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By Célia da Costa Pereira, Andrea G. B. Tettamanzi (auth.), Francesco Masulli, Sushmita Mitra, Gabriella Pasi (eds.)

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Read Online or Download Applications of Fuzzy Sets Theory: 7th International Workshop on Fuzzy Logic and Applications, WILF 2007, Camogli, Italy, July 7-10, 2007. Proceedings PDF

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Additional resources for Applications of Fuzzy Sets Theory: 7th International Workshop on Fuzzy Logic and Applications, WILF 2007, Camogli, Italy, July 7-10, 2007. Proceedings

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We will consider the Smyth ordering among sets, and we will write X S Y if and only if for every y ∈ Y there exists x ∈ X such that x y. Definition 4. Let f : P −→ 2P be a multi-valued function on a poset P : – We say that f is isotone if and only if for all x, y ∈ P we have that x y implies f (x) S f (y). – We say that f is inflationary if and only if {x} S f (x) for every x ∈ P . As our intended application is focused on multilattice-based logic programs, we can assume the existence of minimal fixed points for a given multi-valued function on a multilattice (since in [7] the existence of minimal fixed points was proved for the TP operator).

Mitra, and G. ): WILF 2007, LNAI 4578, pp. 28–36, 2007. c Springer-Verlag Berlin Heidelberg 2007 Measuring the Interpretive Cost in Fuzzy Logic Computations 29 logic programming [11,10]. Informally speaking, a multi–adjoint logic program can be seen as a set of rules each one annotated by a truth degree and a goal is a query to the system plus a substitution (initially the empty substitution, denoted by id). Given a multi–adjoint logic program, goals are evaluated in two separate computational phases.

For further explanations, the reader can see [7, 8]. Definition 1. A complete multilattice is a partially ordered set, M, , such that for every subset X ⊆ M , the set of upper (resp. lower) bounds of X has minimal (resp. maximal) elements, which are called multi-suprema (resp. multi-infima). The sets of multi-suprema and multi-infima of a set X are denoted by multisup(X) and multinf (X). It is straightforward to note that these sets consist of pairwise incomparable elements (also called antichains).

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