Lattice-valued Overlap and Quasi-Overlap Functions

Rui Paiva, Eduardo Palmeira, Regivan Santiago, Benjamin Bedregal

Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of lattices and introduced a more general definition, called of quasi-overlaps, which arise of abolishes the continuity condition. In addition, are investigated the main properties of (quasi-)overlaps on bounded lattices, namely, convex sum, migrativity, homogeneity, idempotency and cancellation law. Moreover, we make a characterization of Archimedian overlaps.

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