When a class of fuzzy value functions constitute a metric space, the completeness and separability is an important problem that must be considered to discuss the approximation of fuzzy systems. In this paper, Firstly, a new tK-integral norm is defined by introducing two induced operators, and prove that the class of tK-integrable fuzzy value functions is a metric space. And then, the integral t...

In this paper, new similarity, inclusion measure and entropy between type-2 fuzzy sets corresponding to grades of memberships are proposed. We also create the relationships among these measures between type-2 fuzzy sets. Several examples are used to present the calculation of these similarity, inclusion measure and entropy between type-2 fuzzy sets. The comparison results show that the proposed...

In this paper, we present a revised similarity measure based onChen-and-Chen's similarity measure for fuzzy risk analysis. The revisedsimilarity measure uses the corrected formulae to calculate the centre ofgravity points, therefore it is more  effective than the Chen-and-Chen'smethod. The revised similarity measure can overcome the drawbacks of theexisting methods. We have also proposed a new ...

In this paper we present some properties concerning non-atomicity of regular null-additive fuzzy set multifunctions. Key–words: fuzzy, null-additive, regular, atom, non-atomic.

In group decision making situations, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved and, as a result, they may present incomplete information. In this paper, we present a new selection process to deal with incomplete fuzzy linguistic information. As part of it, we use an iterative procedure to estimate the missing information. This procedure is...

The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entr...

This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable (negative definite). So local rule stability leads to global system stability. This relationship b...

We deal with the problem of evaluating and ranking fuzzy quantities. We call fuzzy quantity any non-normal and non-convex fuzzy set, defined as the union of two, or more, generalized fuzzy numbers. For this purpose we suggest an evaluation defined by a pair index based on “value” & “ambiguity”. Either value or ambiguity depend on two parameters connected the first with the optimistic/pessimisti...