A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory

Takashi Hasuike, Hideki Katagiri, Hiroe Tsubaki

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    8 Citations (Scopus)

    Abstract

    This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

    Original languageEnglish
    Title of host publicationProcedia Computer Science
    PublisherElsevier
    Pages994-1003
    Number of pages10
    Volume60
    Edition1
    DOIs
    Publication statusPublished - 2015
    Event19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015 - , Singapore
    Duration: 2015 Sep 72015 Sep 9

    Other

    Other19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015
    CountrySingapore
    Period15/9/715/9/9

    Fingerprint

    Information theory
    Nonlinear programming
    Membership functions
    Statistics
    Heuristic methods
    Mathematical programming
    Probability density function
    Entropy
    Decision making

    Keywords

    • Fuzzy entropy
    • Mathematical programming
    • Membership function
    • Smoothing function

    ASJC Scopus subject areas

    • Computer Science(all)

    Cite this

    A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory. / Hasuike, Takashi; Katagiri, Hideki; Tsubaki, Hiroe.

    Procedia Computer Science. Vol. 60 1. ed. Elsevier, 2015. p. 994-1003.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hasuike, T, Katagiri, H & Tsubaki, H 2015, A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory. in Procedia Computer Science. 1 edn, vol. 60, Elsevier, pp. 994-1003, 19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015, Singapore, 15/9/7. https://doi.org/10.1016/j.procs.2015.08.140
    Hasuike, Takashi ; Katagiri, Hideki ; Tsubaki, Hiroe. / A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory. Procedia Computer Science. Vol. 60 1. ed. Elsevier, 2015. pp. 994-1003
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