Aggregation functions and contradictory information

Fuzzy Sets and Systems

Volumn 191, Issue , 2012, Pages 41-61

  Pradera, Ana ^a   Beliakov, Gleb ^b   Bustince, Humberto ^c  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b DEAKIN UNIVERSITY   (Australia)

^c PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Aggregation functions; Bipolar aggregation; Contradictory information; Strong negations

Indexed keywords

AGGREGATION FUNCTIONS; BIVARIATE; CONTRADICTORY INFORMATION; NULLNORMS; STRONG NEGATIONS; T - NORM; UNINORMS;

ARTIFICIAL INTELLIGENCE; FUZZY SETS;

MATHEMATICAL OPERATORS;

EID: 84855543361     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.10.007     Document Type: Article

References (36)

1. C. Alsina, M. Frank, and B. Schweizer Associative Functions. Triangular Norms and Copulas 2006 World Scientific Singapore
2. G. Beliakov Construction of aggregation operators for automated decision making via optimal interpolation and global optimization J. Ind. Manage. Optim. 3 2007 193 208
3. G. Beliakov, and T. Calvo Construction of aggregation operators with noble reinforcement IEEE Trans. Fuzzy Syst. 15 2007 1209 1218 (Pubitemid 350268650)
4. G. Beliakov, T. Calvo, and J. Lázaro Pointwise construction of Lipschitz aggregation operators with specific properties Int. J. Uncertainty Fuzziness Knowl. Based Syst. 15 2007 193 223 (Pubitemid 46675089)
5. G. Beliakov, A. Pradera, and T. Calvo Aggregation Functions: A Guide for Practitioners 2007 Springer Berlin, Heidelberg
6. S. Benferhat, D. Dubois, S. Kaci, and H. Prade Bipolar possibility theory in preference modeling: representation, fusion and optimal solutions Inf. Fusion 7 2006 135 150 (Pubitemid 43133036)
7. T. Calvo, B. De Baets, and J. Fodor The functional equations of Frank and Alsina for uninorms and nullnorms Fuzzy Sets Syst. 120 2001 385 394 (Pubitemid 32372291)
8. T. Calvo, A. Kolesárová, M. Komorníková, and R. Mesiar Aggregation operators: properties, classes and construction methods T. Calvo, G. Mayor, R. Mesiar, Aggregation Operators. New Trends and Applications 2002 Physica-Verlag Heidelberg, New York 3 104
9. R. Cignoli, F. Esteva, L. Godo, and F. Montagna On a class of left-continuous t-norms Fuzzy Sets Syst. 131 2002 283 296
10. B. De Baets Idempotent uninorms Eur. J. Oper. Res. 118 1999 631 642
11. B. De Baets, H. De Meyer, and R. Mesiar Piecewise linear aggregation functions based on triangulation Inf. Sci. 181 2011 466 478
12. P. Drygaś On the structure of continuous uninorms Kybernetika 43 2007 183 196
13. D. Dubois, and H. Prade An overview of the asymmetric bipolar representation of positive and negative information in possibility theory Fuzzy Sets Syst. 160 2009 1355 1366
14. J. Fodor Contrapositive symmetry of fuzzy implications Fuzzy Sets Syst. 69 1995 141 156
15. J. Fodor, R. Yager, and A. Rybalov Structure of uninorms Int. J. Uncertainty Fuzziness Knowl. Based Syst. 5 1997 411 427 (Pubitemid 127531670)
16. M. Grabisch Aggregation on bipolar scales H. de Swart, E. Orlowska, G. Schmidt, M. Roubens, Theory and Applications of Relational Structures as Knowledge Instruments II, Lecture Notes in Computer Science 2006 Springer 355 371
17. M. Grabisch, J. Marichal, R. Mesiar, and E. Pap Aggregation Functions 2009 Cambridge University Press
18. S. Hu, and Z. Li The structure of continuous uni-norms Fuzzy Sets Syst. 124 2001 43 52 (Pubitemid 32833622)
19. S. Jenei New family of triangular norms via contrapositive symmetrization of residuated implications Fuzzy Sets Syst. 110 2000 157 174
20. S. Jenei Structure of Girard monoids on [0,1] E. Klement, S. Rodabaugh, Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets 2003 Kluwer Academic Publishers Dordrecht 277 308
21. S. Jenei How to construct left-continuous triangular norms: state of the art Fuzzy Sets Syst. 143 2004 27 45
22. E. Klement, R. Mesiar, and E. Pap Triangular Norms 2000 Kluwer Dordrecht
23. K.C. Maes, and B. De Baets Commutativity and self-duality: two tales of one equation Int. J. Approx. Reason. 50 2009 189 199
24. K.C. Maes, S. Saminger, and B. De Baets Representation and construction of self-dual aggregation operators Eur. J. Oper. Res. 177 2007 472 487 (Pubitemid 44647618)
25. J.L. Marichal Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral Eur. J. Oper. Res. 155 2004 771 791
26. J. Martín, G. Mayor, and J. Torrens On locally internal monotonic operations Fuzzy Sets Syst. 137 2003 27 42
27. M. Mas, G. Mayor, and J. Torrens T-operators Int. J. Uncertainty Fuzziness Knowl. Based Syst. 7 1999 31 50 (Pubitemid 129629658)
28. R. Mesiar, and M. Komorníková Triangular norm-based aggregation of evidence under fuzziness B. Bouchon-Meunier, Aggregation and Fusion of Imperfect Information 1998 Physica-Verlag Heidelberg 11 35
29. A. Mesiarová-Zemánková, R. Mesiar, and K. Ahmad The balancing Choquet integral Fuzzy Sets Syst. 161 2010 2243 2255
30. R. Nelsen An Introduction to Copulas second ed. 2006 Springer New York
31. A. Pradera Uninorms and non-contradiction V. Torra, Y. Narukawa, MDAI, Lecture Notes in Computer Science vol. 5285 2008 Springer 50 61
32. A. Pradera, and E. Trillas Aggregation, non-contradiction and excluded-middle Mathware Soft Comput. XIII 2006 189 201
33. A. Pradera, and E. Trillas Aggregation operators from the ancient NC and EM point of view Kybernetika 42 2006 243 260
34. V. Torra, and Y. Narukawa Modeling Decisions: Information Fusion and Aggregation Operators 2007 Springer
35. E. Trillas Sobre funciones de negación en la teoría de los subconjuntos difusos Stochastica III 1979 47 59 (in Spanish) Reprinted (English version) in: S. Barro, et al. (Eds.), Advances of Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43
36. R. Yager, and A. Rybalov Uninorm aggregation operators Fuzzy Sets Syst. 80 1996 111 120 (Pubitemid 126682856)