Non-deterministic Algebraic Structures for Soft Computing

Cabrera, Inma P.; Ojeda‐Aciego, Manuel

doi:10.1007/978-3-642-21498-1_55

Cited by 2 publications

(2 citation statements)

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“…A u is the set of all upper bounds 5 of A and A l is the set of all lower bounds 6 . Moreover, A u is an up-set and A l is a down-set.…”

Section: Dedekind-macneille Completionmentioning

confidence: 99%

“…Although out of the scope of this paper, in the future we plan to analyse some canonical extensions for multi-adjoint lattices, formally introduced in [10] (see also [11,31], which study the completion of an n-ordered set) that have associated monotone operators and analyse the results especially for the habitual domains in MALP of bilattices and trilattices [4][5][6][7][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices

Morcillo

Moreno

Penabad

et al. 2012

International Journal of Computer Mathematics

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Fuzzy logic programming tries to introduce fuzzy logic into logic programming in order to provide new generation computer languages which incorporate comfortable programming resources for helping the development of applications where uncertainty could play an important role. In this sense, the mathematical concept of multi-adjoint lattice has been successfully exploited into the so-called Multi-Adjoint Logic Programming approach, MALP in brief, for modelling flexible notions of truth-degrees beyond the simpler case of true and false. In this paper, we focus on two relevant mathematical concepts for this kind of domains useful for evaluating MALP. On the one side, we adapt the classical notion of Dedekind-MacNeille completion in order to relax some usual hypothesis on such kind of ordered sets, and next we study the advantages of generating multi-adjoint lattices as the Cartesian product of previous ones. On the practical side, we show that the formal mechanisms described before have direct correspondences with interesting debugging tasks into the 'Fuzzy Logic Programming Environment for Research', FLOPER in brief, developed in our research group.

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“…A u is the set of all upper bounds 5 of A and A l is the set of all lower bounds 6 . Moreover, A u is an up-set and A l is a down-set.…”

Section: Dedekind-macneille Completionmentioning

confidence: 99%