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We characterize weak BCC-algebras in which the identity (xy)z=(xz)y is satisfied only in the case when elements x and y belong to the same branch. [ABSTRACT FROM AUTHOR]

Characterizations of a (⋶, ⋶ ∨ q̄)-fuzzy subalgebra (ideal) are considered. Given an ∈-soft set, an (⋶, ⋶ ∨ q̄)-fuzzy subalgebra is established. Using the notion of (t, s)-fuzzy subalgebras, characterizations for an∈-soft set to be a (idealistic) soft BCK/BCI-algebra are provided. Using the notion of fuzzy p-ideals, a characterization of an∈-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 (∈,∈ ∨ q)-fuzzy p-ideal are initiated. Conditions for a (∈,∈∨ q)-fuzzy ideal to be a (∈,∈∨ q)-fuzzy p-ideal are stated. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce the notions of (∈,∈∨ q)-FSI-ideals and (∈,∈∨ q)-FSC-ideals of BCI-algebras and to investigate some of their related properties. Some characterization theorems of these generalized fuzzy ideals are derived. The relationship among these generalized fuzzy ideals of BCI-algebras is considered. We show that a fuzzy set of a BCI-algebra is an (∈,∈∨ q)-FSI-ideal if and only if it is both an (∈,∈∨ q)-FSC-ideal and an (∈,∈∨ q)-FPI-ideal. Finally, we consider the concepts of implication-based FSI (resp., FSC)-ideals of BCI-algebras. [ABSTRACT FROM AUTHOR]