To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

In this paper, generalized fuzzy 2-norms are defined on a set of objects endowed with a structure of linear space. The relationships between these fuzzy 2-norms and fuzzy metrics and between these fuzzy 2-norms and the topological structures induced on a linear space are analyzed. Some open problems in this framework are mentioned. Mathematics Subject Classification: 46A19, 54A40

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

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

In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language are studied and we give some closure properties of fuzzy local ω-languages. We also establish relationship between deterministic fuzzy local automaton and fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition...

The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...

and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f 2x , 2.1 for all x, y ∈ X. Recall Df ≡ ...

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.