The concepts of (∈,∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, (∈,∈∨q)-fuzzy (implicative, positiv...

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is ...

we consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $x$, $(x, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $x$. we also show that, for a strong residuated lattice $x$, $bigcap {p_{lambda} ,|,p_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

The aim of this paper is to introduce the notions of interval valued (∈,∈ ∨q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (∈,∈...

In this paper, the authors study the notion of n-fold implicative and fuzzy n-fold implicative filters, which correspond to various sets of provable formulaes, in BL-algebras. Several characterizations of fuzzy n-fold implicative filters are given and the authors analyse some relationships with various n-fold and fuzzy n-fold filters in BL-algebras, while constructing some algorithms for studyi...

BL-algebras have been invented by P. Hájek [3] in order to provide an algebraic proof of the completeness theorem of “Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The above notion is generalized to an algebraic system in which the required conditions are fulfilled (Definition 2.1). Filters in BL-algebras are also defined. A fi...

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

We present high spatial resolution optical images of the BL Lac object MS 0205.7+3509 in the R filter, that allow us to discuss and clarify its anomalous properties. The source was previously claimed to be surrounded by a nebulosity decentered with respect to the bright nucleus. In addition the host was claimed to be a disc dominated galaxy, contrary to the large majority of the hosts of BL Lac...

For any BL-algebra L, we construct an associated lattice ordered Abelian group GL that coincides with the Chang’s `-group of an MV-algebra when the BL-algebra is an MValgebra. We prove that the Chang’s group of the MV-center of any BL-algebra L is a direct summand in GL. We also find a direct description of the complement S(L) of the Chang’s group of the MV-center in terms of the filter of dens...