ON (\epsilon, \epsilon \vee q)-FUZZY IDEALS OF BCI-ALGEBRAS

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.

کلیدواژه ها:

BCI-algebra ، (epsilon ، epsilon vee q)-fuzzy (p- ، q- and a-) ideal ، Fuzzy logic ، Implication operator