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.


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


Zbl 0491.06008
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