Standard fuzzy uniform structures based on continuous t-norms

Standard fuzzy uniform structures based on continuous t-norms

Fuzzy uniform structures and continuous t-norms

We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform spaces in our sense (and fuzzy uniformly continuous mappings) is isomorphic to the category of uniform spaces (and uniformly continuous mappings) by means of a covariant func...

T-Independence Condition for Fuzzy Random Vector Based on Continuous Triangular Norms∗

Min-independence has been proved to be a sufficient condition of a vector of fuzzy random variables to be a fuzzy random vector. The objective of this paper is to study further on the independence condition for fuzzy random vector based on continuous triangular norms. We first discuss measurability criteria for fuzzy random vector, and present two more new equivalent formulations of the measura...

Left-continuous t-norms in Fuzzy Logic: an Overview

In this paper we summarize some fundamental results on left-continuous t-norms. First we study the nilpotent minimum and related operations in considerable details. This is the very first example of a left-continuous but not continuous t-norm in the literature. Then we recall some recent extensions and construction methods.

On Fuzzy φψ-Continuous Function Between L-fuzzy Uniform Spaces

In this paper, by means of operations (is called in [1, 2, 3] φ,ψ) we shall define φψ-continuity between two L-fuzzy quasi-uniform spaces. We shall prove that φψ-continuity between two L-fuzzy quasi-uniformity induces φψ-continuity between L-fuzzy topology generated by them. We shall investigate some Theorems on L-fuzzy uniform spaces. 2000 Mathematics Subject Classification:54A40, 03E72