QL-implications versus D-implications

Kybernetika

Volumn 42, Issue 3, 2006, Pages 351-366

  Mas, Margarita ^a   Monserrat, Miquel ^a   Torrens, Joan ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

D implication; Implication operator; QL implication; t conorm; t norm

Indexed keywords

EID: 33847778398     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (15)

1. 2(x,T(N(x),y)). In: Functional Equations, Results and Advances (Z. Daróczy and Z. Páles, eds.), Kluwer Academic Publishers, Dordrecht 2002, pp. 323-334.
2. H. Bustince, P. Burillo, and F. Soria: Automorphisms, negations and implication operators. Fuzzy Sets and Systems 134 (2003), 209-229.
3. B. De Baets: Model implicators and their characterization. In: Proc. First ICSC International Symposium on Fuzzy Logic (N. Steele, ed.), ICSC Academic Press, Zürich 1995, pp. A42-A49.
4. J. C. Fodor: On fuzzy implication operators. Fuzzy Sets and Systems 42 (1991), 293-300.
5. J. C. Fodor: Contrapositive symmetry on fuzzy implications. Fuzzy Sets and Systems 69 (1995), 141-156.
6. M. J. Frank: On the simultaneous associativity of F(x, y) and x + y- F(x, y). Aequationes Math. 19 (1979), 194-226.
7. S. Jenei: New family of triangular norms via contrapositive symmetrization of residuated implications. Fuzzy Sets and Systems 110 (2000), 157-174.
8. E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000.
9. M. Mas, M. Monserrat, and J. Torrens: QL-Implications on a finite chain. In: Proc. Eusflat-2003, Zittau 2003, pp. 281-284.
10. M. Mas, M. Monserrat, and J. Torrens: On two types of discrete implications. Internat. J. Approx. Reason. 40 (2005), 262-279.
11. M. Nachtegael and E. Kerre: Classical and fuzzy approaches towards mathematical morphology. In: Fuzzy Techniques in Image Processing (E. Kerre and M. Nachtegael, eds., Studies in Fuzziness and Soft Computing, Vol. 52), Physica-Verlag, Heidelberg 2000, pp. 3-57.
12. 0 implication: characteristics and applications. Fuzzy Sets and Systems 131 (2002), 297-302.
13. E. Trillas, C. del Campo, and S. Cubillo: When QM-operators are implication functions and conditional fuzzy relations. Internat. J. Intelligent Systems 15 (2000), 647-655.
14. E. Trillas, C. Alsina, E. Renedo, and A. Pradera: On contra-symmetry and MPT conditionality in fuzzy logic. Internat. J. Intelligent Systems 20 (2005), 313-326.
15. R. R. Yager: Uninorms in fuzzy systems modelling. Fuzzy Sets and Systems 122 (2001), 167-175.