In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of ZZn ⊕ T with no invertible elements, where T is a finite abelian group. We also characterize the lattice ideals that are set-theoretic complete intersections on binomials.

In mathematical morphology (MM), images are viewed as L-fuzzy sets, where the symbol L stands for a complete lattice. In particular, fuzzy MM arises by considering L = [0, 1]. Mathematical morphology provides the theoretical basis for certain lattice computing models called morphological neural networks (MNNs) including morphological associative memories (MAMs) that are the focus of this paper....

In this paper we prove the following conclusions: (1). If E is a complete atomic lattice effect algebra, then E is (o)-continuous ⇔ E is order-topological ⇔ E is a totally order-disconnected ⇔ E is algebraic. (2). If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τid is Hausdorff topology and is finer than its order topology τo, and τid = τo ⇔ 1 is fin...

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered ...

and Applied Analysis 3 such that a ∈⇓ d. Thus d ∈⇑ a ⊆ U. Therefore D ∩ U ̸ = 0, hence U ∈ σ(P). This proves τ(P) ⊆ σ(P). (2) Now assume that P is strongly continuous. Then P is continuous. In a strongly continuous lattice, the relation ≪ and ⇐ are the same by the Theorem 2.5 of [5]. Also by [2] in a continuous lattice, every Scott open set A satisfies the condition A = ↑≪A, it follows that ever...

We present a solution to the problem of finding the complete sublattice of a given concept lattice generated by given set of elements. We construct the closed subrelation of the incidence relation of the corresponding formal context whose concept lattice is equal to the desired complete sublattice. The construction does not require the presence of the original concept lattice. We introduce an e...

This paper constructs a logic of soft constraints where the set of degrees of preference forms a partially ordered set. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations can be used to define a sound and complete proof theory. For the general case, it is shown how sound and complete deduction can be p...

Mathematical Morphology (MM) is a nonlinear approach to image processing that relies on a fundamental structure, the complete lattice L [7] (a nonempty set equipped with an ordering relation). With the complete lattice theory, it is possible to define morphological operators for any type of data once a proper ordering is established [1]. If Mathematical Morphology is well defined for binary and...

We have investigated a method of measuring the complete lattice functions including the coupling parameters at any azimuthal position in a periodic and symplectic system. In particular, the method is applied to measure the lattice functions at the interaction point where the beams collide. It has been demonstrated that a complete set of lattice functions can be accurately measured with two adja...