On the distributivity of fuzzy implications over representable uninorms

Fuzzy Sets and Systems

Volumn 161, Issue 17, 2010, Pages 2256-2275

  Baczyński, Michał ^a  

^a UNIVERSITY OF SILESIA   (Poland)

Author keywords

Functional equations; Fuzzy connectives; Fuzzy implication; Uninorm

Indexed keywords

APPROXIMATE REASONING; CAUCHY FUNCTIONAL EQUATIONS; DISTRIBUTIVE EQUATIONS; DISTRIBUTIVITY; FUNCTIONAL EQUATION; FUZZY CONNECTIVES; FUZZY IMPLICATIONS; T - NORM; T-CONORMS; UNINORMS; VERTICAL SECTION;

FUNCTIONAL ANALYSIS; FUZZY CONTROL;

MATHEMATICAL OPERATORS;

EID: 77955282703     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2010.03.005     Document Type: Article

References (20)

1. J. Aczél Lectures on Functional Equations and their Applications 1966 Academic Press New York
2. M. Baczyński On a class of distributive fuzzy implications Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 9 2001 229 238
3. M. Baczyński Contrapositive symmetry of distributive fuzzy implications Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 10 2002 135 147
4. M. Baczyński On the distributivity of fuzzy implications over continuous and Archimedean triangular conorms Fuzzy Sets and Systems 161 2010 1406 1419
5. M. Baczyński, and B. Jayaram Fuzzy implications Studies in Fuzziness and Soft Computing Vol. 231 2008 Springer Berlin, Heidelberg
6. M. Baczyński, and B. Jayaram On the distributivity of fuzzy implications over nilpotent or strict triangular conorms IEEE Trans. Fuzzy Syst. 17 2009 590 603
7. J. Balasubramaniam, and C.J.M. Rao On the distributivity of implication operators over T- and S-norms IEEE Trans. Fuzzy Syst. 12 2004 194 198
8. H. Bustince, P. Burillo, and F. Soria Automorphisms, negation and implication operators Fuzzy Sets and Systems 134 2003 209 229
9. W.E. Combs, and J.E. Andrews Combinatorial rule explosion eliminated by a fuzzy rule configuration IEEE Trans. Fuzzy Syst. 6 1998 1 11
10. S. Dick, and A. Kandel Comments on "Combinatorial rule explosion eliminated by a fuzzy rule configuration" IEEE Trans. Fuzzy Syst. 7 1999 475 477
11. J. Fodor, and B. DeBaets Uninorm basics P.P. Wang, D. Ruan, E.E. Kerre, Fuzzy Logic: A Spectrum of Theoretical and Practical Issues, Studies in Fuzziness and Soft Computing Vol. 215 2007 Springer Berlin, Heidelberg 49 64
12. J.C. Fodor, and M. Roubens Fuzzy Preference Modelling and Multicriteria Decision Support 1994 Kluwer Dordrecht
13. J.C. Fodor, R.R. Yager, and A. Rybalov Structure of uninorms Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 5 1997 411 427
14. L. Kitainik Fuzzy Decision Procedures With Binary Relations 1993 Kluwer Dordrecht
15. M. Kuczma An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's Inequality 1985 PWN-Polish Scientific Publishers & Silesian University Warszawa, Katowice
16. J.M. Mendel, and Q. Liang Comments on "Combinatorial rule explosion eliminated by a fuzzy rule configuration" IEEE Trans. Fuzzy Syst. 7 1999 369 371
17. D. Ruiz-Aguilera, and J. Torrens Distributivity of strong implications over conjunctive and disjunctive uninorms Kybernetika 42 2005 319 336
18. D. Ruiz-Aguilera, and J. Torrens Distributivity of residual implications over conjunctive and disjunctive uninorms Fuzzy Sets and Systems 158 2007 23 37
19. E. Trillas, and C. Alsina On the law [ p ∧ q → r ] = [ (p → r ) ∨ (q → r ) ] in fuzzy logic IEEE Trans. Fuzzy Syst. 10 2002 84 88
20. R.R. Yager, and A. Rybalov Uninorm aggregation operators Fuzzy Sets and Systems 80 1996 111 120