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Involutory and invertible fuzzy BCK-algebras

✍ Scribed by Young Bae Jun; Xiao Long Xin

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 95 KB
Volume: 117
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(98)00406-0

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✦ Synopsis

The concept of a fuzzy annihilator in a commutative BCK-algebra will be introduced and then we investigate some basic properties. Using this notion, we deÿne an involutory (resp. invertible) fuzzy ideal. We prove that (i) every bounded implicative BCK-algebra is an involutory fuzzy BCK-algebra, and (ii) every categorical commutative BCK-algebra is an invertible fuzzy BCK-algebra. Let X be an involutory and invertible fuzzy BCK-algebra and let FI(X ) denote the set of all fuzzy ideals of X . We show that (iii) (FI(X ); ∪; ∩) is a distributive lattice, and (iv) (FI(X ); Ã; ∪; ∩; ˜) is a quasi-Boolean algebra.

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