On dependencies and independencies of fuzzy implication axioms

Fuzzy Sets and Systems

Volumn 161, Issue 10, 2010, Pages 1388-1405

  Shi, Y ^a   Van Gasse, B ^a   Ruan, D ^a,b   Kerre, E E ^a  

^a GHENT UNIVERSITY   (Belgium)

^b BELGIAN NUCLEAR RESEARCH CENTRE   (Belgium)

Author keywords

Fuzzy implication; Fuzzy implication axioms; Fuzzy logic operators; R implication; S implication

Indexed keywords

FUZZY IMPLICATIONS; FUZZY LOGIC OPERATORS; UNIT INTERVALS;

FUZZY SET THEORY; FUZZY SETS; MATHEMATICAL OPERATORS;

FUZZY LOGIC;

EID: 77949539824     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.12.003     Document Type: Article

References (22)

1. Baczyński M. Residual implications revisited. Notes on the Smets-Magrez theorem. Fuzzy Sets and Systems 145 (2004) 267-277
2. Baczyński M., and Drewniak J. Monotonic fuzzy implications. In: Szczepaniak P.S., Lisboa P.J.G., and Kacprzyk J. (Eds). Fuzzy Systems in Medicine (2000), Physica, Heidelberg 90-111
3. Baczyński M., and Jayaram B. Fuzzy Implications (2008), Springer, Berlin, Heidelberg
4. Bustince H., Burillo P., and Soria F. Automorphisms, negations and implication operators. Fuzzy Sets and Systems 134 (2003) 209-229
5. Bustince H., Pagola M., and Barrenechea E. Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. Information Sciences 177 (2007) 906-929
6. Drewniak J. Invariant fuzzy implications. Soft Computing 10 (2006) 506-513
7. Fodor J.C. Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems 69 (1995) 141-156
8. Fodor J.C., and Roubens M. Fuzzy Preference Modelling and Multicriteria Decision Support (1994), Kluwer Academic Publishers, Dordrecht
9. Jayaram B. Rule reduction for efficient inferencing in similarity based reasoning. International Journal of Approximate Reasoning 48 (2008) 156-173
10. Kerre E.E. A call for crispness in fuzzy set theory. Fuzzy Sets and Systems 29 (1989) 57-65
11. Kerre E.E., and Nachtegael M. Fuzzy Techniques in Image Processing (2000), Physica, New York
12. Klir G.J., and Yuan B. Fuzzy Sets and Fuzzy Logic, Theory and Applications (1995), Prentice-Hall, New Jersey
13. M. Nachtegael, H. Heijmans, D. Van der Weken, E. Kerre, Fuzzy adjunctions in mathematical morphology, in: Proc. JCIS 2003, North Carolina, USA, September 2003, pp. 202-205.
14. 0 implication: characteristics and applications. Fuzzy Sets and Systems 131 (2002) 297-302
15. Ruan D., and Kerre E.E. Fuzzy implication operators and generalized fuzzy method of cases. Fuzzy Sets and Systems 54 (1993) 23-37
16. Ruan D., and Kerre E.E. Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications (2000), Kluwer Academic Publishers, Boston
17. Mas M., Monserrat M., Torrens J., and Trillas E. A survey on fuzzy implication functions. IEEE Transactions on Fuzzy Systems 15 6 (2007) 1107-1121
18. Trillas E. sobre funciones de negación en la teoría de conjuntos difusos. Stochastica 3 1 (1979) 47-60
19. Trillas E., Alsina C., Renedo E., and Pradera A. On contra-symmetry and MPT conditionality in fuzzy logic. International Journal of Intelligent Systems 20 (2005) 313-326
20. Yager R.R. On some new classes of implication operators and their role in approximate reasoning. Information Sciences 167 (2004) 193-216
21. Yan P., and Chen G. Discovering a cover set of ARsi with hierarchy from quantitative databases. Information Sciences 173 (2005) 319-336
22. Zhang H.Y., and Zhang W.X. Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy sets. Fuzzy Sets and Systems 160 (2009) 107-118