Formal Concepts and Residuation on Multilattices

• Autorzy: Koguep Njionou Blaise Blériot , Kwuida Leonard , Lele Celestin

Identyfikatory

DOI

10.3233/FI-222147

• Języki publikacji: EN

Abstrakty

EN

Multilattices are generalisations of lattices introduced by Mihail Benado in [4]. He replaced the existence of unique lower (resp. upper) bound by the existence of maximal lower (resp. minimal upper) bound(s). A multilattice will be called pure if it is not a lattice. Multilattices could be endowed with a residuation, and therefore used as set of truth-values to evaluate elements in fuzzy setting. In this paper we exhibit the smallest pure multilattice and show that it is a sub-multilattice of any pure multilattice. We also prove that any bounded residuated multilattice that is not a residuated lattice has at least seven elements. We apply the ordinal sum construction to get more examples of residuated multilattices that are not residuated lattices. We then use these residuated multilattices to evaluate objects and attributes in formal concept analysis setting, and describe the structure of the set of corresponding formal concepts. More precisely, if i := (Ai, ≤i, ⊤i, ⊙i, →i, ⊥i), i = 1, 2 are two complete residuated multilattices, G and M two nonempty sets and (ϕ, ψ) a Galois connection between A 1 G and A 2 M that is compatible with the residuation, then we show that : = { (h , f) ∈ A 1 G × A 2 M ; φ (h) = f and ψ (f) = h } can be endowed with a complete residuated multilattice structure. This is a generalization of a result by Ruiz-Calviño and Medina [20] saying that if the (reduct of the) algebras i, i = 1; 2 are complete multilattices, then is a complete multilattice.

Słowa kluczowe

EN

multilattices; sub-multilattices; residuated multilattices; Formal Concept Analysis; ordinal sum of residuated multilattices

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2022
• Tom: Vol. 188, nr 4
• Strony: 217--237
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Koguep Njionou Blaise Blériot

• Department of Mathematics and Computer Science University of Dschang, BP 67, Cameroon

autor

Kwuida Leonard

• Bern University of Applied Sciences, Bern, Switzerland

autor

Lele Celestin

• Department of Mathematics and Computer Science University of Dschang, BP 67, Cameroon

Bibliografia

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