Characterizations on interval valued fuzzy ideals in BF-algebras | |
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( Volume 1 Issue 1,July 2015 ) OPEN ACCESS | |
Author(s): | |
S. Muhammad, A. Rehman, M. Zulfiqar, M. Idrees | |
Abstract: | |
In this paper, we introduced the notion of -interval valued fuzzy ideals in BF-algebra, where , are any one of , , , and investigate some of their related properties. We prove that an interval valued fuzzy set of a BF-algebra X is an interval valued fuzzy ideal of X if and only if is an -interval valued fuzzy ideal of X. We show that an interval valued fuzzy set of a BF-algebra X is an -interval valued fuzzy ideal of X if and only if for any [0.5, 0.5] ˂ ≤ [1, 1], = {x Î X | (x) ≥ } is an ideal of X. Finally we prove that the intersection and union of any family of -interval valued fuzzy ideals of a BF-algebra X are an - interval valued fuzzy ideal of X. |
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