Idempotent uninorms on finite ordinal scales

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 17, Issue 1, 2009, Pages 1-14

  De Baets, Bernard ^a   Fodor, János ^b   Ruiz Aguilera, Daniel ^c   Torrens, Joan ^c  

^a GHENT UNIVERSITY   (Belgium)

^b OBUDA UNIVERSITY   (Hungary)

^c UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

Decreasing function; Discrete idempotent uninorm; Finite ordinal scale; Symmetry

Indexed keywords

SOFTWARE ENGINEERING;

DECREASING FUNCTIONS; DISCRETE IDEMPOTENT UNINORM; FINITE ORDINAL SCALE; IDEMPOTENT UNINORM; NEUTRAL ELEMENTS; ORDINAL SCALE; SYMMETRY;

ARTIFICIAL INTELLIGENCE;

EID: 65249160177     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021848850900570X     Document Type: Article

References (19)

1. B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems 104 (1999) 61-75.
2. J. C. Fodor, Smooth associative operations on finite ordinal scales, IEEE Trans. Fuzzy Systems 8 (2000) 791-795.
3. M. Mas, G. Mayor and J. Torrens, t-operators and uninorms on a finite totally ordered set, Int. J. Intelligent Systems 14 (1999) 909-922.
4. M. Mas, M. Monserrat and J. Torrens, On bisymmetric operators on a finite chain, IEEE Trans. Fuzzy Systems 11 (2003) 647-651.
5. M. Mas, M. Monserrat and J. Torrens, On left and right uninorms on a finite chain, Fuzzy Sets and Systems 146 (2004) 3-17.
6. G. Mayor and J. Torrens, On a class of operators for expert systems, Int. J. Intelligent Systems 8 (1993) 771-778.
7. R. Yager and A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996) 111-120.
8. B. De Baets and R. Mesiar, Discrete triangular norms, in Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, eds. S. Rodabaugh and E.-P. Klement (Kluwer Academic Publishers, 2003), 20, pp. 389-400.
9. G. Mayor and J. Torrens, Triangular norms in discrete settings, in Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, eds. E. P. Klement and R. Mesiar (Elsevier, Amsterdam, 2005), pp. 189-230.
10. G. Mayor, J. Sũner and J. Torrens, Copula-like operations on finite settings, IEEE Trans. Fuzzy Systems 13 (2005) 468-477.
11. P. Dryga's, Discussion of the structure of uninorms, Kybernetika 41 (2005) 213-226.
12. B. De Baets, J. C. Fodor and T. Calvo, Characterization of uninorms with given continuous underlying t-norms and t-conorms, submitted.
13. J. Fodor and B. De Baets, Uninorm basics, in Fuzzy Logic: A Spectrum of Theoretical and Practical Issues, Studies in Fuzziness and Soft Computing, eds. P.Wang, D. Ruan and E. Kerre (Springer, 2007), 215, pp. 49-64.
14. B. De Baets, J. Fodor, D. Ruiz-Aguilera and J. Torrens, Uninorms: Classification and representation, in preparation.
15. F. S. Roberts, Measurement Theory, Encyclopedia of Mathematics and its Applications (Addison-Wesley, Reading, MA, 1978), Vol. 7.
16. B. De Baets, Idempotent uninorms, European J. Oper. Res. 118 (1999) 631-642.
17. J. Mart'In, G. Mayor and J. Torrens, On locally internal monotonic operations, Fuzzy Sets and Systems 137 (2003) 27-42.
18. E. Czogala and J. Drewniak, Associative monotonic operations in fuzzy set theory, Fuzzy Sets and Systems 12 (1984) 249-269.
19. K. C. Maes and B. De Baets, Orthosymmetrical monotone functions, Bulletin of the Belgian Mathematical Society - Simon Stevin 14 (2007) 99-116.