Taking into account the notion of BL-general fuzzy automaton, in the present study we define the notation of BL-intuitionistic general L-fuzzy automaton and I-bisimulation for BL-intuitionistic general L-fuzzy automaton.Then for a given BL-intuitionistic general L-fuzzy automaton, we obtain the greatest I-bisimulation. According to this notion, we give the structure of quotient BL-intuiti...

In this study, we define the concept of an ω-fuzzy set subring and show that intersection two subrings is also a given ring. Moreover, give notion ideal investigate different fundamental results phenomenon. We extend ideology to propose coset develop quotient ring with respect particular fuzzy analog into classical Additionally, found subring. idea support prove various important characteristic...

Among other applications, multi-adjoint lattices have been successfully used for modeling flexible notions of truth-degrees in the fuzzy extension of logic programming called MALP (Multi-Adjoint Logic Programming). In this paper we focus in the completion of such mathematical construct by adapting the classical notion of Dedekind-MacNeille in order to relax this usual hypothesis on such kind of...

New results on fuzzy concepts and concept lattices are presented. The issue of logical precision, a phenomenon that—although completely degenerate in two-valued logic—naturally arises in the context of fuzzy logic is studied. We present basic results regarding logical precision and concept lattices. Since, as far as we know, the phenomenon has not been discussed in literature so far, we briefly...

The purpose of this note is the study of L-multialgebras and fuzzy congruences of multialgebras. In this regards first the notion of a L-multialgebras are introduced and studied and then the notion of a P -fuzzy relations on multialgebra are given and is applied to introduce the notion of P -fuzzy congruence of multialgebras. Finally, the lattices of P -fuzzy (resp. strong) congruences of multi...

In this article we deal with the free Banach lattice generated by a and its behavior respect to subspaces. general, any embedding $i\colon \mathbb{L} \longrightarrow \mathbb{M}$ between two lattices $\mathbb{L} \subseteq induces homomorphism $\hat \imath\colon FBL \langle \rangle \mathbb{M}\rangle$ corresponding lattices. We show that mapping \imath$ might not be an isometric neither isomorphic...

 In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...

We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some con...

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...