Concept lattices associated with L-Fuzzy W-contexts

\begin{abstract}

\noindent We generalize in this paper the
$L$-Fuzzy concept theory we developed in a previous paper ([1]),
using the composition of $L$-Fuzzy relations. This theory models knowledge
acquisition and
classification and takes as departure point Wille's idea ([5]).

We begin the work defining $L$-Fuzzy W-contexts as the tuples (L,W,X,Y,
$\underset{\textstyle \backsim}{R}$) where W, X and Y are the sets of labels, objects and
attributes respectively, and
$\underset{\textstyle \backsim}{R}\in L^{X\times Y}$ is an $L$-Fuzzy relation.

From these contexts, we will give the operators needed to define the \linebreak
$L$-Fuzzy W-concepts.
These concepts will be pairs of relations ($\underset{\textstyle \backsim}{P},
\underset{\textstyle \backsim}{Q}$) where $\underset{\textstyle \backsim}{P}\in L^{W\times X}$,
$\underset{\textstyle \backsim}Q\in L^{W\times Y}$ satisfying $\underset{\textstyle \backsim}{P_{1}}=
\underset{\textstyle \backsim}Q$ and $\underset{\textstyle \backsim}Q_{2}=
\underset{\textstyle \backsim}P$ with the operator 1 and 2 definitions given.


After proving the lattice structure of the $L$-Fuzzy W-concepts set, we
analyse a practical
example where we interpret the new concept definition

\bigskip
\noindent {\bf Key words:}
$L$-Fuzzy concepts, $L$-Fuzzy W-concepts,
$L$-Fuzzy W-contexts, Conceptual knowledge.

\end{abstract}