The concept of L-fuzzy lattice is presented by means of an L-fuzzy partially ordered set. An L-fuzzy partially ordered set A is an L-fuzzy lattice if and only if one of A[a], A([a]), and A(a) is a lattice.

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n2 log2 n), where n = |L|. This paper is motivated by the problem of efficiently calculating and representing the congruence lattice Con L of a finite lattice L. Of c...

a common fixed point result for weakly increasing mappings satisfying generalized contractive type of zhang in ordered metric spaces are derived.

In this section we will talk about some simple algorithms for looking up items in a sorted list. Broadly speaking, an algorithm is a group of instructions that completely characterize the process of converting a set of inputs into desired outputs. To illustrate this concept, we shall solve a basic search problem. Let L = {l1, l2, . . . , lK} denote a set of ordered objects, where lk precedes lk...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

A computable presentation of the linearly ordered set (ω,≤), where ω is the set of natural numbers and ≤ is the natural order on ω, is any linearly ordered set L = (ω,≤L) isomorphic to (ω,≤) such that ≤L is a computable relation. Let X be subset of ω and XL be the image of X in the linear order L under the isomorphism between (ω,≤) and L. The degree spectrum of X is the set of all Turing degree...

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

Problems from Review of Set Theory Notes 3 (c) We prove that A× (B −C) = (A×B)− (A×C). We show that A× (B −C) ⊂ (A×B)−(A×C), and (A×B)−(A×C) ⊂ A×(B−C). For the first containment, let x ∈ A× (B − C). Then x = (a, b) where a ∈ A and b ∈ B − C. We certainly have x ∈ A × B, and since the second coordinate of x is not in C, we conclude that x / ∈ A× C. For the second containment, let x ∈ (A× B)− (A×...