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Soft ideals of BCK/BCI-algebras based on fuzzy set theory. (English) Zbl 1245.06034

Summary: Characterizations of a \((\overline\in,\overline\in\vee\overline q)\)-fuzzy subalgebra (ideal) are considered. Given an \(\in\)-soft set, an \((\overline\in,\overline\in\vee\overline q)\)-fuzzy subalgebra is established. Using the notion of \((t,s)\)-fuzzy subalgebras, characterizations for an \(\in\)-soft set to be an (idealistic) soft BCK/BCI-algebra are provided. Using the notion of fuzzy \(p\)-ideals, a characterization of an \(\in\)-soft set to be a \(p\)-idealistic soft BCI-algebra is constructed. An equivalent condition for a \(q\)-soft set to be a \(p\)-ideal is given. Characterizations of a \((\in,\in\vee q)\)-fuzzy \(p\)-ideal are initiated. Conditions for a \((\in,\in\vee q)\)-fuzzy ideal to be a \((\in,\in \vee q)\)-fuzzy \(p\)-ideal are stated.

MSC:

06F35 BCK-algebras, BCI-algebras
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