General Pseudo Quasi-Overlap Functions on Lattices

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties.

Automated summary

This paper discusses the concepts of general quasi-overlaps and general pseudo-overlap functions on bounded lattices, and introduces methods for constructing these functions. By using the notions of pseudo-t-norms and pseudo-t-conorms, the concepts of additive and multiplicative generators for general pseudo-quasi-overlap functions on lattices are generalized, and some related properties are explored.