Solutions to Open Problems on Fuzzy Filters ofBL-algebras

On open problems based on fuzzy filters of pseudo BCK-algebras

We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: “In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the ...

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...

On fuzzy filters of pseudo BL-algebras

The aim of this paper is to introduce the notion of (∈,∈∨ q)-fuzzy (implicative, MV and G-) filters of pseudo-BL algebras and to investigate some of their related properties. Some characterization theorems of these generalized fuzzy (implicative) filters are derived. The relationship among these generalized fuzzy filters of pseudo-BL algebras is considered. It is proved that an (∈,∈ ∨q)-fuzzy f...

Fuzzy Filters in Bci-algebras

On semi maximal filters in BL-algebras

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...