Some results on fuzzy semi maximal filters in BL-algebras

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.