Migrativity properties of 2-uninorms over semi-t-operators

Li-Jun, Ying ; Feng, Qin

Kybernetika, Tome 58 (2022) no. 3, pp. 354-375.

Résumé

In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$.

Détail

DOI : 10.14736/kyb-2022-3-0354

Classification : 03B52, 94D05
Keywords: 2-uninorms; uninorms; semi-t-operators; triangular norms; triangular conorms