An L-fuzzy context is a triple consisting of a set of objects, a set of attributes and an L-fuzzy binary relation between them. An l-cut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater or equal than l. Proto-fuzzy concept is a triple made of a set of objects and a set of attributes, which form a con...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

In this paper, we introduce a good definition of semiprecompactness in L-fuzzy topological spaces in Šostak’s sense, where L is a fuzzy lattice. We define this concept on arbitrary L-fuzzy sets, obtain a different characterization and study some of its properties. 2010 AMS Classification: 54A40, 54D30, 53A05

The goal of this work is to prove a link between the Fuzzy Mathematical Morphology and the L-fuzzy Concept Analysis when we are using structuring relations which represent the effect that we want to produce over an initial fuzzy image or signal. In this case, we prove that the problem of obtaining the Lfuzzy concepts of an L-fuzzy context is equivalent to the problem of finding fuzzy images or ...

One of the main problems in FCA (especially in fuzzy setting) is to reduce a concept lattice to appropriate size to make it graspable and understandable. We generalize known results on the correspondence of block relations of formal contexts and complete tolerances on concept lattices to fuzzy setting. Using an illustrative example we show that the results can be used for reduction of fuzzy con...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...

With the emergence of the fundamental paper [5] by Zadeh in 1965 number of papers have appeared in literature featuring the application of fuzzy sets to pattern recognition, decision problems, function approximation, system theory, fuzzy logic, fuzzy algorithms, fuzzy automata, fuzzy grammars, fuzzy languages, fuzzy algebras, fuzzy topology, etc. [2], [7]. In this note, our interests are in the...

In formal concept analysis of data with fuzzy attributes, both the extent and the intent of a formal (fuzzy) concept may be fuzzy sets. In this paper we focus on so-called crisply generated formal concepts. A concept 〈A,B〉 ∈ B (X,Y, I) is crisply generated if A = D↓ (and so B = D↓↑) for some crisp (i.e., ordinary) set D ⊆ Y of attributes (generator). Considering only crisply generated concepts ...

Algebraic structures like fuzzy sub rings of L-Fuzzy sets have been well studied in the case where lattice L is distributive. In this paper axioms concepts can be generalised to not The aim current define concept L-fuzzy meet semi almost ideals and also Intutionistic . Investigate some theorems examples.

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....