Title :
Fuzzy systems approximation by frames-SISO case
Author :
Shmilovici, Armin ; Maimon, Oded Z.
Author_Institution :
Dept. of Ind. Eng., Tel Aviv Univ., Israel
Abstract :
In this paper, the approximation problem of SISO fuzzy systems by frames is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basis functions (FBF), we first discuss the mathematical theory of frames in a Hilbert space, and then the conditions under which a FBF is a valid frame. Fuzzy membership functions which constitute a valid frame can universally approximate any continuous function. The triangular membership function is demonstrated as such, and it´s approximation properties are discussed
Keywords :
Hilbert spaces; approximation theory; frame based representation; fuzzy systems; Hilbert space; SISO fuzzy systems; frames; fuzzy basis functions; fuzzy membership functions; fuzzy systems approximation; triangular membership function; Computer aided software engineering; Function approximation; Fuzzy control; Fuzzy sets; Fuzzy systems; Hilbert space; Industrial engineering; Neural networks; Pulp manufacturing; Shape;
Conference_Titel :
Fuzzy Systems, 1995. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium., Proceedings of 1995 IEEE Int
Conference_Location :
Yokohama
Print_ISBN :
0-7803-2461-7
DOI :
10.1109/FUZZY.1995.409961
