Analysis of the Changes in Processes Using the Kosinski's Fuzzy Numbers
Piotr Prokopowicz
DOI: http://dx.doi.org/10.15439/2016F140
Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 121–128 (2016)
Abstract. This paper presents the analysis of potential of the Kosinski's Fuzzy Number (KFN) idea in the modeling trends of the processes which are described imprecisely. KFNs conception is an alternative for the classical fuzzy numbers ideas as model to represent of the imprecise quantitative data. They introduces new feature into vagueness of the information - a direction. It is base for good arithmetical properties of calculations. Furthermore, a direction also extends a potential in the modeling of information by the additional interpretation, what is a subject of this article. This new potential is presented and explained basing on the example of modeling of quantity of liquid in a reservoir. The environment is changing dynamically what is described as the changes in inflow and outflow. Proposed example explains how to interpret the direction of KFN and how to understand the results of calculations and its influence.
References
- E. Sanchez, “Solution of fuzzy equations with extended operations,” Fuzzy Sets and Systems, vol. 12, no. 3, pp. 237 – 248, 1984. [Online]. Available: http://dx.doi.org/10.1016/0165-0114(84)90071-X
- G. J. Klir, “Fuzzy arithmetic with requisite constraints,” Fuzzy Sets and Systems, vol. 91, no. 2, pp. 165 – 175, 1997, fuzzy Arithmetic. http://dx.doi.org/10.1016/S0165-0114(97)00138-3
- M. Wagenknecht, R. Hampel, and V. Schneider, “Computational aspects of fuzzy arithmetics based on archimedean t-norms,” Fuzzy Sets and Systems, vol. 123, no. 1, pp. 49 – 62, 2001. http://dx.doi.org/10.1016/S0165-0114(00)00096-8
- W. Kosiński, P. Prokopowicz, and D. Ślęzak, “Ordered fuzzy numbers,” Biulletin of the Polish Academy of Sciences Mathematics, vol. 51, no. 3, pp. 327 – 338, 2003.
- W. Kosiński, P. Prokopowicz, and D. Ślęzak, Intelligent Information Processing and Web Mining: Proceedings of the International IIS: IIPWM’03 Conference held in Zakopane, Poland, June 2–5, 2003. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003, ch. On Algebraic Operations on Fuzzy Numbers, pp. 353–362. http://dx.doi.org/10.1007/978-3-540-36562-4_37
- W. Kosiński, P. Prokopowicz, and D. Ślęzak, “Calculus with fuzzy numbers,” in Intelligent Media Technology for Communicative Intelligence, ser. Lecture Notes in Computer Science, L. Bolc, Z. Michalewicz, and T. Nishida, Eds. Springer Berlin Heidelberg, 2005, vol. 3490, pp. 21–28. http://dx.doi.org/10.1007/11558637_3
- P. Prokopowicz, “Flexible and simple methods of calculations on fuzzy numbers with the ordered fuzzy numbers model,” in Artificial Intelligence and Soft Computing, ser. Lecture Notes in Computer Science, L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L. Zadeh, and J. Zurada, Eds. Springer Berlin Heidelberg, 2013, vol. 7894, pp. 365–375. http://dx.doi.org/10.1007/978-3-642-38658-9_33
- P. Prokopowicz and W. Pedrycz, “The directed compatibility between ordered fuzzy numbers - a base tool for a direction sensitive fuzzy information processing,” in Artificial Intelligence and Soft Computing, ser. Lecture Notes in Computer Science, L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L. A. Zadeh, and J. M. Zurada, Eds. Springer International Publishing, 2015, vol. 9119, pp. 249–259. http://dx.doi.org/10.1007/978-3-319-19324-3_23
- A. Marszałek and T. Burczyński, “Modelling financial high frequency data using ordered fuzzy numbers,” in Artificial Intelligence and Soft Computing, ser. Lecture Notes in Computer Science, L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L. Zadeh, and J. Zurada, Eds. Springer Berlin Heidelberg, 2013, vol. 7894, pp. 345–352. http://dx.doi.org/10.1007/978-3-642-38658-9_31
- D. Kacprzak, W. Kosiński, and K. W. Kosiński, Artificial Intelligence and Soft Computing: 12th International Conference, ICAISC 2013, Zakopane, Poland, June 9-13, 2013, Proceedings, Part I. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, ch. Financial Stock Data and Ordered Fuzzy Numbers, pp. 259–270. http://dx.doi.org/10.1007/978-3-642-38658-9_24
- M. Kacprzak, W. Kosiński, and K. Węgrzyn-Wolska, Artificial Intelligence and Soft Computing: 12th International Conference, ICAISC 2013, Zakopane, Poland, June 9-13, 2013, Proceedings, Part I. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, ch. Diversity of Opinion Evaluated by Ordered Fuzzy Numbers, pp. 271–281. http://dx.doi.org/10.1007/978-3-642-38658-9_25
- J. M. Czerniak, Ł. Apiecionek, and H. Zarzycki, Beyond Databases, Architectures, and Structures: 10th International Conference, BDAS 2014, Ustron, Poland, May 27-30, 2014. Proceedings. Cham: Springer International Publishing, 2014, ch. Application of Ordered Fuzzy Numbers in a New OFNAnt Algorithm Based on Ant Colony Optimization, pp. 259–270. http://dx.doi.org/10.1007/978-3-319-06932-6_25
- W. Kosiński and P. Prokopowicz, “Fuzziness - representation of dynamic changes?” in EUSFLAT, 2007.
