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Research Paper | Mathematics | Turkey | Volume 3 Issue 6, June 2014

Harmonic Analysis in Fuzzy Systems

Timur Karacay

Abstract: This work introduces methods of harmonic analysis into Fuzzy Systems via the complexification of the system. Let X be a universe; F be a family of fuzzy sets in X. It is shown that X and F generate topological groups G and ; respectively; that are dual to each other. These structures then provide us with powerful mathematical tools of harmonic analysis; enabling us to prove the postulates 0) 0; 0) 1; 1) 1 of boolean logic as well as the introduction of the notions logical dependencies; and the comparisons of propositions.

Keywords: HARMONIC ANALYSIS

Edition: Volume 3 Issue 6, June 2014,

Pages: 1300 - 1306