Congruence Relations and Direct Decomposition of Uninorms on Bounded Lattices
Funda Karaçal, Ümıt Ertuğrul, Samet Arpacı, M. Nesibe Kesicioğlu · International Journal of Uncertainty Fuzziness and Knowledge-Based Systems · 2023
In this paper, the concept of [Formula: see text]-compatible congruence and its related properties are studied. We also focus on homomorphism theorems for uninorms. Decomposition of uninorms is investigated via factor congruences, at first. Subsequently, we investigate decomposition of conjunctive and disjunctive uninorms, respectively. After all, we determine necessary and sufficient conditions for decomposition of some uninorms that are neither conjunctive nor disjunctive. In addition to all these, we shed light on the application of our results with the examples.