ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
نویسندگان
1 Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
2 Department of Mathematics, Yazd University, Yazd, Iran.
3 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province,445000, P. R. China
doi
10.22111/ijfs.2009.222چکیده
The aim of this paper is to introduce the notions of ($\epsilon, \epsilon \vee q$)-fuzzy p-ideals, ($\epsilon, \epsilon \vee q$)-fuzzy q-ideals and ($\epsilon, \epsilon \vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras is discussed. It is shownthat a fuzzy set of a BCI-algebra is an ($\epsilon, \epsilon \vee q$)-fuzzy a-ideal if and only if itis both an ($\epsilon, \epsilon \vee q$)-fuzzy p-ideal and an ($\epsilon, \epsilon \vee q$)-fuzzy q-ideal. Finally, the concept of implication-based fuzzy a-ideals in BCI-algebras is introduced and,in particular, the implication operators in Lukasiewicz system of continuousvaluedlogic are discussed.
