The main result of this paper is the following theorem: If a projective Boolean algebra B is generated by its sublattice L, then there is a projective distributive lattice D which is a sublattice of L and generates B.

In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally,...

As topology-like mathematical structures, convex structures can be characterized by betweenness relations via (restricted) hull operators in spaces. In a topological approach, the aim of this paper is to present fuzzy counterpart based on points Concretely, notion L-betweenness restricted L-hull introduced. Firstly, it proved that are categorically isomorphic and L-remotehood systems, respectiv...

In this paper, we give the correlation and difference between M-convex fuzzy process and SLW-convex fuzzy process, and present some basic properties of these convex fuzzy processes, which improve some known results about the connection between those convex fuzzy processes and their graphs. In addition, we introduce a new notion of s-convex fuzzy process as a generalization of M-convex fuzzy pro...

In this note, we first define the concept of convex fuzzy processes. Second, we present some basic properties of convex fuzzy processes and important connection between convex fuzzy processes and their graphs. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-convex fuzzy sets, Convex fuzzy cones, Convex fuzzy processes.

in this paper, we propose a new method for fuzzy numbers. in this method, we assume that ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. so, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. then, mic and mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. finally,...

In this article, a number of the results relevant to the concept of sublattices of a basic crystallographic lattice are reviewed, emphasizing particularly previously unpublished work on the algebraic aspects. A three-dimensional geometric lattice L can be considered as an infinite Abelian group under addition. A sublattice S of L, which is also three-dimensional, is a subgroup of L such that th...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

is finite, where λ denotes Lebesgue measure. Let ρ be the gauge functional of the convex hull of the unit ball {f : q(f) ≤ 1} of the quasi-norm q, and let N be the null space of ρ. The normed envelope of WeakL, which we denote by W , is the space (WeakL/N, ρ). The Banach envelope of WeakL, W , is the completion of W . We show that W is isometrically lattice isomorphic to a sublattice of W . It ...