. " solvability of fuzzy relation equations" . "We have developed the theory of fuzzy functions, considered their representations by formulas. We considered generalized normal forms, a new representation of a fuzzy function using a fuzzy relation and composition, and the theory of fuzzy transforms."@en . " extensional fuzzy set" . "Rozv\u00EDjeli jsme teorii fuzzy funkc\u00ED a jejich reprezentaci pomoc\u00ED formul\u00ED. Navrhovali jsme zobecn\u011Bl\u00E9 norm\u00E1ln\u00ED formy, nov\u00FD zp\u016Fsob reprezentace fuzzy funkce pomoc\u00ED fuzzy relace a operace kompozice a teorii fuzzy transformace."@cs . " fuzzy relation" . . "A theory of fuzzy functions is supposed to be developed. It will be based on the well estabilished logical and algebraic backrounds have been created till now. We will take as a prototype the theory of generalized functions and extend it in ehat concerns a choice of a basic algebra. Our construction will be based on a BL-algebra of operations know as the algebra of continuous t-norms. The following problems are supposed to be solved: - Characterization of the universe of extensional fuzzy sets as a BL-algebra and as a topological space. - Introduction of sup-homomorphisms between universes of extensional fuzzy sets as fuzzy functions. Algebraic operations over fuzzy functions. - Representation of fuzzy functions by formulas. - Fuzzy functions as solutions to system of fuzzy relation equations. Fuzzy functions as special generalized functions. Approximation models on the basis of special generalised functions and their utilization in numerical methods."@en . . " extensional function" . . . . . . "1"^^ . . . "0"^^ . . "0"^^ . . . . "Theory of Fuzzy Functions and Their Representation"@en . " fuzzy equality" . "P\u0159edpokl\u00E1d\u00E1me v\u00FDvoj teorie fuzzy func\u00ED, kter\u00E1 bude zalo\u017Eena na modern\u00EDch logick\u00FDch a algebraick\u00FDch z\u00E1kladech. Jako prototyp vezmeme teorii zobecn\u011Bn\u00FDch funkc\u00ED a roz\u0161\u00ED\u0159\u00EDme ji o to, co souvis\u00ED s v\u00FDb\u011Brem z\u00E1kladn\u00ED algebry. Na\u0161e konstrukce bude zalo\u017Eena na BL-algeb\u0159e operac\u00ED zn\u00E1m\u00E9 jako algebra spojit\u00FDch T-norem. P\u0159edpokl\u00E1d\u00E1me \u0159e\u0161en\u00ED n\u00E1sleduj\u00EDc\u00EDch probl\u00E9m\u016F: -Charakterizace univerza extenzion\u00E1ln\u00EDch fuzzy mno\u017Ein jako BL-algebry a jako topologick\u00E9ho prostoru, - Zaveden\u00ED sup-homomorfism\u016F mezi univerzy extenzion\u00E1ln\u00EDch fuzzy mno\u017Ein jako fuzzy funkc\u00ED. Algebraick\u00E9 operace na fuzzy funkc\u00ED. - Reprezentace fuzzy funkc\u00ED formulemi. - Fuzzy funkce jako \u0159e\u0161en\u00ED syst\u00E9m\u016F rovnic s fuzzy relacemi. - Fuzzy funkce jako speci\u00E1ln\u00ED zobecn\u011Bn\u00E9 funkce. Aproxima\u010Dn\u00ED modely na z\u00E1klad\u011B speci\u00E1ln\u00EDch zobecn\u011Bn\u00FDch funkc\u00ED a jejich pou\u017Eit\u00ED v numerick\u00FDch metod\u00E1ch." . . . . . "Teorie fuzzy funkc\u00ED a jejich reprezentace" . " generalized function" . "IAA1187301" . "fuzzy function" . . "2007-09-26+02:00"^^ . "fuzzy function; generalized function; fuzzy relation; fuzzy equality; extensional function; extensional fuzzy set; solvability of fuzzy relation equations; BL-algebra of functions"@en . "42"^^ . "http://www.isvav.cz/projectDetail.do?rowId=IAA1187301"^^ . "42"^^ .