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An adjoint pair for intuitionistic \(L\)-fuzzy values. (English) Zbl 1430.68334

Cornejo, María Eugenia (ed.) et al., Trends in mathematics and computational intelligence. Selected papers based on the presentations at the 9th European symposium on computational intelligence and mathematics, ESCIM 2017, Faro, Portugal, October 4–7, 2017. Cham: Springer. Stud. Comput. Intell. 796, 167-173 (2019).
Summary: We continue our prospective study of the generalization of formal concept analysis in terms of intuitionistic \(L\)-fuzzy sets. The main contribution here is an adjoint pair in the set \({\mathcal L}_\mathrm{ILF}\) of intuitionistic \(L\)-fuzzy values associated to a complete residuated lattice \(\mathcal L\), which allows the definition of a pair of derivation operators which form an antitone Galois connection.
For the entire collection see [Zbl 1404.68011].

MSC:

68T30 Knowledge representation
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B23 Complete lattices, completions
06F05 Ordered semigroups and monoids
68T37 Reasoning under uncertainty in the context of artificial intelligence
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