Comparison of two kinds of fuzzy arithmetic, LR and OFN, applied to fuzzy observation of the cofferdam water level

Jacek M. Czerniak, Wojciech Dobrosielski, Rafal A. Angryk

Abstract


This paper presents certain important aspects of the fuzzy logic extension, one of which is OFN. It includes basic definitions of that discipline. It also compares fuzzy logic arithmetic with the arithmetic of ordered fuzzy numbers in L-R notation. Computational experiments were based on fuzzy observation of the impounding basin. The results of the study show that there is a connection between the order of OFN number and trend of changes in the environment. The experiment was carried out using computer software developed specially for that purpose. When comparing the arithmetic of fuzzy numbers in L-R notation with the arithmetic of ordered fuzzy numbers on the grounds of the experiment, it has been concluded that with fuzzy numbers it is possible to expand the scope of solutions in comparison to fuzzy numbers in classic form. The symbol of OFN flexibility is the possibility to determine the X number that always satisfies the equation A+X=C, regardless of the value of arguments. Operations performed on OFN are less complicated, as they are performed in the same way regardless the sign of the input data and their results are more accurate in the majority of cases. The promising feature of ordered fuzzy numbers is their lack of rapidly growing fuzziness. Authors expect to see implication of that fact in practice in the near future.

Keywords


Fuzzy Logic, Fuzzy Number, Ordered Fuzzy Numbers

Full Text:

PDF

References


Zadeh L. A., Fuzzy sets, Information and Control, vol. 8, no. 3, pp. 338-353, June 1965

Łukasiewicz J., 1920, O logice trójwartościowej (in Polish). Ruch filozoficzny 5:170–171. English translation: On three-valued logic, in L. Borkowski (ed.), Selected works by Jan Łukasiewicz, North–Holland, Amsterdam, 1970, pp. 87–88

Dubois D., Prade H., Operations on fuzzy numbers, Int. J. Systems Science, vol. 9, pp. 613–626, 1978.

Dubois D., Prade H., Fuzzy elements in a fuzzy set Proc. 10th Inter. Fuzzy Systems Assoc. (IFSA) Congress, Beijing, 2005, Springer. pdf Revised version: Gradual ele-ments in a fuzzy set. Soft Computing, 12: 165-175, 2008

Kosiński W., Słysz P., Fuzzy numbers and their quotient space with algebraic opera-tions, Bull. Polish Acad. Sci.Ser. Tech. Sci.41, 1993, pp.285-295

Kosinski W., P. Prokopowicz P., Ślęzak D., Ordered fuzzy number, Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 53(3), 2003, pp.327-338

Kosiński W., Prokopowicz P., Ślęzak D., On Algebraic Oprerations on Fuzzy Num-bers, Inteligent Information Processing and Web Mining: proceedings of the Interna-tional IIS:IIPWM’03 Conference held In Zakopane , Poland, June 2-5, 2003.

Kosiński W., On Fuzzy Number Calculus, Int. J. Appl. Math. Comput.Sci., 2006, Vol. 16, No. 1, pp.51-57

Kosiński W., Koleśnik R., Prokopowicz P., Frischmuth K., On Algebra of Ordered Fuzzy Numbers, Soft Computing Foundations and Theoretical Aspects, Atanassov K., Hryniewicz O., Kacprzyk J. (Eds.), Exit, Warszawa 2004 str.291-302

Kosiński W., Prokopowicz P., Ślęzak D., On Algebraic Oprerations on Fuzzy Num-bers, Inteligent Information Processing and Web Mining: proceedings of the Interna-tional IIS:IIPWM’03 Conference held In Zakopane , Poland, June 2-5, 2003.

Prokopowicz P., Algorytmization of Operations on Fuzzy Numbers and its Applica-tions (in Polish), Ph.D. Thesis, IFTR PAS, 2005

Gerla G.,Fuzzy Logic Programming and Fuzzy Control, Studia Logica Volume: 79, Issue: 2, March 2005, pp. 231 - 254

Gottwald S., Mathematical aspects of fuzzy sets and fuzzy logic: Some reflections after 40 years,Fuzzy Sets and Systems Volume: 156, Issue: 3, December 16, 2005, pp. 357-364

Walker C.L., Walker E.A., The algebra of fuzzy truth values, Fuzzy Sets and Systems Volume: 149, Issue: 2, January 16, 2005, pp. 309-347

Pang C.T., Onthea symptotic period of powers of a fuzzy matrix, Computers Math. Appl.54, 2007, pp. 310–318

Dubois D., Prade H., Gradual elements in a fuzzy set, Soft Comput. 12(2), 2008, pp.165–176

Couso I., Montes S., An axiomatic definition of fuzzy divergence measures, Inter-nat.J.of Uncertainty Fuzziness and Knowledge-Based Systems, 16(1) (2008), pp.1–18.

Dombi J.,Towards a general class of operators for fuzzy systems, IEEETrans.on Fuzzy Systems, 16(2), 2008, pp. 477–484

Zadeh L.A., Is there a need for fuzzy logic?, Information Sciences Volume: 178, Issue: 13, July 1, 2008, pp. 2751-2779

Bosnjak I., Madarász R., Vojvodic G., Algebras of fuzzy sets, Fuzzy Sets and Systems Volume: 160, Issue: 20, October 16, 2009, pp. 2979-2988

Xu Z., Shang S., Qian W., Shu W., A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers, Expert Systems With Applications Volume: 37, Issue: 3, March 15, 2010, pp. 1920-1927

Kosinski W., On defuzzyfication functionals in fuzzy number calculus, Proceedings of the 9th WSEAS International Conference on Fuzzy Systems, pp.212-218, May 02-04, 2008, Sofia, Bulgaria

Kosiński W., Kurt Frischmuth, Dorota Wilczyńska-Sztyma, A new fuzzy approach to ordinary differential equations, Proceedings of the 10th international conference on Ar-tificial intelligence and soft computing: Part I, June 13-17, 2010, Zakopane, Poland

Klir G.J., Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems - Special issue: fuzzy arithmetic archive, Volume 91 Issue 2, Oct. 16, 1997

Kosiński W., Kacprzak M., Fuzzy implications on lattice of ordered fuzzy numbers, in Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy sets, Generalized Nets and Related Topics, Volume I: Foundations, Atanssov K.T., Baczyński M., Drewniak J., Kacprzyk J., Krawczyk M., Szmidt E., Wygralek M., Zadrożny S. (Eds.), SRI PAS, Warsaw, 2010, pp. 95-110

Węgrzyn-Wolska K., Borzymek P., Kosiński W., Evolutionary algorithm in fuzzy data problem, in Evolutionary Algorithms, Eisuke Kita (Ed.), InTech, Publ., April 2011, pp.201-218




DOI: https://doi.org/10.7494/csci.2013.14.3.443

Refbacks

  • There are currently no refbacks.