Center-of-gravity fuzzy systems based on normal fuzzy implications

  • Authors:

  • Xue-hai Yuan;Zeng-liang Liu;E. Stanley Lee

  • Affiliations:

  • Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;Institute of Information Operation, National Defence University of PLA, Beijing 100091, China;Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506, USA

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2011

Quantified Score

Hi-index 0.09

Visualization

Abstract

In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for the output fuzzy set are proposed. Then, by using this method and this concept of an adaptive universe, SISO fuzzy systems based on center-of-gravity defuzzifier and normal implications such as the Kleene-Dienes implication or the Lukasiewicz implication are constructed. The constructed fuzzy systems have the general form S@?(x)=A"i^*(x)f(x"i)+A"i"+"1^*(x)f(x"i"+"1), with A"i^*(x)+A"i"+"1^*(x)=1, and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given.