Constructing membership function based on fuzzy shannon entropy and human's interval estimation

Takashi Hasuike, Hideki Katagiri, Hiroe Tsubaki, Hiroshi Tsuda

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

5 Citations (Scopus)

Abstract

This paper develops a new constructing approach of an appropriate membership function to integrate a given probability density function and fuzzy Shannon entropy extending the statistical theory into the heuristic method based on the human cognitive behavior and subjectivity. The proposed approach is formulated as a more general mathematical programming problem than previous approaches due to using a general S-curve function and the fuzzy Shannon entropy. Then, performing deterministic equivalent transformations to the initial problem, the optimal condition of parameters is obtained. Furthermore, in order to show the appropriate membership function using the proposed approach, some probability density functions are provided as numerical examples.

Original languageEnglish
Title of host publication2012 IEEE International Conference on Fuzzy Systems, FUZZ 2012
DOIs
Publication statusPublished - 2012 Oct 23
Externally publishedYes
Event2012 IEEE International Conference on Fuzzy Systems, FUZZ 2012 - Brisbane, QLD, Australia
Duration: 2012 Jun 102012 Jun 15

Publication series

NameIEEE International Conference on Fuzzy Systems
ISSN (Print)1098-7584

Other

Other2012 IEEE International Conference on Fuzzy Systems, FUZZ 2012
CountryAustralia
CityBrisbane, QLD
Period12/6/1012/6/15

Keywords

  • S-curve function
  • constructing membership function
  • fuzzy entropy
  • mathematical programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

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  • Cite this

    Hasuike, T., Katagiri, H., Tsubaki, H., & Tsuda, H. (2012). Constructing membership function based on fuzzy shannon entropy and human's interval estimation. In 2012 IEEE International Conference on Fuzzy Systems, FUZZ 2012 [6251199] (IEEE International Conference on Fuzzy Systems). https://doi.org/10.1109/FUZZ-IEEE.2012.6251199