalArticle

    Abstract

    This paper proposes an objective approach to the construction of an appropriate membership function that extends to our previous studies. It is important to set a membership function with subjectivity and objectivity to obtain a reasonable optimal solution that complies with the decision maker's feelings in real-world decision making. To ensure objectivity and subjectivity of the obtained membership function, an entropybased approach based on mathematical programming is integrated into the interval estimation considered by the decision maker. Fuzzy Harvda-Charvat entropy, which is a natural extension of fuzzy Shannon entropy, is introduced as general entropy with fuzziness. The main steps of our proposed approach are to set intervals with membership values 0 and 1 to enable a decision maker to judge confidently, and to solve the proposed mathematical programming problem strictly using nonlinear programming. In this paper, the given membership function is assumed to be a piecewise linear membership function as an approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.

    Original languageEnglish
    Pages (from-to)535-542
    Number of pages8
    JournalJournal of Advanced Computational Intelligence and Intelligent Informatics
    Volume20
    Issue number4
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    Mathematical programming
    Membership functions
    Entropy
    Nonlinear programming
    Decision making

    Keywords

    • Constructing approach with subjectivity and objectivity
    • Fuzzy entropy
    • Mathematical programming
    • Membership function

    ASJC Scopus subject areas

    • Artificial Intelligence
    • Computer Vision and Pattern Recognition
    • Human-Computer Interaction

    Cite this

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    abstract = "This paper proposes an objective approach to the construction of an appropriate membership function that extends to our previous studies. It is important to set a membership function with subjectivity and objectivity to obtain a reasonable optimal solution that complies with the decision maker's feelings in real-world decision making. To ensure objectivity and subjectivity of the obtained membership function, an entropybased approach based on mathematical programming is integrated into the interval estimation considered by the decision maker. Fuzzy Harvda-Charvat entropy, which is a natural extension of fuzzy Shannon entropy, is introduced as general entropy with fuzziness. The main steps of our proposed approach are to set intervals with membership values 0 and 1 to enable a decision maker to judge confidently, and to solve the proposed mathematical programming problem strictly using nonlinear programming. In this paper, the given membership function is assumed to be a piecewise linear membership function as an approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.",
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