Abstract
In the article, the authors undertook to resolve a burdensome problem in the OFN calculus concerning so-called improper shapes. Although the calculations are possible for all shapes of the numbers in the OFN notation but the interpretation of the numbers of improper shapes has been rather poor and little intuitive. Moreover, indeed, an effective fast calculus in OFN arithmetic has lost some of its reliability due to those shapes, which was indicated by the critics. First the authors presented the definition for the adoption of an order by the created OFN number, which has a significant impact on the results of the calculations. Then they defined a new, unprecedented normalization operator - ShapeNO. For given four coordinates of an OFN number the authors presented all 256 variants of its theoretically possible shapes and normalized all of them, which resulted in only a dozen or so repetitions. This article is another element of the series of related basic studies on the artificial intelligence inspired by nature, where new methods in the OFN area allow creation and development of new meta-heuristic methods of swarm intelligence. Thanks to that operator, arithmetic operations have been simplified, fuzzy input and output data do not cause consternation during the interpretation and the time needed to perform the calculation itself has been shortened.
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References
Angryk, R.A., Czerniak, J.: Heuristic algorithm for interpretation of multi-valued attributes in similarity-based fuzzy relational databases. Int. J. Approximate Reasoning 51(8), 895–911 (2010)
Apiecionek, L., Czerniak, J., Dobrosielski, W.: Quality of services method as a DDoS protection tool. In: Intelligent Systems 2014, Vol. 2: Tools, Architectures, Systems, Applications, Advances in Intelligent Systems and Computing, vol. 323, pp. 225–234. Springer, Heidelberg (2015)
Apiecionek, L., Czerniak, J.M.: QoS solution for network resource protection. In: Proceedings of the Twelfth International Conference on Informatics, INFORMATICS 2013, pp. 73–76 (2013)
Apiecionek, L., Czerniak, J.M., Ewald, D.: NEW QoS CONCEPT for protecting network resources, pp. 234–239. Springer, Cham (2017)
Apiecionek, L., Czerniak, J.M., Zarzycki, H.: Protection tool for distributed denial of services attack. In: Beyond Databases, Architectures and Structures, BDAS 2014, vol. 424, pp. 405–414 (2014)
Chan, F.T., Au, K., Chan, L., Lau, T.: Using genetic algorithms to solve quality-related bin packing problem. Robot. Comput. Integr. Manufact. 23, 71–81 (2007)
Czerniak, J., Ewald, D., Macko, M., Smigielski, G., Tyszczuk, K.: Approach to the monitoring of energy consumption in eco-grinder based on ABC optimization. In: Beyond Databases, Architectures and Structures, BDAS 2015, vol. 521, pp. 516–529 (2015)
Czerniak, J., Zarzycki, H.: Application of rough sets in the presumptive diagnosis of urinary system diseases. In: Artificial Intelligence and Security in Computing Systems, vol. 752, pp. 41–51 (2003)
Czerniak, J.: Evolutionary approach to data discretization for rough sets theory. Fundamenta Informaticae 92(1–2), 43–61 (2009)
Czerniak, J.M., Apiecionek, L., Zarzycki, H.: Application of ordered fuzzy numbers in a new OFNAnt algorithm based on ant colony optimization. In: Beyond Databases, Architectures and Structures, BDAS 2014, vol. 424, pp. 259–270 (2014)
Czerniak, J.M., Dobrosielski, W., Zarzycki, H., Apiecionek, L.: A proposal of the new owlANT method for determining the distance between terms in ontology. In: Intelligent Systems 2014, Vol 2: Tools, Architectures, Systems, Applications, vol. 323, pp. 235–246 (2015)
Czerniak, J.M., Dobrosielski, W.T., Apiecionek, Ł., Ewald, D., Paprzycki, M.: Practical Application of OFN Arithmetics in a Crisis Control Center Monitoring, pp. 51–64. Springer, Cham (2016)
Czerniak, J.M., Ewald, D.: A New MGlaber Approach as an Example of Novel Artificial Acari Optimization, pp. 545–557. Springer, Cham (2016)
Czerniak, J.M., Ewald, D., Śmigielski, G., Dobrosielski, W.T., Apiecionek, Ł.: Optimization of Fuel Consumption in Firefighting Water Capsule Flights of a Helicopter, pp. 39–49. Springer, Cham (2016)
Czerniak, J.M., Zarzycki, H.: Artificial Acari optimization as a new strategy for global optimization of multimodal functions. J. Comput. Sci. (2017)
Czerniak, J.M., Zarzycki, H., Ewald, D.: AAO as a new strategy in modeling and simulation of constructional problems optimization. In: Simulation Modelling Practice and Theory (2017). http://www.sciencedirect.com/science/article/pii/S1569190X17300709
