On the computational aspects of the BK-subproduct inference mechanism

IEEE International Conference on Fuzzy Systems

Volumn , Issue , 2009, Pages 1181-1186

  Štěpnička, Martin ^a   Jayaram, Balasubramaniam ^b  

^a UNIVERSITY OF OSTRAVA   (Czech Republic)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE REASONING; COMPOSITIONAL RULE OF INFERENCES; COMPUTATIONAL ASPECTS; INFERENCE MECHANISM;

FUZZY SETS; FUZZY SYSTEMS;

FUZZY INFERENCE;

EID: 71249163778     PISSN: 10987584     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FUZZY.2009.5277076     Document Type: Conference Paper

References (36)

1. I. B. Turksen and Z.Zhong, "An Approximate Reasoning schema based on Similarity measures and Interval valued fuzzy sets," IEEE Trans. Systems, Man, and Cybernetics, vol. 18, pp. 1049-1056, 1988.
2. J. F. Baldwin, "A new approach to approximate reasoning using fuzzy logic," Fuzzy Sets and Systems, vol. 2, pp. 309-325, 1979.
3. V. Novák and I. Perfilieva, "On the semantics of perception-based fuzzy logic deduction," International Journal of Intelligent Systems, vol. 19, pp. 1007-1031, 2004.
4. V. Novák, "Perception-based logical deduction," in Computational Intelligence, Theory and Applications (Advances in Soft Computing), Edited by B. Reusch, Berlin: Springer, 2005, pp. 237-250.
5. V. Cross and T. Sudkamp, "Patterns of fuzzy rule-based inference", Int. J. of Approximate Reasoning, vol. 11, pp. 235-255, 1994.
6. B. Bouchon-Meunier, R. Mesiar, C. Marsala and M. Rifqi, "Compositional rule of inference as an analogical scheme," Fuzzy Sets and Systems, vol. 138, pp. 53-65, 2003.
7. E.P. Klement, R. Mesiar and E. Pap, Triangular norms, Dordrecht, Netherlands: Kluwer Academic Publishers, 2000.
8. 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.
9. M. Baczyński. and B. Jayaram, Fuzzy Implications (Studies in Fuzziness and Soft Computing series), Heidelberg, Germany: Springer-Verlag, 2008.
10. L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans. Systems, Man, and Cybernetics, vol. 3, no. 1, pp. 28-44, 1973.
11. T. Vetterlein and M. Štěpnička, "Completing fuzzy if-then rule bases by means of smoothing splines," Int. J. of Uncertainty, Fuzziness and Knowledge-Based Syst., vol. 14, pp. 235-244, 2006.
12. I. Perfilieva and S. Lehmke, "Correct models of fuzzy IF-THEN rules are continuous," Fuzzy Sets and Systems, vol. 157, pp. 3188-3197, 2006.
13. V. Novák, I. Perfilieva and J. Močkoř, Mathematical Principles of Fuzzy Logic, Boston: Kluwer Academic Publishers, 1999.
14. E. Sanchez, "Resolution of composite fuzzy relation equations," Inform. and Control, vol. 30, pp. 38-48, 1976.
15. A. Di Nola, S. Sessa., W. Pedrycz and E. Sanchez, Fuzzy Relational Equations and their Applications to Knowledge Engineering, Boston: Kluwer Academic Publishers, 1989.
16. F. Klawonn, "Fuzzy points, fuzzy relations and fuzzy functions," in Discovering the World with Fuzzy Logic (Studies in Fuzzines and Soft Computing), Edited by V. Novák and I. Perfilieva, Heidelberg: Springer Physica-Verlag, 2000, pp. 431-453.
17. M. Štěpnička, B. De Baets and L. Nosková, "On additive and multiplicative fuzzy models," in New Dimensions in Fuzzy Logic and Related Technologies - Vol 2., Proc. 5th Int. Conf. European Society for Fuzzy Logic and Technology, Edited by M. Ště pnička, V. Novák and U. Bodenhofer, Ostrava: University of Ostrava, 2007, pp. 95-102.
