The quest for rings on bipolar scales

Michel Grabisch, Bernard de Baets and Janos Fodor
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Bernard de Baets: UGENT - Universiteit Gent = Ghent University = Université de Gand
Janos Fodor: Szent István University

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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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Date: 2004
Note: View the original document on HAL open archive server: https://hal.science/hal-00271217v1
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Citations: View citations in EconPapers (4)

Published in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004, 12 (4), pp.499-512

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00271217

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