About: Algebras with fuzzy equalities

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ~, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ~. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic and have been studied from this point of view before. On the other hand, they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones. The present paper aims at developing fundamental points of algebras with fuzzy equalities: we introduce the notion of an algebra with fuzzy equality, present natural examples, compare the notion with other approaches, and introduce and develop basic structural notions (subalgebras, morphisms, products, direct unions). In a follow-up paper [30], we deal with advanced topics in algebras with fuzzy eq An algebra with fuzzy equality is a set with operations on it that is equipped with similarity ~, i.e. a fuzzy equivalence relation, such that each operation f is compatible with ~. Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic and have been studied from this point of view before. On the other hand, they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones. The present paper aims at developing fundamental points of algebras with fuzzy equalities: we introduce the notion of an algebra with fuzzy equality, present natural examples, compare the notion with other approaches, and introduce and develop basic structural notions (subalgebras, morphisms, products, direct unions). In a follow-up paper [30], we deal with advanced topics in algebras with fuzzy eq (en) Studie algeber s fuzzy rovnostmi. (cs)
Title	Algebras with fuzzy equalities Algebras with fuzzy equalities (en) Algebry s fuzzy rovnostmi (cs)
skos:prefLabel	Algebras with fuzzy equalities Algebras with fuzzy equalities (en) Algebry s fuzzy rovnostmi (cs)
skos:notation	RIV/61989592:15310/06:00002564!RIV07-AV0-15310___
http://linked.open.../vavai/riv/strany	205-211
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(KJB1137301), Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2007
http://linked.open...aciTvurceVysledku	Vychodil, Vilém Bělohlávek, Radim
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	464566
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/06:00002564
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	algebra; fuzzy equality (en)
http://linked.open.../riv/klicoveSlovo	fuzzy equality algebra
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[66D4F97DB41E]
http://linked.open...i/riv/nazevZdroje	Fuzzy Sets and Systems
http://linked.open...in/vavai/riv/obor	BD
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Relational systems in presence of vagueness and uncertainty:mathematical foundations for applications
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	157
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim Vychodil, Vilém
http://linked.open...n/vavai/riv/zamer	Matematické modely a struktury
issn	0165-0114
number of pages	7 (xsd:int)
http://localhost/t...ganizacniJednotka	15310

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