Harmonic Analysis in Fuzzy Systems
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
How to Cite?: Timur Karacay, "Harmonic Analysis in Fuzzy Systems", Volume 3 Issue 6, June 2014, International Journal of Science and Research (IJSR), Pages: 1300-1306, https://www.ijsr.net/getabstract.php?paperid=2014540, DOI: https://dx.doi.org/10.21275/2014540