The quest for rings on bipolar scales
| dc.creator | Grabisch, Michel | |
| dc.creator | De Baets, Bernard | |
| dc.creator | Fodor, Janos | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T12:18:12Z | |
| dc.date.available | 2026-07-07T12:18:12Z | |
| dc.description | We consider the interval $]{-1},1[$ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t. 0 are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conorms and t-norms, and we relate this construction to uninorms. We show that the only way to build a group is to use strict t-norms, and that there is no way to build a ring. Lastly, we show that the main result of this paper is connected to the theory of ordered Abelian groups. | |
| dc.identifier | https://arxiv.org/abs/0804.1270 | |
| dc.identifier | http://arxiv.org/abs/0804.1270 | |
| dc.identifier | International Journal of Uncertainty Fuzziness and Knowledge-Based Systems (2004) 499-512 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212331 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Rings and Algebras | |
| dc.title | The quest for rings on bipolar scales | |
| dc.type | text |