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

Takashi Hasuike*, Hideki Katagiri

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)4443-4452
ページ数10
ジャーナルJournal of Intelligent and Fuzzy Systems
32
6
DOI
出版ステータスPublished - 2017

ASJC Scopus subject areas

  • 統計学および確率
  • 工学(全般)
  • 人工知能

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