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Implication operators generating pairs of weak negations and their algebraic structure. (English) Zbl 1464.03091

Summary: Negations operators have been developed and applied in many fields such as image processing, decision making, mathematical morphology, fuzzy logic, etc. One of the most effective non-monotonic operators are weak negations. This paper studies the algebraic structure and the characterization of the adjoint triples and Galois implication pairs which provides a fixed pair of weak negations. The obtained results allow the user to select the best conjunctor and implications associated with the most suitable negation to be used in the computations of the problem to be solved.

MSC:

03G10 Logical aspects of lattices and related structures
03B52 Fuzzy logic; logic of vagueness
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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