The Cai δ-equality of fuzzy sets corresponds to the Lukasiewicz t-norm. In this paper we study the notion of (∗, δ)-equality, a concept which generalizes the δ-equality to the case of the fuzzy set theory based on an arbitrary continuous t-norm ∗. We investigate the robustness of some fuzzy implication operators in terms of (∗, δ)-equality.

In this paper, we redefine the notion of fuzzy 2-normed linear space using t-norm and fuzzy anti-2-normed linear space using t-conorm and introduced the definition of intuitionistic fuzzy 2-norm on a linear space. Mathematics Subject Classification: 46S40, 03E72

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of general concept inclusion axioms (GCIs),...

In this thesis, In this thesis, general structure of fuzzy normed linear spaces is examined and basic concepts of bounded and continuous operators defined on these spaces are studied. Firstly, fuzzy norm on finite-dimensional linear spaces is defined and by means of α -cut set some properties of this norm are mentioned. In the second part, generalizing the definition of fuzzy norm given on fini...

The application of conjunctive aggregation operators in fuzzy control systems with 2 inputs is discussed and the effect of the choice of a continuous t-norm operator in inference phase for TSK systems is computed. It is shown that the choice of a continuous t-norm modelling AND connective in antecedent part of fuzzy rules can be reduced just to strict or nilpotent t-norm. Moreover, it is shown ...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

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...

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.