Type-2 fuzzy subalgebras of BCK-algebras and BCI-algebras

초록

Using the type-2 fuzzy set theory, we study the subalgebra of BCK/BCI-algebras. We introduce the concept of (strong) type-2 fuzzy subalgebras of BCK/BCI-algebras and investigate several properties. We establish the relationship between the fuzzy subalgebra, the strong type-2 fuzzy subalgebra and the type-2 fuzzy subalgebra. We find a way to derive the (strong) type-2 fuzzy subalgebra from the fuzzy subalgebra and vice versa. Given a type-2 fuzzy set, we create the slice and the cut, and find the conditions for the slice to be a fuzzy subalgebra. We use the cut to explore the characterization of a strong type-2 fuzzy subalgebra. We introduce the support and the core for the slice and explore the conditions under which they become subalgebras. We introduce the super level set and the infer level set for type-2 fuzzy set and explore the conditions under which they become subalgebras.

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