Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ L which is reflexive and symmetric, certain fuzzy relations Ĥ ∈ L are characterized as solutions of X C R = X. These solutions Ĥ can be determinated by means of the L-fuzzy concepts associated with the K-labeled L-fuzzy context (L,K,E,E,R).

In this article we firstly summarize some notions on L−fuzzy sets, where L denotes a complete lattice. We then study a special case of L−fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is being defined independently from the fuzzy membership function. The latter implies both flexibility and effectiveness in fuzzy inference a...

We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones propose...

In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, sin...

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 ...

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...

matroids are important combinatorial structures and connect close-lywith graphs. matroids and graphs were all generalized to fuzzysetting respectively. this paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. for a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. a fuzzy matroid, named graph fuzzy matro...

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...