\((ε,δ)\)-Characteristic Fuzzy Sets Approach to the Ideal Theory of \(BCK/BCI\)-Algebras (Journal of Informatics and Mathematical Sciences, 2018)
The notion of \((ε,δ)\)-characteristic fuzzy sets is introduced. Given an ideal \(F\) of a \(BCK/BCI\)-algebra \(X\), conditions for the \((ε,δ)\)-characteristic fuzzy set in \(X\) to be an \((\in, \in \! \vee \, {q})\)-fuzzy ideal, an \((\in, {q})\)-fuzzy ideal, an \((\in, \in \! \wedge \, {q})\)-fuzzy ideal, a \((q,q)\)-fuzzy ideal, a \((q, \in)\)-fuzzy ideal, a \((q, \in \! \vee \, {q})\)-fuzzy ideal and a \((q, \in \! \wedge \, {q})\)-fuzzy ideal are provided. Using the notions of \((α, β)\)-fuzzy ideal \(μ_F^{(ε,δ)}\), conditions for the \(F\) to be an ideal of \(X\) are investigated where \((α, β)\) is one of \((\in, \in \! \vee \, {q})\), \((\in, \in \! \wedge \, {q})\), \((\in,q)\), \((q,\in \! \vee\, {q})\), \((q,\in \! \wedge \,{q})\), \((q, \in)\) and \((q, {q})\).
Keywords: \((ε; δ)\)-characteristic fuzzy set; (Fuzzy) ideal; \((α; β)\)-fuzzy ideal