Czerniak, J., Apiecionek, Ł., Zarzycki, H., Ewald, D.: Proposed CAEva simulation method for evacuation of people from a buildings on fire. Adv. Intell. Syst. Comput. 401, 315–326 (2016)
Czerniak, J., Dobrosielski, W., Apiecionek, L.: Representation of a trend in OFN during fuzzy observance of the water level from the crisis control center. In: Proceedings of the Federated Conference on Computer Science and Information Systems, IEEE Digital Library, ACSIS, vol. 5, pp. 443–447 (2015)
Czerniak, J., Macko, M., Ewald, D.: The cutmag as a new hybrid method for multi-edge grinder design optimization. Adv. Intell. Syst. Comput. 401, 327–337 (2016)
Czerniak, J., Smigielski, G., Ewald, D., Paprzycki, M.: New proposed implementation of ABC method to optimization of water capsule flight. In: Proceedings of the Federated Conference on Computer Science and Information Systems, IEEE Digital Library, ACSIS, vol. 5, pp. 489–493 (2015)
Dyczkowski, K.: A less cumulative algorithm of mining linguistic browsing patterns in the world wide web (2007)
Dyczkowski, K., Wygralak, M.: On triangular norm-based generalized cardinals and singular fuzzy sets. Fuzzy Sets Syst. 133(2), 211–226 (2003)
Ewald, D., Czerniak, J.M., Zarzycki, H.: Approach to solve a criteria problem of the ABC algorithm used to the WBDP multicriteria optimization. In: Intelligent Systems 2014, Vol 1: Mathematical Foundations, Theory, Analyses, Advances in Intelligent Systems and Computing, vol. 322, pp. 129–137. Springer, Cham (2015)
Kacprzyk, J., Zadrożny, S.: Linguistic database summaries and their protoforms: towards natural language based knowledge discovery tools. Inf. Sci. 173(4), 281–304 (2005)
Kosiński, W., Prokopowicz, P., Ślezak, D.: On algebraic operations on fuzzy reals. In: Rutkowski, L., Kacprzyk, J. (eds.) Advances in Soft Computing, pp. 54–61. Poland, Zakopane (2002)
Macko, M., Flizikowski, J.: The method of the selection of comminution design for non-brittle materials. In: AIChE Annual Meeting, Conference Proceedings (2010)
Macko, M., Flizikowski, J., Szczepański, Z., Tyszczuk, K., Śmigielski, G., Mroziński, A., Czerniak, J., Tomporowski, A.: CAD/CAE Applications in Mill’s Design and Investigation, pp. 343–351. Springer, Cham (2017)
Mikolajewska, E., Mikolajewski, D.: E-learning in the education of people with disabilities. Adv. Clin. Exp. Med. 20(1), 103–109 (2011)
Mikolajewska, E., Mikolajewski, D.: Exoskeletons in neurological diseases - current and potential future applications. Adv. Clin. Exp. Med. 20(2), 227–233 (2011)
Mikolajewska, E., Mikolajewski, D.: Non-invasive EEG-based brain-computer interfaces in patients with disorders of consciousness. Mil. Med. Res. 1, 14 (2014)
Mrozek, D., Socha, B., Kozielski, S., Małysiak-Mrozek, B.: An efficient and flexible scanning of databases of protein secondary structures. J. Intell. Inf. Syst. 46(1), 213–233 (2016)
Piegat, A.: A new definition of the fuzzy set. J. Appl. Math. Comput. Sci. 15(1), 125–140 (2005)
Piegat, A., Plucinski, M.: Fuzzy number addition with the application of horizontal membership functions. Sci. World J. 16 (2015). doi:10.1155/2015/367214. Article ID 367214
Poli, R., Kennedy, J., Blackwell, T.: Particle swarm optimization. Swarm Intell. 1(1), 33–57 (2007)
Prokopowicz, P.: Methods based on the ordered fuzzy numbers used in fuzzy control. In: Proceedings of the Fifth International Workshop on Robot Motion and Control, RoMoCo 2005, pp. 349–354 (2005)
Prokopowicz, P.: Flexible and simple methods of calculations on fuzzy numbers with the ordered fuzzy numbers model. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) Proceedings of ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 365–375 (2013)
Sitnik, L., Wrobel, R., Magdziak-Toklowicz, M., Kardasz, P.: Vehicle vibration in human health. J. KONES 20(4), 411–418 (2013)
Stachowiak, A., Dyczkowski, K.: A similarity measure with uncertainty for incompletely known fuzzy sets. In: Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 390–394 (2013)
Stachowiak, A., Dyczkowski, K., Wojtowicz, A., Zywica, P., Wygralak, M.: A bipolar view on medical diagnosis in OvaExpert system (2016)
Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114, 505–518 (2000)
Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.: Outline of new approach to the analysis of complex systems and decision process. IEEE Syst. Man Cybern. SMC–3, 28–44 (1973)
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Czerniak, J.M., Filipowicz, I., Ewald, D. (2018). The Novel Shape Normalization Operator for Fuzzy Numbers in OFN Notation. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_49
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