- W. Kosiński, P. Prokopowicz, and D. Kacprzak, Views on Fuzzy Sets and Systems from Different Perspectives: Philosophy and Logic, Criticisms and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, ch. Fuzziness – Representation of Dynamic Changes by Ordered Fuzzy Numbers, pp. 485–508. http://dx.doi.org/10.1007/978-3-540-93802-6_24
- W. Kosiński, P. Prokopowicz, and D. Śl ̨ezak, Neural Networks and Soft Computing: Proceedings of the Sixth International Conference on Neural Networks and Soft Computing, Zakopane, Poland, June 11–15, 2002. Heidelberg: Physica-Verlag HD, 2003, ch. On Algebraic Operations on Fuzzy Reals, pp. 54–61. http://dx.doi.org/10.1007/978-3-7908-1902-1_8
- P. Prokopowicz, “Adaptation of rules in the fuzzy control system using the arithmetic of ordered fuzzy numbers,” in Artificial Intelligence and Soft Computing - ICAISC 2008, ser. Lecture Notes in Computer Science, L. Rutkowski, R. Tadeusiewicz, L. Zadeh, and J. Zurada, Eds. Springer Berlin Heidelberg, 2008, vol. 5097, pp. 306–316. http://dx.doi.org/10.1007/978-3-540-69731-2_30
- L. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning I,” Information Sciences, vol. 8, no. 3, pp. 199–249, 1975. http://dx.doi.org/10.1016/0020-0255(75)90036-5
- H. T. Nguyen, “A note on the extension principle for fuzzy sets,” Journal of Mathematical Analysis and Applications, vol. 64, no. 2, pp. 369 – 380, 1978. http://dx.doi.org/10.1016/0022-247X(78)90045-8
- D. Dubois and H. Prade, “Operations on fuzzy numbers,” International Journal of Systems Science, vol. 9, no. 6, pp. 613–626, 1978, cited By 1218. http://dx.doi.org/10.1080/00207727808941724
- W. Kosiński, P. Prokopowicz, and A. Rosa, “Defuzzification functionals of ordered fuzzy numbers,” Fuzzy Systems, IEEE Transactions on, vol. 21, no. 6, pp. 1163–1169, Dec 2013. http://dx.doi.org/10.1109/TFUZZ.2013.2243456
- P. Prokopowicz, Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015. Cham: Springer International Publishing, 2016, ch. The Directed Inference for the Kosinski’s Fuzzy Number Model, pp. 493–503. http://dx.doi.org/10.1007/978-3-319-29504-6_46
- E. Kaucher, Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis). Vienna: Springer Vienna, 1980, ch. Interval Analysis in the Extended Interval Space IR, pp. 33–49. http://dx.doi.org/10.1007/978-3-7091-8577-3_3
- W. Pedrycz and F. Gomide, An introduction to fuzzy sets: analysis and design. With a foreword by Lotfi A. Zadeh. Cambridge, MA: MIT Press, 1998.
- A. Piegat, Fuzzy modeling and control. Heidelberg: Physica-Verlag, 2001.
- R. Kolesnik, P. Prokopowicz, and W. Kosinski, “Fuzzy calculator - useful tool for programming with fuzzy algebra,” in Artificial Intelligence and Soft Computing - ICAISC 2004, 7th International Conference, Zakopane, Poland, June 7-11, 2004, Proceedings, 2004, pp. 320–325. http://dx.doi.org/10.1007/978-3-540-24844-6_45
- J. M. Czerniak, W. Dobrosielski, Ł. Apiecionek, and D. Ewald, “Representation of a trend in ofn during fuzzy observance of the water level from the crisis control center,” in Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, ser. Annals of Computer Science and Information Systems, M. Ganzha, L. Maciaszek, and M. Paprzycki, Eds., vol. 5. IEEE, 2015, pp. 443–447. http://dx.doi.org/10.15439/2015F217
- P. Prokopowicz and S. Golsefid, “Aggregation operator for ordered fuzzy numbers concerning the direction,” in Artificial Intelligence and Soft Computing, ser. Lecture Notes in Computer Science, L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L. Zadeh, and J. Zurada, Eds. Springer International Publishing, 2014, vol. 8467, pp. 267–278. http://dx.doi.org/10.1007/978-3-319-07173-2_24