THE QUEST FOR RINGS ON BIPOLAR SCALES
2004 ◽
Vol 12
(04)
◽
pp. 499-512
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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.
2021 ◽
Keyword(s):
1989 ◽
Vol 82
(5)
◽
pp. 260-263
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2004 ◽
Vol 10
(1)
◽
pp. 32-39
Keyword(s):
2004 ◽
Vol 9
(1)
◽
pp. 41-43