The law of importation versus the exchange principle on fuzzy implications

Fuzzy Sets and Systems

Volumn 168, Issue 1, 2011, Pages 47-69

  Massanet, Sebastia ^a   Torrens, Joan ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

(S,N) implication; (U,N) implication; Exchange principle; Fuzzy connectives and aggregation operators; Implication function; Law of importation; R implication; RU implication; Uninorm

Indexed keywords

(S,N)-IMPLICATION; (U,N)-IMPLICATION; EXCHANGE PRINCIPLE; FUZZY CONNECTIVES AND AGGREGATION OPERATORS; IMPLICATION FUNCTION; LAW OF IMPORTATION; R-IMPLICATION; RU-IMPLICATION; UNINORMS;

MATHEMATICAL OPERATORS;

EID: 79551507550     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2010.12.012     Document Type: Article

References (35)

1. I. Aguiló, J. Suñer, J. Torrens, A characterization of residual implications derived from uninorms, in: Proceedings of IFSA-EUSFLAT2009, Lisbon, 2009, pp. 333-338.
2. C. Alsina, J.L. Castro, E. Trillas, On the characterization of S and R implications, in: Proceedings of VIth IFSA World Congress, 1995, pp. 317-319.
3. M. Baczyński, and B. Jayaram On the characterization of (S,N)-implications Fuzzy Sets and Systems 158 2007 1713 1727
4. M. Baczyński, and B. Jayaram Fuzzy Implications 2008 Springer Berlin, Heidelberg
5. M. Baczyński, and B. Jayaram (S,N)- and R-implications: a state-of-the-art survey Fuzzy Sets and Systems 159 2008 1836 1859
6. M. Baczyński, and B. Jayaram (U,N)-implications and their characterizations Fuzzy Sets and Systems 160 2009 2049 2062
7. M. Baczyński Residual implications revisited. notes on the smets-magrez theorem Fuzzy Sets and Systems 145 2004 267 277
8. B. De Baets, Model implicators and their characterization, in: Proceedings of 1st ICSC International Symposium on Fuzzy Logic, 1995, pp. A42-A49.
9. H. Bustince, V. Mohedano, E. Barrenechea, and M. Pagola Definition and construction of fuzzy DI-subsethood measures Information Sciences 176 2006 3190 3231
10. H. Bustince, M. Pagola, and E. Barrenechea Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images Information Sciences 177 2007 906 929
11. B. De Baets, and J.C. Fodor Residual operators of uninorms Soft Computing 3 1999 89 100
12. J.C. Fodor, and M. Roubens Fuzzy Preference Modelling and Multicriteria Decision Support 1994 Kluwer Academic Publishers Dordrecht
13. J.C. Fodor, R.R. Yager, and A. Rybalov Structure of uninorms International Journal of Uncertainty, Fuzziness and Knowledge 5 1997 411 427
14. J.C. Fodor A new look at fuzzy connectives Fuzzy Sets and Systems 57 1993 141 148
15. J.C. Fodor Contrapositive symmetry on fuzzy implications Fuzzy Sets and Systems 69 1995 141 156
16. J.A. Goguen The logic of inexact concepts Synthese 19 1968 325 373
17. S. Gottwald A Treatise on Many-Valued Logic 2001 Research Studies Press Baldock
18. B. Jayaram On the law of importation (x ∧ y ) → z ≡ (x → (y → z ) ) in fuzzy logic IEEE Transactions on Fuzzy Systems 16 2008 130 144
19. E.E. Kerre, C. Huang, and D. Ruan Fuzzy Set Theory and Approximate Reasoning 2004 Wu Han University Press Wu Chang
20. E.P. Klement, and R. Mesiar Open problems posed at the eighth international conference in fuzzy set theory and applications (FSTA 2006 Liptovský Ján Slovakia) Kybernetika 42 2006 225 235
21. E.P. Klement, R. Mesiar, and E. Pap Triangular Norms 2000 Kluwer Academic Publishers Dordrecht
22. M. Mas, M. Monserrat, J. Torrens, and E. Trillas A survey on fuzzy implication functions IEEE Transactions on Fuzzy Systems 15 6 2007 1107 1121
23. M. Mas, M. Monserrat, J. Torrens, On the law of importation for some kinds of fuzzy implications derived from uninorms, in: Proceedings of IPMU'08, Torremolinos (M'alaga), 2008, pp. 1303-1310.
24. M. Mas, M. Monserrat, and J. Torrens The law of importation for discrete implications Information Sciences 179 2009 4208 4218
25. J. Pavelka, On fuzzy logic i, ii, iii., Zeit. Math. Logic. Grundl. Math. 25:45, 52, 119, 134, 447, 464, 1979.
26. D. Ruiz-Aguilera, and J. Torrens R-implications and S-implications from uninorms continuous in ] 0, 1 [ 2 and their distributivity over uninorms Fuzzy Sets and Systems 160 2009 832 852
27. D. Ruiz, and J. Torrens Residual implications and co-implications from idempotent uninorms Kybernetika 40 2004 21 38
28. B. Schweizer, and A. Sklar Probabilistic Metric Spaces 1983 North-Holland Amsterdam
29. P. Smets, and P. Magrez Implications in fuzzy logic International Journal of Approximate Reasoning 1 1987 327 347
30. R. Smogura A note on the article: residual implications revisited. Notes on the Smets-Magrez theorem Fuzzy Sets and Systems 157 2006 466 469
31. E. Trillas, L. Valverde, On implication and indistinguishability in the setting of fuzzy logic, Management Decision Support Systems using Fuzzy Sets and Possibility Theory, 1985, pp. 196-212.
32. E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica III/1, 1979, pp. 47-60.
33. I.B. Türksen, V. Kreinovich, and R.R. Yager A new class of fuzzy implications. Axioms of fuzzy implication revisited Fuzzy Sets and Systems 100 1998 267 272
34. R.R. Yager, and A. Rybalov Uninorm aggregation operators Fuzzy Sets and Systems 80 1996 111 120
35. P. Yan, and G. Chen Discovering a cover set of ARsi with hierarchy from quantitative databases Information Sciences 173 2005 319 336