We introduce nearly Frank t-norms as t-norms which are generated from Frank t-norms by means of a negation-preserving automorphism. We state basic properties of nearly Frank t-norms and we show their speci c role in the characterization of T -measures. 1 Basic facts about T -norms A t-norm (fuzzy conjunction) is a binary operation T : [0; 1]2 ! [0; 1] which is commutative, associative, nondecre...

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...

It is known that the standard intersection and union of type-1 fuzzy sets (i.e., the intersection and union under the minimum t-norm and maximum tconorm) are the only cutworthy operations for type1 fuzzy sets. The aim of this paper is to show that similar property holds also for type-2 fuzzy sets, with respect to some special cutting. As was already demonstrated, the intersection and union of t...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

Recent results show that ontology consistency is undecidable for a wide variety of fuzzy Description Logics (DLs). Most notably, undecidability arises for a family of inexpressive fuzzy DLs using only conjunction, existential restrictions, and residual negation, even if the ontology itself is crisp. All those results depend on restricting reasoning to witnessed models. In this paper, we show th...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzyHv-submodules of anHv-module with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued in...