18. W. Bandler and L. J. Kohout, "Fuzzy relational products and fuzzy implication operators," Proc. Int. Workshop Fuzzy Reasoning Theory and Applications, Queen Mary College, University of London, 1978.
19. W. Bandler and L. J. Kohout, "Semantics of implication operators and fuzzy relational products," Int. J. Man-Mach. Stud., vol. 12, pp. 89-116, 1979.
20. W. Pedrycz, "Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data," Fuzzy Sets and Systems, vol. 16, pp. 163-175, 1985.
21. L. Nosková, "Systems of fuzzy relation equation with inf→ composition: solvability and solutions," J. of Electrical Eng., vol. 12(s), pp. 69-72, 2005.
22. M. Štěpnička M. and B. Jayaram, "The Bandler-Kohout Subproduct as a Suitable Inference Mechanism," Proc. 2009 IFSA/EUSFLAT World Congress, Lisbon, 2009, to appear.
23. F. Klawonn and J. L. Castro, "Similarity in Fuzzy Reasoning," Mathware & Soft Computing, vol. 2, pp. 197-228, 1995.
24. B. Jayaram, "On the law of importation (x ∧ y) → z ≡ (x → (y → z)) in fuzzy logic," IEEE Trans. Fuzzy Syst., vol. 16, no. 1 pp. 130-144, 2008.
25. W. Bandler and L. J. Kohout, "Fuzzy power sets and fuzzy implication operators," Fuzzy Sets and Systems, vol. 4, pp. 183-190, 1980.
26. S. Gottwald, "On a generalization of fuzzy relation equations," in Proc. 11th Information Processing and Management of Uncertainty Knowledge, Paris, France, 2006, pp. 2572-2577.
27. Ch. Cornelis, M. DeCock. and E. E. Kerre, "Efficient approximate reasoning with positive and negative information," in Knowledge-Based Intelligent Information and Engineering Systems (Lecture Notes in Artifical Intelligence series 3214), Edited by M. Gh. Negoita, R. J. Howlett and L. C. Jain, Berlin: Springer, 2004, pp.779-785.
28. R. Martin-Clouaire, "A fast generalized modus ponens," BUSEFAL, vol. 18, pp. 75-82, 1984.
29. K. Demirli and I. B. Türksen, "Rule break up with compositional rule of inference," Proc. 1992 IEEE Int. Conf. on Fuzzy Systems, San Diego, USA, 1992, pp. 749-756.
30. R. Fullér, Fuzzy Reasoning and Fuzzy Optimization, Turku, Finland: TUCS General Publication, 1998.
31. R. Fullér and H.-J. Zimmermann, "On computation of the compositional rule of inference under triangular norms," Fuzzy Sets and Systems, vol. 51, pp. 267-275, 1992.
32. B. Moser and M. Navara, "Which triangular norms are convenient for fuzzy controllers?," Proc. 4th Int. Conf. European Society for Fuzzy Logic and Technology, Palma, Spain, 1999, p. 75-78.
33. B. Moser and M. Navara, "Conditionally firing rules extend the possibilities of fuzzy controllers," Proc. Int. Conf. on Computational Intelligence for Modelling, Vienna, Austria, 1999, pp. 242-245.
34. B. Moser and M. Navara, "Fuzzy controllers with conditionally firing rules," IEEE Trans. Fuzzy Syst., vol. 10, no. 3, pp. 340-348, 2002.
35. D. Ruan and E. E. Kerre, "On the extension of the compositional rule of inference," Int. J. Intell. Syst., vol. 8, pp. 807-817, 1993.
36. U. Bodenhofer, M. Daňková, M. Štěpnič ka M. and V. Novák, "A plea for the usefulness of the deductive interpretation of fuzzy rules in engineering applications," Proc. 2007 IEEE Int. Conf. on Fuzzy Systems, London, UK, 2007, pp. 1567-1572.