It is the purpose of this paper to go somewhat deeper into the structure of fuzzy topological spaces. In doing so we found we had to alter the definition of a fuzzy topology used up to now. We shall also introduce two functors 3 and i which will allow us to see more clearly the connection between fuzzy topological spaces and topological spaces. Finally we shall introduce the concept of fuzzy co...

Using a gradation of openness in a (Chang fuzzy) I-topological space, we introduce degrees of compactness that we call α-fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α-locally compact spaces and construct a one-point α-fuzzy compactification of an I-topological space. 1. Introduction....

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the r...

In this work, we introduce definitions of smooth strong compactness and smooth P-closedness for arbitrary L-fuzzy sets in smooth Lfuzzy topological spaces and study some of their properties. We also investigate relations between these concepts and the other definitions of compactness in smooth L-fuzzy spaces. Mathematics Subject Clasification: 54A40

In this paper, the new concept of near PS-compactness in L-topological spaces is introduced. It is defined for any L-subset. Its characterizations and topological properties are systematically studied. And the relationship is exposed between near PScompactness and PS-compactness, and also fuzzy compactness. 2003 Elsevier Inc. All rights reserved.