This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

We give a generalization of possibility and necessity measures: their domains are extended towards fields of sets, and their codomains towards arbitrary complete lattices. In this way, these measures can be associated with (Q,≤)-fuzzy sets, where (Q,≤) is at least a poset. An important inconsistency problem, intricately linked with this association, is solved. It is argued that order lies at th...

Quantum Logic: A logic (血,←, þ), where the proof-theoretic and the semantic-consequence relations violate some characteristic classical principles like the distributivity of conjunction and disjunction. Adjoint: If A is a bounded operator on a Hilbert space , then the adjoint of A is the unique bounded operator A食 that satisfies (A~ φ) = (ψIA* φ) for all vectors ψ, φin the space. Algebraic Mode...

There is a canonical way to associate two simplicial complexes K, L to any relation R ⊂ X×Y . Moreover, the geometric realizations of K and L are homotopy equivalent. This was studied in the fifties by C.H. Dowker [8]. In this article we prove a Galois-type correspondence for relations R ⊂ X × Y when X is fixed and use these constructions to investigate finite posets (or equivalently, finite T0...

With a finite graph G = (V,E), we associate a partially ordered set P = (X, P) with X = V U E and x < e in P if and only if x is an endpoint of e in G. This poset is called the incidence poset of G. In this paper, we consider the function M ( p , d ) defined for p, d~>2 as the maximum number of edges a graph G can have when it has p vertices and the dimension of its incidence poset is at most d...