We prove that discrete compact quantum groups (or more generally locally compact, under additional hypotheses) with coamenable dual are continuous fields over their central closed subgroups, and the same holds for free products of amalgamated a common subgroup. Along way we also show [Formula: see text]-algebras again via Fell-topology characterization text]-field continuity, recovering result ...

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...

The purpose of this paper is to prove common fixed point theorem for four mappings without continuity and compatibility on intuitionistic fuzzy metric space.

The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discus...

n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0, 1]). This paper aims to investigate a special extension from [0, 1] – n-representable fuzzy negations on Ln([0, 1]), summarizing the class of such function...

A real world fuzzy set should be able to tolerate ”small amounts” of perturbations. In type II fuzzy set represents each grade is represented by a fuzzy number. In other words, each grade may be perturbed independently. Such an ”independent perturbation” is inadequate, when a membership function is required to be continuous, differentiable, and etc. Pointwise perturbation cannot guarantee the c...

Two extensions of classical Shepard operators to the fuzzy case are presented. We study Shepard-type interpolation/approximation operators for functions with domain and range in the fuzzy number’s space and max-product approximation operators. Error estimates are obtained in terms of the modulus of continuity.

In this paper we introduce the notion of levelwise convergence of sequence of fuzzy random variables. We derive equivalent conditions for left quasi uniform convergence of fuzzy random variables. Conditions are obtained for eventually equi-right continuity for the sequence of fuzzy random variables. A necessary and sufficient condition is obtained under which for a sequence of fuzzy random vari...