In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

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 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.

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

In three case studies on notions of fuzzy logic and fuzzy set theory (Dubois–Prade’s gradual elements, the entropy of a fuzzy set, and aggregation operators), the paper exemplifies methodological differences between traditional and deductive fuzzy logic. While traditional fuzzy logic admits various interpretations of membership degrees, deductive fuzzy logic always interprets them as degrees of...

In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

Irrepressible growth of complex interconnectedness of information systems besides its obvious benefits unfortunately brought up the questions of their vulnerability. Practically universal access to computers has enabled hackers and would-be terrorists to attack information systems and critical infrastructures worldwide. Fuzzy preference relation, based on fuzzy satisfaction function is applied ...

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...