پژوهشهای ریاضی (Nov 2022)
Some results on fuzzy semi maximal filters in BL-algebras
Abstract
In this paper, first, the concept of the fuzzy semi maximal filters in BL-algebras has been introduced, then several properties of fuzzy semi maximal filters have been studied and its relationship with other fuzzy filters including fuzzy (positive)implicative fuzzy filters and fuzzy fantastic filters are investigated. In the following, using the level subsets of fuzzy sets in a BL-algebra, fuzzy semi maximal filters have been studied. It has also been proved that a fuzzy filter is a fuzzy semi maximal filters if and only if all level subsets are semi maximal filters filter. In addition, it proves that the preimage of a semi maximal fuzzy filter under the BL-homomorphism and the image of a fuzzy semi maximal filter under the BL-isomorphism , is also a fuzzy semi maximal filter. Also, the Extension property has been proved for fuzzy semi maximal filters in BL-algebra. Finally, the relationships between the fuzzy semi maximal filters and semi simple BL-algebras have been studied.
