On ordinal sums of t-norms and t-conorms on bounded posets

• Autoři: DVOŘÁK Antonín; HOLČAPEK Michal; PASEKA Jan
• Rok publikování: 2020
• Druh: Článek ve sborníku
• Konference: 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://ieeexplore.ieee.org/document/9177618
• Doi: https://doi.org/10.1109/FUZZ48607.2020.9177618
• Klíčová slova: t-norms; t-conorms; bounded posets; ordinal sum
• Popis: This paper continues and generalizes the line of research on ordinal sum of t-norms and t-conorms on bounded lattices. We introduce a new ordinal sum construction on bounded posets based on interior and closure operators. Our proposed method provides a simple tool to introduce new classes of t-norms and t-conorms. Several necessary and sufficient conditions are presented for ensuring whether our generalized ordinal sum on a bounded posets of arbitrary t-norms is, in fact, a t-norm. We show that in this general setting the existence of our ordinal sum for t-norms requires that the respective interior operators are t-norm preserving.

Související projekty

• Nové přístupy k agregačním operátorům v analýze a zpracování dat