An objective formulation of membership function based on fuzzy entropy and pairwise comparison

Takashi Hasuike, Hideki Katagiri

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    This paper proposes a mathematical programming approach to construct an appropriate membership function extending our previous studies. It is important to set a membership function with both subjectivity and objectivity to obtain a reasonable optimal solution based on decision maker's feelings in real-world decision making. In order to ensure objectivity of obtained membership function as well as subjectivity, an entropy-based approach based on mathematical programming is integrated into interval estimation considered by the decision maker. As a general entropy with fuzziness, fuzzy Harvda-Charvat entropy is introduced, which is a natural extension of fuzzy Shannon entropy. In addition, qualitative and subjective evaluations based on the pairwise comparison are introduced to represent the differences between two membership values. The main step of our revised approach is 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 approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.

    Original languageEnglish
    Pages (from-to)4443-4452
    Number of pages10
    JournalJournal of Intelligent and Fuzzy Systems
    Volume32
    Issue number6
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Harvda-Charvat entropy
    • mathematical programming
    • Membership function
    • scale for measuring

    ASJC Scopus subject areas

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

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