In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$  the set of all real numbers. A great many standard mappings on algebr...

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 ...

In this paper, we propose a generalized concept of openness and closedness with respect to arbitrary fuzzy relations, along with appropriate opening and closure operators. We will show that this framework includes the existing concept defined for fuzzy preorderings as well as the triangular norm-based approach to fuzzy mathematical morphology.

We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a mixture of completion rules and bounded mixed integer programming.

A t-norm is a binary operation on [0, 1] that is associative, commutative, with identity 1 and non-decreasing in both argument. The notion of t-norm is very important in the context of fuzzy logic, for it is used in modeling a general form of the propositional conjunction. The basic fuzzy logic (BL logic) was introduced by Hájek in [9,10] and it was inspired by a continuous t-norm and its resid...

In the paper aggregations of fuzzy relations using functions of n variables are considered. After recalling properties of fuzzy relations, aggregation functions which preserve: reflexivity, irreflexivity, T -asymmetry, T -antisymmetry, symmetry, S-connectedness, T -transitivity, negative Stransitivity, T -S-semitransitivity and T -S-Ferrers property of fuzzy relations, where T is a t-norm and S...

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.

In this paper, we investigate renewal theories in the T -independent random fuzzy environment based on the concept of fuzzy variable and random fuzzy variable. For special cases, we consider the case for T = min and T =Archimedean t-norm. Mathematics Subject Classification: 60A86

We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a mixture of completion rules and bounded mixed integer programming.

Recommended by Akbar Rhemtulla We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.