Computer Science – Discrete Mathematics
Scientific paper
2008-04-08
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems (2004) 499-512
Computer Science
Discrete Mathematics
Scientific paper
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.
Baets Bernard de
Fodor Janos
Grabisch Michel
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