In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

There has been lots of research in the field of fuzzy spatial data and the topology of fuzzy spatial objects. In this contribution, an extension to the 9-intersection model is presented, to allow for the relative position of overlapping fuzzy regions to be determined. The topology will be determined by means of a new intersection matrix, and a set of numbers, expressing the similarity between t...

The concepts of fuzzy e-open sets and fuzzy e-continuous are introduced and studied in fuzzifying topology and by making use of these concepts, we introduce and study T e 0 -, R e 0-, T e 1 -, R e 1-, T e 2 -, T e 3 -, T e 4 -, strong T e 3 and strong T e 4 separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separa...

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...

Considering vast and miscellaneous contents in P2P system, intelligent P2P network topology is required to route queries to a relevant subset of peers. Based on the incremental clustering capability of Fuzzy Adaptive Resonance Theory (Fuzzy ART), this paper made use of the modified fuzzy ART to provide small-world P2P construction mechanism, which was not only to categorize peers so that all th...

On a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. In this paper we extend thisconcepts to the fuzzy case. We give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation f...