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

Takashi Hasuike*, Hideki Katagiri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number6
Publication statusPublished - 2017


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

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Artificial Intelligence


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