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 order to apply the concept of boundedness, so crucial in the theory of metric spaces, to the case of a general topological space Hu Sze-Tsen introduced the notions of a bornological space and of boundedness for a mapping of bornological spaces. In this work we discuss two alternative approaches how the concepts of bornology and boundedness can be extended to the case of fuzzy sets and many-v...

The aim of this paper is to introduce the concept of fuzzy generalized closed set and study its properties. Secondly the concept of infra L-fuzzy topological space is introduced. Making use of fuzzy -closed sets and fuzzy -generalized closed sets the concept of fuzzy -generalized continuous mapping is introduced. Lastly the concept of fuzzy generalized closed irresolute map in L-fuzzy topologic...

Let H denote the set {f1, f2, ..., fn}, 2 the collection of all subsets of H and F ⊆ 2 be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1 ≤ k < l) is empty. This problem is reduced to a covering problem. If we have the conditions that any two subsets have a non-empty intersection and the intersection of any...

Criteria sets are a necessary step in(the systematic devopment of evaluation in education. Evaluation results from the c bination of criteria and evidence% There is a need lo develop xplicit tools for evaluating criteria, similar to those used in evaluating evidende. The formulationiof Such criteria depdnds on distinguishing between terms (concepts) and statements (linkages among concepts) . Fo...

Given a set R of red points and a set B of blue points in the plane of total size n, we study the problem of determining all angles for which there exists an L-shape containing all points from B without containing any points from R. We propose an algorithm to solve the problem in O(n log n) time and O(n) storage. We also describe an output-sensitive algorithm that reports all angles in O(n + k ...

Let C be any complexity class closed under log-lin reductions. We show that all sets complete for C under 1-L reductions are polynomialtime isomorphic to each other. We also generalize the result to reductions computed by finite-crossing machines. As a corollary, we show that all sets complete for C under 2-way DFA reductions are polynomial-time isomorphic to each other.

Complete lattices are considered with suitable families of lattice morphisms that provide a structure (L,Φ), useful to characterize ground categories of L-sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators presented here extends and unifies most approaches previously considered, allowing the use of noncri...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

Let Ω be a domain in the N -dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. It is proved in this paper the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every Tn al...