\((\varepsilon,\delta)\)-Characteristic Fuzzy Sets Approach to the Ideal Theory of \(BCK/BCI\)-Algebras

G. Muhiuddin, Shuaa Aldhafeeri, K. P. Shum

Abstract


The notion of \((\varepsilon,\delta)\)-characteristic fuzzy sets is introduced. Given an ideal \(F\) of a \(BCK/BCI\)-algebra \(X\), conditions for the \((\varepsilon,\delta)\)-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 \((\alpha, \beta)\)-fuzzy ideal \(\mu_F^{(\varepsilon,\delta)}\), conditions for the \(F\) to be an ideal of \(X\) are investigated where \((\alpha, \beta)\) 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


\((\varepsilon,\delta)\)-characteristic fuzzy set; (Fuzzy) ideal; \((\alpha, \beta)\)-fuzzy ideal

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v10i4.1130

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