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

Takashi Hasuike, Hideki Katagiri, Hiroe Tsubaki

Research output: Contribution to journalConference articlepeer-review

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
Pages (from-to)994-1003
Number of pages10
JournalProcedia Computer Science
Volume60
Issue number1
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

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)

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