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Conceptual knowledge from \(L\)-fuzzy contexts. (English) Zbl 0876.68105

Summary: Taking as departure point the concept theory of R. Wille [Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445-470 (1982; Zbl 0491.06008)] and the fuzzy sets theory, in this paper, we develop a new model called \(L\)-fuzzy concept theory using \(L\)-fuzzy relations between objects and attributes.
We begin this paper with the definitions of some new operators that serve to make the \(L\)-fuzzy concepts. We obtain the concepts using a constructive version of the fixed points theorem of Tarski. We introduce an order relation that expresses the hierarchy between \(L\)-fuzzy concepts, and we prove below the lattice structure of the \(L\)-fuzzy concept set. Also, we recover the Wille’s theory as a particular case when \(L=\{0,1\}\) and we give the iso-structured \(L\)-fuzzy context definition that is used to analyze certain \(L\)-fuzzy contexts from others. In particular, we will be able to study \(L\)-fuzzy contexts from Wille’s context. Finally, we provide an example to illustrate this theory.

MSC:

68T30 Knowledge representation
06B23 Complete lattices, completions

Citations:

Zbl 0491.06008
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