About: Theory of Fuzzy Functions and Their Representation

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Attributes	Values
rdf:type	http://linked.opendata.cz/ontology/domain/vavai/Projekt
rdfs:seeAlso	http://www.isvav.cz/projectDetail.do?rowId=IAA1187301
Description	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) Předpokládáme vývoj teorie fuzzy funcí, která bude založena na moderních logických a algebraických základech. Jako prototyp vezmeme teorii zobecněných funkcí a rozšíříme ji o to, co souvisí s výběrem základní algebry. Naše konstrukce bude založena na BL-algebře operací známé jako algebra spojitých T-norem. Předpokládáme řešení následujících problémů: -Charakterizace univerza extenzionálních fuzzy množin jako BL-algebry a jako topologického prostoru, - Zavedení sup-homomorfismů mezi univerzy extenzionálních fuzzy množin jako fuzzy funkcí. Algebraické operace na fuzzy funkcí. - Reprezentace fuzzy funkcí formulemi. - Fuzzy funkce jako řešení systémů rovnic s fuzzy relacemi. - Fuzzy funkce jako speciální zobecněné funkce. Aproximační modely na základě speciálních zobecněných funkcí a jejich použití v numerických metodách.
Title	Theory of Fuzzy Functions and Their Representation (en) Teorie fuzzy funkcí a jejich reprezentace
skos:notation	IAA1187301
http://linked.open...avai/cep/aktivita	Grants of distinctly investigative character focused on the sphere of research pursued at present particularly in the Academy of Sciences of the Czech Republic
http://linked.open...kovaStatniPodpora	http://linked.opendata.cz/resource/domain/vavai/projekt/IAA1187301/celkovaStatniPodpora
http://linked.open...ep/celkoveNaklady	http://linked.opendata.cz/resource/domain/vavai/projekt/IAA1187301/celkoveNaklady
http://linked.open...datumDodatniDoRIV	2007-09-26 (xsd:date)
http://linked.open...i/cep/druhSouteze	VS - Veřejná soutěž ve výzkumu a vývoji
http://linked.open...ep/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open.../cep/fazeProjektu	33613055
http://linked.open...ai/cep/hlavniObor	BA - Obecná matematika
http://linked.open...hodnoceniProjektu	U - Uspěl podle zadání, tj. byly splněny cíle a jeho předpokládané výsledky uvedené ve smlouvě / rozhodnutí o poskytnutí podpory
http://linked.open...vai/cep/kategorie	ZV - Základní výzkum
http://linked.open.../cep/klicovaSlova	fuzzy function; generalized function; fuzzy relation; fuzzy equality; extensional function; extensional fuzzy set; solvability of fuzzy relation equations; BL-algebra of functions (en)
http://linked.open...ep/partnetrHlavni	Přírodovědecká fakulta
http://linked.open...inujicichPrijemcu	0 (xsd:int)
http://linked.open...cep/pocetPrijemcu	1 (xsd:int)
http://linked.open...ocetSpoluPrijemcu	0 (xsd:int)
http://linked.open.../pocetVysledkuRIV	42 (xsd:int)
http://linked.open...enychVysledkuVRIV	42 (xsd:int)
http://linked.open...okUkonceniPodpory	2005
http://linked.open...okZahajeniPodpory	2003
http://linked.open...iciPoslednihoRoku	2006
http://linked.open...atUdajeProjZameru	2006
http://linked.open.../vavai/cep/soutez	SAV02003-A
http://linked.open...usZobrazovaneFaze	DUU
http://linked.open...ai/cep/typPojektu	P - Projekt výzkumu a vývoje financovaný ze státního rozpočtu
http://linked.open...jektu+dodavatelem	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) Rozvíjeli jsme teorii fuzzy funkcí a jejich reprezentaci pomocí formulí. Navrhovali jsme zobecnělé normální formy, nový způsob reprezentace fuzzy funkce pomocí fuzzy relace a operace kompozice a teorii fuzzy transformace. (cs)
http://linked.open...tniCyklusProjektu	ZBKU
http://linked.open.../cep/klicoveSlovo	fuzzy function extensional function extensional fuzzy set fuzzy equality fuzzy relation generalized function solvability of fuzzy relation equations
is http://linked.open...vavai/riv/projekt of	Fuzzy function as an approximate solution to a system of fuzzy relation equations Fuzzy Transforms and Their Application on Heat Flow Equation Fuzzy Transforms Fuzzy Transforms and Their Applications to Wave Equation Generalized extensionality of fuzzy relations Lipschitz Continuity and Extensionality of Functions Represented by BL-algebra Formulas Fuzzy Transforms and Universal Approximation Extensionality and Continuity Fuzzy Transform: Application to Reef Growth Problem Fuzzy Transformation and Its Applications in A/D Converter Fuzzy Transforms for Functions with Two Variables Normal Forms for Fuzzy Relations and their Contribution to Universal Approximation New Criteria of Solvability of a System of Fuzzy Relation Equations Normal forms for fuzzy logic functions Normal Forms for Fuzzy Logic Functions Normal Forms in BL-algebra of functions and their contribution to universal approximation Normal forms in BL and LP algebras of functions Fuzzy Transforms: Theory and Applications Functional system of BL-algebra with infinite formulas Completing Fuzzy If-then Rule Bases by Means of Smoothing Splines Fuzzy Transform as an Additive Normal Form Generating a Fuzzy Rule Base with an Additive Interpretation System of fuzzy relation equations as a continuous model of if-then rules Algebraic Analysis of Fuzzy Systems System of fuzzy relation equations with dual compositiona: solvability and solutions Approximation of Fuzzy Functions by Extended Fuzzy Transforms Fuzzy Transforms in Removing Noise Numerical Solution of Partial Differential Equations with Help of Fuzzy Transform System of fuzzy relation equations with dual compositions: solvability and solutions Safe Modeling of Fuzzy If--Then Rules Generic View On Continuous T-Norms and T-Conorms System of fuzzy relation equations with dual composition: solvability and solutions Approximating models based on fuzzy transforms Solvability and Approximate Solvability of Fuzzy Relation Equations Solvability of a System of Fuzzy Relation Equations: Easy to Check Conditions Solvability of a System of Fuzzy Relation Equations: Easy to Check Conditions Functions Represented by BL-Algebra Formulas: Characterization and Approximate Representation Genetic Algorithms in Fuzzy Approximation Generating a fuzzy rule base with an additive interpretation Representation of Fuzzy Logic Functions by Normal Forms Characterization and approximate representation of extensional fuzzy relations Numerical Solution of Partial Differential Equations with Help of Fuzzy Transform
is http://linked.open...vavai/cep/projekt of	http://linked.opendata.cz/resource/domain/vavai/cep/ucast/IAA1187301/2003/orjk%3A17310 http://linked.opendata.cz/resource/domain/vavai/cep/ucast/IAA1187301/2004/orjk%3A17310 http://linked.opendata.cz/resource/domain/vavai/cep/ucast/IAA1187301/2005/orjk%3A17310 http://linked.opendata.cz/resource/domain/vavai/cep/ucast/IAA1187301/2006/orjk%3A17310 http://linked.opendata.cz/resource/domain/vavai/cep/ucast/IAA1187301/2007/orjk%3A17310

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