Practical inference with systems of gradual implicative rules

IEEE Transactions on Fuzzy Systems

Volumn 17, Issue 1, 2009, Pages 61-78

  Jones, Hazaël ^a,b   Charnomordic, Brigitte ^c   Dubois, Didier ^d,e,f   Guillaume, Serge ^a  

^a UMR ITAP   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^c CEMAGREF   (France)

^d UNIVERSITÉ PAUL SABATIER   (France)

^e CNRS   (France)

^f UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Fuzzy inputs; Fuzzy rules; Gradual implicative rules; Inference method; Input decomposition

Indexed keywords

ARTIFICIAL INTELLIGENCE; FUZZY RULES; FUZZY SETS;

CHEESE-MAKING PROCESS; DOUBLE DECOMPOSITION; FUZZY INPUT; GRADUAL IMPLICATIVE RULES; HIGHER-DIMENSIONAL; INFERENCE METHODS; INPUT DECOMPOSITION; INTERPOLATIVE REASONING;

FUZZY INFERENCE;

EID: 60549101544     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2008.2007851     Document Type: Article

References (33)

1. E. H. Mamdani and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," Int. J. Man-Mach. Stud., vol. 7, pp. 1-13, 1975.
2. D. Dubois and H. Prade, "What are fuzzy rules and how to use them," Fuzzy Sets Syst., vol. 84, no. 2, pp. 169-185, 1996.
3. J. F. Baldwin and N. C. F. Guild, "Modelling controllers using fuzzy relations," Kybernetes, vol. 9, pp. 223-229, 1980.
4. A. Di Nola, W. Pedrycz, and S. Sessa, "An aspect of discrepancy in the implementation ofmodus ponens in the presence of fuzzy quantities," Int. J. Approx. Reason., vol. 3, no. 3, pp. 259-265, 1989.
5. J.Mendel, "Fuzzy logic systems for engineering: A tutorial," Proc. IEEE, vol. 83, no. 3, pp. 345-377, Mar. 1995.
6. H. Jones, S. Guillaume, B. Charnomordic, and D. Dubois, "Practical use of fuzzy implicative gradual rules in knowledge representation and comparison with Mamdani rules," presented at the EUSFLAT, Barcelona, Spain, 2005.
7. D. Dubois and H. Prade, "Gradual inference rules in approximate reasoning," Inf. Sci., vol. 61, pp. 103-122, 1992.
8. S. Galichet, D. Dubois, and H. Prade, "Imprecise specification of ill-known functions using gradual rules," Int. J. Approx. Reason. vol. 35, no. 3, pp. 205-222, 2004.
9. L. Ughetto, D. Dubois, and H. Prade, "Implicative, conjunctive fuzzy rules - A tool for reasoning from knowledge examples," in Proc. AAAI 1999. Orlando FL/Cambridge, MA: AAAI Press/MIT Press, pp. 214-219.
10. N. Karnik, J. Mendel, and Q. Liang, "Type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 643-658, Dec. 1999.
11. D. Dubois, H. Prade, and L. Ughetto, "A new perspective on reasoning with fuzzy rules," Int. J. Intell. Syst., vol. 18, no. 5, pp. 541-567, 2003.
12. L. A. Zadeh, "A theory of approximate reasoning," Mach. Intell., vol. 9, pp. 149-194, 1979.
13. D. Dubois, H. Prade, and M. Grabisch, "Gradual rules and the approximation of control laws," in Theoretical Aspects of Fuzzy Control. New York: Wiley, 1995, pp. 147-181.
14. R. Martin-Clouaire, "Semantics and computation of the generalized modus ponens: The long paper," Int. J. Approx. Reason., vol. 3, pp. 195-217, 1987.
15. E. Trillas and L. Valverde, "On some functionally expressible implications for fuzzy set theory," in Proc. 3rd Int. Semin. Fuzzy Set Theory, E. Klement, Ed., 1981, pp. 173-190.
16. D. Dubois, H. Prade, and L. Ughetto, "Fuzzy logic, control engineering and artificial intelligence," in Fuzzy Algorithms for Control, H. Verbruggen, H.-J. Zimmermann, and R. Babuska, Eds. Dordrecht, The Netherlands: Kluwer, 1999, pp. 17-57.
17. B. Schott and T. Whalen, "Nonmonotonicity and discretization error in fuzzy rule-based control using coa and mom defuzzification," in Proc. 5th IEEE Int. Conf. Fuzzy Syst., 1996, pp. 450-456.
18. E. Van Broekhoven, "Monotonicity aspects of linguistic fuzzy models" Ph.D. dissertation, Univ. Gent, Ghent, Belgium, Mar. 30, 2007.
19. D. Dubois, H. Prade, and L. Ughetto, "Checking the coherence and redundancy of fuzzy knowledge bases," IEEE Trans. Fuzzy Syst., vol. 5, no. 3, pp. 398-417, Aug. 1997.
20. D. Dubois, R. Martin-Clouaire, and H. Prade, "Practical computing in fuzzy logic," in Fuzzy Computing: Theory, Hardware, and Applications M. M. Gupta and T. Yamakawa, Eds. Amsterdam, The Netherlands: North Holland, 1988, pp. 11-34.
21. L. Ughetto, D. Dubois, and H. Prade, "Efficient inference procedures with fuzzy inputs," in Proc. FUZZY IEEE, Barcelona, Spain, 1997, pp. 567-572.
22. M. Sugeno and T. Takagi, "Multi-dimensional fuzzy reasoning," Fuzzy Sets Syst., vol. 9, pp. 313-325, 1983.
23. D. Dubois and H. Prade, "Basic issues on fuzzy rules and their application to fuzzy control," in Proc. Workshops Fuzzy Logic Fuzzy Control (IJCAI 1991). Springer-Verlag, London, U.K., 1994, pp. 3-14.
24. L. Koczy and K. Hirota, "Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases," Inf. Sci., vol. 71, pp. 169-201, 1993.
25. S. Jenei, E.-P. Klement, and R. Konzel, "Interpolation and extrapolation of fuzzy quantities revisited - An axiomatic approach," Soft Comput., vol. 5, no. 3, pp. 179-193, 2001.
26. S. Jenei, E.-P. Klement, and R. Konzel, "Interpolation and extrapolation of fuzzy quantities - The multiple-dimensional case," Soft Comput., vol. 6, no. 3/4, pp. 258-270, 2002.
27. L. Ughetto, "Inferential independence of fuzzy rules," in Proc. ECAI, 1998, pp. 605-609.
28. N. N. Morsi and A. A. Fahmy, "On generalized modus ponens with multiple rules and a residuated implication," Fuzzy Sets Syst., vol. 129, no. 2, pp. 267-274, 2002.
29. N. N. Morsi, "A small set of axioms for residuated logic," Inf. Sci., vol. 175, no. 1/2, pp. 85-96, 2005.
30. D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Plenum, 1988.
31. D. Dubois and H. Prade, "Rough fuzzy sets and fuzzy rough sets," Int. J. Gen. Syst., vol. 17, pp. 191-209, 1990.
32. S. Guillaume, B. Charnomordic, and J.-L. Lablée, FisPro: An open source portable software for fuzzy inference systems, 2002.
33. J. Gebhardt and R. Kruse, "Background to and perspectives on possibilistic graphical models," in Applications of Uncertainty Formalisms (Lecture Notes in Computer Science 1455), A. Hunter and S. Parsons, Eds. New York: Springer-Verlag, 1998, pp. 397-414.