6. Development of Membership Functions

  1. Timothy J. Ross

Published Online: 27 DEC 2010

DOI: 10.1002/9781119994374.ch6

Fuzzy Logic with Engineering Applications, Third Edition

Fuzzy Logic with Engineering Applications, Third Edition

How to Cite

Ross, T. J. (2010) Development of Membership Functions, in Fuzzy Logic with Engineering Applications, Third Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994374.ch6

Author Information

  1. University of New Mexico, USA

Publication History

  1. Published Online: 27 DEC 2010
  2. Published Print: 15 JAN 2010

ISBN Information

Print ISBN: 9780470743768

Online ISBN: 9781119994374

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Keywords:

  • genetic algorithms;
  • inductive reasoning;
  • inference;
  • intuition;
  • membership function development;
  • neural network;
  • rank ordering

Summary

This chapter describes a few procedures to develop these membership functions based on deductive intuition or numerical data. Since the membership function essentially embodies all fuzziness for a particular fuzzy set, its description is the essence of a fuzzy property or operation. The chapter also describes six procedures that have been used to build membership functions. The following is a list of six straightforward methods described in the literature to assign membership values or functions to fuzzy variables. The six methods are: intuition, inference, rank ordering, neural networks, genetic algorithms, and inductive reasoning. The chapter illustrates each of these methods illustrated in simple examples. Intuition involves contextual and semantic knowledge about an issue; it can also involve linguistic truth values about this knowledge. In the inference method the author uses knowledge to perform deductive reasoning. The chapter explains how a neural network can be used to determine membership functions.

Controlled Vocabulary Terms

ART neural nets; genetic algorithms; inference mechanisms