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A comparative study of adjoint triples. (English) Zbl 1272.03111

Summary: Adjoint triples are helpful as basic operators used in several domains. For example, adjoint triples play an important role in two important frameworks: multi-adjoint logic programming and multi-adjoint concept lattices. This paper shows that adjoint triples are an interesting generalization of t-norms and their residuated implications, since they preserve their main properties as well as help to increase the flexibility of the operators used for computation in the considered framework. Furthermore, these operators are related to other important general triples, specifically implication triples, and the definition of these latter operators is improved.

MSC:

03B52 Fuzzy logic; logic of vagueness
03G25 Other algebras related to logic
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