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...

Fuzzy classification rules are widely considered a well-suited representation of classification knowledge, as they allow readable and interpretable rule bases. The goal of this paper is to discuss the shapes of the resulting classification borders under consideration of different types of fuzzy sets, rule bases and t-norms and thus which class distributions can be represented by such classifica...

In this paper, we revisit and study the basic properties of two families fuzzy implications, so-called (T,N)− (N′,T,N)− implications. More specific, when these implications satisfy, or not, neutrality property (NP), exchange principle (EP), identity (IP) ordering (OP). Moreover, a is presented for law importation (LI) with respect to t- norm. Also, relation Φ−conjugation in

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

Fuzzy Hamming Distance is successfully used in a Content-Based Image Retrieval (CBIR) system as a similarity measure. The system performs a m × n partitioning of the compared images and for each partitions pairs evaluates FHD. In the last step the FHD are defuzzified and the results are combined in a final score. In order to take full advantage of the use of fuzzy sets, the current study invest...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

Rule-driven processing is a proven way of achieving high-speed in fuzzy processing. Up to now, ruledriven architectures where designed to work with minimum or product as T-norm. Nevertheless, a Lukasiewicz T-norm is typically used with the compositional rule of inference in expert systems applications that are based on a fuzzy inference engine. This paper presents a rule-driven processing archi...

In this paper some algebraic structures for linguistic fuzzy models are defined for the first time. By definition linguistic fuzzy norm, stability of these systems can be considered. Two methods (normed-based & graphical-based) for stability analysis of linguist fuzzy systems will be presented. At the follow a new simple method for linguistic fuzzy numbers calculations is defined. At the end tw...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...