About: An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In his note (this issue of this journal), Demirci shows that fields with fuzzy equalities have only trivial fuzzy equalities, concludes that Therefore, in case L-algebras contain field structure, all results in [14] are evident from their classical counterparts., and asks a question does there exist any L-algebra with an L-equality different from trivial L-equalities in case the ordinary part of the L-algebra includes two binary operations that define group, ring, module or vector space structure?. In our reply, we show the following. First, by presenting examples of group-based L-algebras with nontrivial L-equalities, we show that the answer to Demircis question is positive. Second, we clarify the meaning of Demircis result and show that it is in fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demircis interpretation of his result is mistaken and that it is not true that all results in [14] are evid In his note (this issue of this journal), Demirci shows that fields with fuzzy equalities have only trivial fuzzy equalities, concludes that Therefore, in case L-algebras contain field structure, all results in [14] are evident from their classical counterparts., and asks a question does there exist any L-algebra with an L-equality different from trivial L-equalities in case the ordinary part of the L-algebra includes two binary operations that define group, ring, module or vector space structure?. In our reply, we show the following. First, by presenting examples of group-based L-algebras with nontrivial L-equalities, we show that the answer to Demircis question is positive. Second, we clarify the meaning of Demircis result and show that it is in fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demircis interpretation of his result is mistaken and that it is not true that all results in [14] are evid (en) Studie problematiky oboru s fuzzi rovností v kontextu L-algeber joko odpověd na Demirciovu otevřenou otázku. (cs)
Title	An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result (en) Odpověď na Demirciovu otevřenou otázku, objasnění výsledku a korekce jeho interpretace výsledků (cs)
skos:prefLabel	An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result (en) Odpověď na Demirciovu otevřenou otázku, objasnění výsledku a korekce jeho interpretace výsledků (cs)
skos:notation	RIV/61989592:15310/06:00002565!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	464762
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/06:00002565
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	fields; fuzzy equalities; L-algebras; Demirci's open question (en)
http://linked.open.../riv/klicoveSlovo	Demirci's open question L-algebras fuzzy equalities fields
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[B06ADA879312]
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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