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The Directed Inference for the Kosinski’s Fuzzy Number Model

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Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 427))

Abstract

The Kosinski’s Fuzzy Number (KFN) model (former name the Ordered Fuzzy Number) is a tool for processing an imprecise information interpreted in a similar way as the classical convex fuzzy numbers. The specificity of KFNs is an additional property for the fuzzy number—the direction. Thanks to that, the calculations can be done as flexibly as with real numbers. Especially, we are not doomed to get the more fuzzy results after many arithmetical operations. Apart good calculations, the direction also has additional potential in the interpretation of fuzzy data. It can be treated as a direction of process, not only the value. For example “an income is high and process is growing” is a different situation than “an income is high, but process is lowering”. The direction of KFN can be used to represent difference between these sentences. Since we deal with an additional information, there is need for the new methods which let benefit a full potential of KFNs in the modeling of linguistic data. This paper introduces algorithm of the inference operation for fuzzy rule constructed with the KFNs. Presented proposal consider the direction of values in processing. It bases on the ideas presented in previous studies on this subject—the Direction Determinant. It was proposed as the general basic tool for defining methods, where we need sensitivity for the direction.

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References

  1. Kosiński W., Prokopowicz P., Ślȩzak D.: On algebraic operations on fuzzy reals. In: Rutkowski, L., Kacprzyk, J. (eds.), Advances in Soft Computing. Proceedings of the Sixth International Conference on Neutral Networks and Soft Computing, Zakopane, Poland, 11–15 June 2002, pp. 54–61. Physica-Verlag, Heidelberg (2003)

    Google Scholar 

  2. Kosiński W., Prokopowicz P., Ślȩzak D.: Ordered fuzzy numbers. Bull. Polish Acad. Sci. Ser. Sci. Math. 51(3), 327–338 (2003)

    Google Scholar 

  3. Kosiński, W.: On fuzzy number calculus. Int. J. Appl. Math. Comput. Sci. 16(1), 51–57 (2006)

    MathSciNet  Google Scholar 

  4. Prokopowicz, P.: Flexible and Simple Methods of Calculations on Fuzzy Numbers with the Ordered Fuzzy Numbers Model, LNCS (LNAI), vol. 7894, pp. 365–375. Springer, Heidelberg (2013)

    Google Scholar 

  5. Pedrycz, W., Gominde, F.: An Introduction to Fuzzy Sets. The MIT Press, Cambridge (MA), London (1998)

    MATH  Google Scholar 

  6. Wagenknecht, M., Hampel, R., Schneider, V.: Computational aspects of fuzzy arithmetic based on archimedean \(t\)-norms. Fuzzy Sets Syst. 123(1), 49–62 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Piegat, A.: Fuzzy Modeling and Control. Studies in Fuzziness and Soft Computing. Springer, Berlin, Heidelberg (2001)

    Book  MATH  Google Scholar 

  8. Buckley James, J., Eslami, E.: An Introduction to Fuzzy Logic and Fuzzy Sets, Physica-Verlag, A Springer-Verlag Company, Heidelberg (2005)

    Google Scholar 

  9. Prokopowicz, P., Malek, S.: Aggregation Operator for Ordered Fuzzy Numbers Concerning the Direction, LNCS (LNAI), vol. 8467, pp. 267–278. Springer International Publishing, Switzerland (2014)

    Google Scholar 

  10. Prokopowicz P., Pedrycz W.: The directed compatibility between ordered fuzzy numbers—a base tool for a direction sensitive fuzzy information processing. In: Proceedings of ICAISC 2015, Part I LNAI, vol. 9119 pp. 249–259. Springer International Publishing, Switzerland (2015)

    Google Scholar 

  11. Kosiński W., P. Prokopowicz P., Ślȩzak D.: On algebraic operations on fuzzy numbers. In: Intelligent Information Processing and Web Mining. ASC, vol. 22, pp. 353–362. Springer (2003)

    Google Scholar 

  12. Kosiński, W., Prokopowicz, P.:Fuzziness—representation of dynamic changes, using ordered fuzzy numbers arithmetic, new dimensions in fuzzy logic and related technologies. In: Proceedings of the 5th EUSFLAT, Ostrava, Czech Republic, vol. I, pp. 449–456. University of Ostrava (2007)

    Google Scholar 

  13. Prokopowicz, P.: Adaptation of Rules in the Fuzzy Control System Using the Arithmetic of Ordered Fuzzy Numbers. LNCS (LNAI), vol. 5097, pp. 306–316. Springer, Heidelberg (2008)

    Google Scholar 

  14. Kosiński, W., Prokopowicz, P., Kacprzak, D.: Fuzziness representation of dynamic changes by ordered fuzzy numbers. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems from Different Perspectives. STUDFUZZ, vol. 243, pp. 485–508. Springer, Heidelberg (2009)

    Google Scholar 

  15. Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64, 369–380 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kosiński, W., Prokopowicz, P., Rosa, A.: Defuzzification functionals of ordered fuzzy numbers. IEEE Trans. Fuzzy Syst. 21(6), 1163–1169 (2013). doi:10.1109/TFUZZ.2013.2243456

    Google Scholar 

  17. Kaucher, E.: Interval analysis in the extended interval space IR. Comput. Suppl. 2, 33–49 (1980)

    Article  MathSciNet  Google Scholar 

  18. Koleśnik, R., Prokopowicz, P., Kosiński, W.: Fuzzy calculator—usefull tool for programming with fuzzy algebra. In: ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 320–325. Springer, Heidelberg (2004)

    Google Scholar 

  19. Kacprzak, D., Kosiński, W., Kosiński, K.: Financial Stock Data and Ordered Fuzzy Numbers, LNCS (LNAI), vol. 7894, pp. 259–270. Springer, Heidelberg (2013)

    Google Scholar 

  20. Kacprzak, M., Kosiński, W., Wegrzyn-Wolska, K.: Diversity of opinion evaluated by ordered fuzzy numbers, LNCS (LNAI), vol. 7894, pp. 271–281. Springer, Heidelberg (2013)

    Google Scholar 

  21. Czerniak, J., Apiecionek, L., Zarzycki, H.: Application of ordered fuzzy numbers in a new OFNAnt algorithm based on ant colony optimization. Beyond databases, architectures, and structures. Commun. Comput. Inf. Sci. 424, 259–270 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland

    Piotr Prokopowicz

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  1. Piotr Prokopowicz
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Correspondence to Piotr Prokopowicz .

Editor information

Editors and Affiliations

  1. Sci. Network for Innovation & Rec. Exell, Machine Intelligence Research Labs (MIR, Auburn, Washington, USA

    Ajith Abraham

  2. Membre du Groupe Efrei, ESIGETEL, Villejuif, France

    Katarzyna Wegrzyn-Wolska

  3. Faculty of Computers & Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

  4. VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Vaclav Snasel

  5. ENIS, University of Sfax, Sfax, Tunisia

    Adel M. Alimi

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Prokopowicz, P. (2016). The Directed Inference for the Kosinski’s Fuzzy Number Model. In: Abraham, A., Wegrzyn-Wolska, K., Hassanien, A., Snasel, V., Alimi, A. (eds) Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015. Advances in Intelligent Systems and Computing, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-319-29504-6_46

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  • DOI: https://doi.org/10.1007/978-3-319-29504-6_46

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29503-9

  • Online ISBN: 978-3-319-29504-6

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