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The compositional rule of Inference vs the Bandler-Kohout subproduct : a comparison of two standard rules of inference

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Warianty tytułu
Konferencja
17th Conference on Computer Science and Intelligence Systems
Języki publikacji
EN
Abstrakty
EN
This contribution focuses on the most popular scheme of reasoning in approximate reasoning, generalized modus ponens. Also, we consider the case when the reasoning is performed with one fuzzy rule. Usually, the compositional rule of inference introduced by Zadeh is involved. However, it is also common to use the Bandler-Kohout subproduct. We compare these two rules showing by experimental results the conditions when applying one of them is more appropriate. We concentrate on an example of image transformation where applying a different rule of inference gives a different conclusion. Moreover, we point out some theoretical justifications for particular fuzzy connectives used in both methods (fuzzy implication functions, triangular norms and, in general, fuzzy conjunctions).
Słowa kluczowe
Rocznik
Tom
Strony
19--26
Opis fizyczny
Bibliogr. 15 poz., fot., wykr.
Twórcy
  • University of Silesia in Katowice Bankowa 14, 40-007 Katowice, Poland
  • University of Silesia in Katowice Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • 1. L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst., Man, Cybern., vol. 3, pp. 28-44, 1973. http://dx.doi.org/https://doi.org/10.1016/S0019-9958(65)90241-X
  • 2. W. Bandler and L. J. Kohout, Fuzzy Relational Products as a Tool for Analysis and Synthesis of the Behaviour of Complex Natural and Artificial Systems. Boston, MA: Springer US, 1980, pp. 341-367. ISBN 978-1-4684-3848-2.
  • 3. M. Štěpnička and B. Jayaram, “On the Suitability of the Bandler-Kohout Subproduct as an Inference Mechanism,” IEEE Trans. Fuzzy Syst, vol. 18, no. 2, pp. 285-298, 2010. http://dx.doi.org/https://doi.org/10.1109/TFUZZ.2010.2041007
  • 4. S. Mandal and B. Jayaram, “Bandler-Kohout Subproduct with Yager’s classes of Fuzzy Implications,” IEEE Trans. Fuzzy Syst., vol. 22, no. 3, pp. 469-482, 2014. http://dx.doi.org/https://doi.org/10.1109/TFUZZ.2013.2260551
  • 5. J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support. Dordrecht: Kluwer Academic Publishers, 1994.
  • 6. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norms. Dordrecht: Kluwer Academic Publishers, 2000. [Online]. Available: https://doi.org/10.1007/978-94-015-9540-7
  • 7. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality. Warszawa, Kraków, Katowice: Państwowe Wydawnictwo Naukowe (Polish Scientific Publishers) and Uniwersytet Śla̧ski, 1985.
  • 8. M. Baczyński and B. Jayaram, Fuzzy Implications, ser. Studies in Fuzziness and Soft Computing. Berlin Heidelberg: Springer, 2008, vol. 231.
  • 9. C. Pappis and N. Karacapilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Sets and Systems, vol. 56, pp. 171-174, 1993. http://dx.doi.org/https://doi.org/10.1016/0165-0114(93)90141-4
  • 10. J. Fan and W. Xie, “Some notes on similarity measure and proximity measure,” Fuzzy Sets and Systems, vol. 101, pp. 403-412, 1999. http://dx.doi.org/https://doi.org/10.1016/S0165-0114(97)00108-5
  • 11. I. Jenhani, S. Benferhat, and Z. Elouedi, Possibilistic Similarity Measures. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 99-123. ISBN 978-3-642-10728-3.
  • 12. Y. Li, K. Qin, and X. He, “Some new approaches to constructing similarity measures,” Fuzzy Sets and Systems, vol. 234, pp. 46-60, 2014. http://dx.doi.org/https://doi.org/10.1016/j.fss.2013.03.008
  • 13. K. Miś and M. Baczyński, “Some Remarks on Approximate Reasoning and Bandler-Kohout Subproduct,” in Information Processing and Management of Uncertainty in Knowledge-Based Systems, ser. Communications in Computer and Information Science, M.-J. Lesot, S. Vieira, M. Reformat, J. Carvalho, B. Bouchon-Meunier, and R. Yager, Eds., vol. 1238. Springer, 2020. http://dx.doi.org/https://doi.org/10.1007/978-3-030-50143-3_60 pp. 775-787.
  • 14. J. D. Hunter, “Matplotlib: A 2d graphics environment,” Computing in Science & Engineering, vol. 9, no. 3, pp. 90-95, 2007. http://dx.doi.org/https://doi.org/10.1109/MCSE.2007.55
  • 15. C. Harris, K. Millman, S. van der Walt, and et al., “Array programming with NumPy,” Nature, vol. 585, pp. 357-362, 2020. http://dx.doi.org/https://doi.org/10.1038/s41586-020-2649-2
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ef2b7555-d9e5-410f-ae0b-c2bebd59b32f
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