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1 DECISION LIP6 - Laboratoire d-Informatique de Paris 6 2 Ghent University 3 Szent Istvan University

Abstract : 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.

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Autor: Michel Grabisch - Bernard De Baets - Janos Fodor -



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