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Fuzzy BCI-subalgebras with interval-valued membership functions. (English) Zbl 0971.06018
Summary: The purpose of this paper is to define the notion of an interval-valued fuzzy BCI-subalgebra (briefly, an i-v fuzzy BCI-subalgebra) of a BCI-algebra. Necessary and sufficient conditions for an i-v fuzzy set to be an i-v fuzzy BCI-subalgebra are stated. A way to construct a new i-v fuzzy BCI-subalgebra from an old one is given. The images and inverse images of i-v fuzzy BCI-subalgebras are defined, and it is studied how the images or inverse images of i-v fuzzy BCI-subalgebras become i-v fuzzy BCI-subalgebras.
MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
03E72 Theory of fuzzy sets, etc.
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