## Multi-adjoint relation equations: definition, properties and solutions using concept lattices.(English)Zbl 1320.68173

Summary: This paper generalizes fuzzy relation equations following the multi-adjoint philosophy. Moreover, the solutions of these general fuzzy relation equations and the concepts of a multi-adjoint property-oriented concept lattice are related, and several results are obtained from the theory of concept lattices.
As a consequence of this relevant relation, more properties about these general equations can be proven from the theory of concept lattices and the algorithms developed to compute concept lattices can be used to obtain solutions. Furthermore, an interesting application to fuzzy logic programming has been introduced, in which an important problem in this topic has been interpreted in terms of solving a multi-adjoint relation equation.

### MSC:

 68T30 Knowledge representation 03E72 Theory of fuzzy sets, etc. 06A15 Galois correspondences, closure operators (in relation to ordered sets)
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