In this paper, we study (L, )-fuzzy topologies induced by operations and (L, )-filters on strictly two-sided, commutative quantale lattices (L, ) and (L, ∗). Mathematics Subject Classification: 03E72, 54A40, 54B10

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical p...

Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intuitionistic fuzzy set theory. In this paper we study the relation between Atanassov intuitionistic fuzzy and the proposed extension called Multi-fuzzy. Also we present the notion of Multi-fuzzy mappings and Atanassov Intuitionistic Fuzzy Sets Generating Maps. Mathematics Subject Classification: MSC: ...

In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...

In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.

A definition of L-fuzzy bags is introduced and studied. In this approach, according to the concept given by M. Delgado et al. (2009), each bag has two parts: function and summary information. Then, the definition of L-fuzzy bag expected value is introduced. In the case L = [0, 1], several integral-based fuzzy bag expected values are prepared. By some examples, the new concepts are illustrated.

The aim of this paper is to study the concept of -induced L-fuzzy topological spaces. Some properties of the functions (namely Scott-continuous function) are studied. The Scott-continuous functions turn out to be the natural tool for studying the -induced L-fuzzy topological space. We also discuss the connections between some separations, countability and covering properties of an ordinary topo...

In this work, we introduce and study the composition of two L-fuzzy contexts that share the same attribute set. Besides studying its properties, this composition allows to establish relations between the sets of objects associated to both L-fuzzy contexts. We also define, as a particular case, the composition of an L-fuzzy context with itself. In all the cases, we show some examples that illust...

This paper deals with the uniqueness of L-fuzzy sets in the representation of a given family of subsets of a nonempty set. It first shows a formula of the number of L-fuzzy sets whose collection of cuts coincides with a given family of subsets of a nonempty set, and then provides a necessary and sufficient condition under which such L-fuzzy set is unique. MSC: 03E72; 06D05