The quest for rings on bipolar scales

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 12, Issue 4, 2004, Pages 499-512

  Grabisch, Michel ^a   De Baets, Bernard ^b   Fodor, János ^c  

^a UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

^b GHENT UNIVERSITY   (Belgium)

^c SZENT ISTVÁN UNIVERSITY   (Hungary)

Author keywords

Ordered group; Pseudo addition; Pseudo multiplication; t conorm; t norm; Uninorm

Indexed keywords

DECISION THEORY; FUZZY SETS; MATHEMATICAL MODELS; PROBABILITY; THEOREM PROVING; UNCERTAIN SYSTEMS;

ORDERED GROUPS; PSEUDO-ADDITION; PSEUDO-MULTIPLICATION; UNINORMS;

LINEAR ALGEBRA;

EID: 4644336744     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488504002941     Document Type: Article

References (17)

1. B. De Baets. Coimplicators, the forgotten connectives. Tatra Mt. Math. Publ., 12:229-240, 1997.
2. B. De Baets. Idempotent uninorms. European J. Oper. Res., 118:631-642, 1999.
3. J. Fodor, B. De Baets, and T. Calvo. Characterization of uninorms with given continuous underlying t-norms and t-conorms. submitted.
4. L. Fuchs. Partially Ordered Algebraic Systems. Addison-Wesley, 1963.
5. M. Grabisch. Symmetric and asymmetric fuzzy integrals: the ordinal case. In 6th Int. Conf. on Soft Computing (Iizuka 2000), lizuka, Japan, October 2000.
6. M. Grabisch. The symmetric Sugeno integral. Fuzzy Sets and Systems, 139:473-490.
7. M. Grabisch. The Möbius function on symmetric ordered structures and its application to capacities on finite sets. Discrete Mathematics, submitted.
8. G. Grätzer. General Lattice Theory. Birkhaüser, 2nd edition, 1998.
9. P. Hájek, T. Havránek, and R. Jiroušek. Uncertain Information Processing in Expert Systems. CRC Press, 1992.
10. E.P. Klement, R. Mesiar, and E. Pap. On the relationship of associative compensatory operators to triangular norms and conorms. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 4:129-144, 1996.
11. E.P. Klement, R. Mesiar, and E. Pap. Triangular Norms. Kluwer Academic Publishers, 2000.
12. G. Mayor and J. Torrens. On a class of operators for expert systems. Int. J. of Intelligent Systems, 8:771-778, 1993.
13. R. Mesiar and M. Komorniková. Triangular norm-based aggregation of evidence under fuzziness. In: B. Bouchon-Meunier, editor, Aggregation and Fusion of Imperfect Information, Studies in Fuzziness and Soft Computing, pages 11-35. Physica Verlag, 1998.
14. T. Murofushi and M. Sugeno. Fuzzy t-conorm integrals with respect to fuzzy measures : generalization of Sugeno integral and Choquet integral. Fuzzy Sets and Systems, 42:57-71, 1991.
15. A. Tversky and D. Kahneman. Advances in prospect theory: cumulative representation of uncertainty. J. of Risk and Uncertainty, 5:297-323, 1992.
16. S. Weber. ⊥-decomposable measures and integrals for archimedean t-conorms ⊥. J. Math. Anal. Appl., 101:114-138, 1984.
17. R. Yager and A. Rybalov. Uninorm aggregation operators. Fuzzy Sets and Systems, 80:111-120, 1996.