Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quest for rings on bipolar scales   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.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin