{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:08:33Z","timestamp":1759032513119},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218488504002941","type":"journal-article","created":{"date-parts":[[2004,10,21]],"date-time":"2004-10-21T02:02:01Z","timestamp":1098324121000},"page":"499-512","source":"Crossref","is-referenced-by-count":23,"title":["THE QUEST FOR RINGS ON BIPOLAR SCALES"],"prefix":"10.1142","volume":"12","author":[{"given":"MICHEL","family":"GRABISCH","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris I \u2014  Panth\u00e9on-Sorbonne, LIP6, 8 rue du Capitaine Scott, 75015 Paris, France"}]},{"given":"BERNARD","family":"DE BAETS","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B9000 Gent, Belgium"}]},{"given":"J\u00c1NOS","family":"FODOR","sequence":"additional","affiliation":[{"name":"Faculty of Veterinary Science, Szent  Istv\u00e1n University, Istv\u00e1n u. 2, H1078 Budapest, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","first-page":"229","volume":"12","author":"De Baets B.","journal-title":"Tatra Mt. Math. Publ."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(98)00325-7"},{"key":"rf4","volume-title":"Partially Ordered Algebraic Systems","author":"Fuchs L.","year":"1963"},{"key":"rf8","volume-title":"General Lattice Theory","author":"Gr\u00e4tzer G.","year":"1998"},{"key":"rf9","volume-title":"Uncertain Information Processing in Expert Systems","author":"H\u00e1jek P.","year":"1992"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488596000081"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1002\/int.4550080703"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1889-5_2"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90089-9"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00122574"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90061-1"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00133-6"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488504002941","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:00:18Z","timestamp":1565146818000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488504002941"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2004,8]]}},"alternative-id":["10.1142\/S0218488504002941"],"URL":"https:\/\/doi.org\/10.1142\/s0218488504002941","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}