Some construction methods for pseudo-overlaps and pseudo-groupings and their application in group decision making

In many real-world scenarios, the importance of different factors may vary, making commutativity an unreasonable assumption for aggregation functions, such as overlaps or groupings. To address this issue, researchers have introduced pseudo-overlaps and pseudo-groupings as their corresponding non-commutative generalizations. In this paper, we explore various construction methods for obtaining pseudo-overlaps and pseudo-groupings using overlaps, groupings, fuzzy negations, convex sums, and Riemannian integration. We then show the applicability of these construction methods in a multi-criteria group decision-making problem, where the importance of both the considered criteria and the experts vary. Our results highlight the usefulness of pseudo-overlaps and pseudo-groupings as a non-commutative alternative to overlaps and groupings.Diego García-Zamora is supported by the Spanish Ministry of Universities through a Formación de Profesorado Universitario (FPU2019/01203) grant. Rui Paiva is supported by the Brazilian funding agency CNPq (Brazilian Research Council) under Project 200282/2022-0