Distributivity of strong implications over conjunctive and disjunctive uninorms

Kybernetika

Volumn 42, Issue 3, 2006, Pages 319-336

  Ruiz Aguilera, Daniel ^a   Torrens, Joan ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

Distributivity; Implication operator; R implication; S implication; t conorm; t norm; Uninorm

Indexed keywords

EID: 33750723879     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (18)

1. J. Balasubramaniam and C. J. M. Rao: On the distributivity of implication operators over T and S norms. IEEE Trans. Fuzzy Systems 12 (2004), 194-198.
2. W. E. Combs: Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Trans. Fuzzy Systems 6 (1998), 1-11.
3. W. E. Combs and J. E. Andrews: Author's reply. IEEE Trans. Fuzzy Systems 7(1999), 371.
4. W. E. Combs and J. E. Andrews: Author's reply. IEEE Trans. Fuzzy Systems 7(1999), 478-479.
5. B. De Baets and J. C. Fodor: Residual operators of uninorms. Soft Computing 5 (1999), 89-100.
6. S. Dick and A. Kandel: Comments on "combinatorial rule explosion eliminated by a fuzzy rule configuration". IEEE Trans. Fuzzy Systems 7 (1999), 475-477.
7. J.C. Fodor, R. R. Yager, and A. Rybalov: Structure of uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 5 (1997), 4, 411-427.
8. M. Gonzalez, D. Ruiz, and J. Torrens: Algebraic properties of fuzzy morphological operators based on uninorms. In: Artificial Intelligence Research and Development (I. Aguiló, L. Valverde, and M. Escrig, eds.), IOS Press 2003, pp. 27-38.
9. E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000.
10. J. Martín, G. Mayor, and J. Torrens: On locally internal monotonic operations. Fuzzy Sets and Systems 137 (2003), 1, 27-42.
11. M. Mas, G. Mayor, and J. Torrens: The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems 128 (2002), 209-225.
12. M. Mas, G. Mayor, and J. Torrens: Corrigendum to "The distributivity condition for uninorms and t-operators". Fuzzy Sets and Systems 128 (2002), 209-225, Fuzzy Sets and Systems 153 (2005), 297-299.
13. J. M. Mendel and Q. Liang: Comments on "combinatorial rule explosion eliminated by a fuzzy rule configuration". IEEE Trans. Fuzzy Systems 7 (1999), 369-371.
14. D. Ruiz and J. Torrens: Distributive idempotent uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 11 (2003), 413-428.
15. D. Ruiz and J. Torrens: Residual implications and co-implications from idempotent uninorms. Kybernetika 40 (2004), 21-38.
16. D. Ruiz and J. Torrens: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm. IEEE Trans. Fuzzy Systems 14 (2006), 180-190.
17. D. Ruiz and J, Torrens: Distributive residual implications from uninorms. In: Proc. EUSFLAT-2005, Barcelona 2005, pp. 369-374.
18. E. Trillas and C. Alsina: On the law [p ∧ q → r] ≡ [(p → r) ∨ (q → r)] in fuzzy logic. IEEE Trans. Fuzzy Systems 10 (2002), 84-88.