## The study of the $$L$$-fuzzy concept lattice.(English)Zbl 0827.06004

Summary: The $$L$$-fuzzy concept theory that we have developed in “Aplicación de técnicas $$L$$-fuzzy a la representación formal del conocimiento conceptual” [III Congreso Español sobre Tecnologías y Lógica Fuzzy, Santiago de Compostela (1993)] sets up classifications from the objects and attributes of a context through $$L$$-fuzzy relations. This theory generalizes the formal concept theory of R. Wille [“Restructuring lattice theory: An approach based on hierarchies of concepts”, Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445-470 (1982; Zbl 0491.06008)].
In this paper we begin with the $$L$$-fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the $$L$$-fuzzy concept set, giving a constructive method for calculating this method. At the end, we apply this constructive method to an example that has been studied by other methods.

### MSC:

 06B99 Lattices 03E72 Theory of fuzzy sets, etc.

Zbl 0491.06008
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