Odpověď na Demirciho otevřené otázky, objasnění jeho výsledků a oprava jeho interpretace dosažených výsledků

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F06%3A00003268" target="_blank" >RIV/61989592:15310/06:00003268 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989592:15310/06:00002565

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 [1-4] 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 Demirci's question is positive. Second, we clarify the meaning of Demirci's result and show that it isin fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demirci's interpretation of his result is mistaken and that it is

Název v anglickém jazyce

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

Popis výsledku anglicky

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 [1-4] 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 Demirci's question is positive. Second, we clarify the meaning of Demirci's result and show that it isin fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demirci's interpretation of his result is mistaken and that it is

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

<a href="/cs/project/KJB1137301" target="_blank" >KJB1137301: Relační systémy v podmínkách vágnosti a nejistoty:matematické základy pro aplikace</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2006

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

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Svazek periodika

157

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

205-211

Kód UT WoS článku

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EID výsledku v databázi Scopus

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