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This paper presents certain important aspect soft he fuzzy logic extension, one of whichis OFN. It includes basic definition soft hat 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 soft ware developed specially for that purpose.When comparing the arithmetic of fuzzy numbers in L-R notation with the arithmetic of ordered fuzzy number son the ground soft he experiment, it has been concluded that with fuzzy numbers it ispossible to expand the scope of solutions in comparison to fuzzy numbers inclassic form. The symbol of OFN flexibility is the possibility to determine the number that always satisfies the equation A+X=C, regardles soft hevalue of arguments. Operations performed on OFN are less complicated, as the yare performed in the same way regard less the sign of the input data and the irresults are more accuratein 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.
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Czasopismo
Rocznik
Tom
Strony
443--457
Opis fizyczny
Bibliogr. 26 poz., rys., wykr.
Twórcy
autor
- Foundation for Development of Mechatronics, ul. Jeżynowa 19, 85-343 Bydgoszcz, Poland
autor
- Casimir the Great University, Institute of Technology, ul. Chodkiewicza 30, 85-064 Bydgoszcz, Poland
autor
- Montana State University, Department of Computer Science, Bozeman MT59717-3880 USA
Bibliografia
- [1] Zadeh L.A.:Fuzzy sets, Information and Control ,8(3):338–353, June 1965.
- [2] Łukasiewicz J.:O logice trójwartościowej (in Polish). Ruch filozoficzny 5:170–171, 1920.English translation: On three-valued logic,in L.Borkowski (ed.),Selected works by Jan Łukasiewicz, North-Holland, Amsterdam,1970, pp.87–88.
- [3] Dubois D., Prade H.: Operations on fuzzy numbers, Int. J. Systems Science,vol.9, pp.613–626, 1978.
- [4] Systems Assoc. (IFSA) Congress, Beijing, 2005, Springer. pdf Revised version: Gradual elements in a fuzzy set.Soft Computing,12:165–175, 2008.
- [5] Kosiński W., Słysz P.: Fuzzy numbers and their quotient space with algebraicoperations, Bull. Polish Acad. Sci. Ser. Tech. Sci., 41:285–295, 1993.
- [6] Kosiński W., P. Prokopowicz P., Ślęzak D.: Ordered fuzzy number, Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 53(3):327–338, 2003.
- [7] Kosiński W., Prokopowicz P., Ślęzak D.: On Algebraic Oprerations on Fuzzy Numbers, Inteligent Information Processing and Web Mining:proceesings of the International IIS: IIPWM’03 Conference held In Zakopane, Poland, June 2–5, 2003.
- [8] Kosiński W.: On Fuzzy Number Calculus, Int. J. Appl. Math. Comput. Sci.,16(1):51–57,2006.
- [9] 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.
- [10] Kosiński W., Prokopowicz P., Ślęzak D.: On Algebraic Oprerations on Fuzzy Numbers, Inteligent Information Processing and Web Mining: proceedings of the International IIS: IIPWM’03 Conference held In Zakopane, Poland, June 2–5,2003.
- [11] Prokopowicz P.: Algorytmization of Operations on Fuzzy Number sand its Applications (in Polish), Ph.D.Thesis, IFTRPAS, 2005.
- [12] Gerla G.: Fuzzy Logic Programming and Fuzzy Control, Studia Logica 79(2):231–254, March 2005.
- [13] Gottwald S.:Mathematical aspect so ffuzzy set sand fuzzy logic: Some reflections after 40 years, Fuzzy Sets and Systems 156(3):357–364, December 16, 2005.
- [14] Walker C.L., Walker E.A.: The algebra of fuzzy truth values, Fuzzy Sets and Systems,149(2):309–347, January16, 2005.
- [15] Pang C.T.:On the a symptotic period of powers of a fuzzy matrix, Computers Math. Appl., 54:310–318, 2007.
- [16] Dubois D.,Prade H.:Gradual element sin a fuzzy set, Soft Comput.,12(2):165–176, 2008.
- [17] CousoI., Montes S.: An axiomatic definition of fuzzy divergence measures, Internat. J. of Uncertainty Fuzzinessand Knowledge-Based Systems, 16(1):1–18, 2008
- [18] Dombi J.:Towards a general class of operators for fuzzy systems, IEEE Trans. on Fuzzy Systems ,16(2):477–484, 2008.
- [19] Zadeh L.A.:Is there a need for fuzzy logic?, Information Sciences,178(13):2751–2779, July 1, 2008.
- [20] Bosnjak I., Madarasz R., Vojvodic G.: Algebras of fuzzy sets, Fuzzy Sets and Systems 160(20):2979–2988, October 16, 2009.
- [21] 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,37(3):1920–1927, March 15, 2010.
- [22] Kosiński 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.
- [23] Kosiński W., Kurt Frischmuth, Dorota Wilczyńska-Sztyma: A new fuzzy approach to ordinary differential equations, Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I, June 13–17, 2010, Zakopane, Poland.
- [24] Klir G.J.: Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems–Specialissue:fuzzy arithmetic archive, Volume 91 Issue 2, Oct.16, 1997.
- [25] Kosiński W., Kacprzak M.: Fuzzy implications on lattice of ordered fuzzy numbers, in Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy sets, Generalized Netsand Related Topics, Volume I:Foundations, Atanssov K.T., Baczyński M., Drewniak J., Kacprzyk J.,Krawczyk M.,Szmidt E.,Wygralek M., Zadrożny S. (Eds.), SRIPAS, Warsaw, 2010, pp.95–110.
- [26] Węgrzyn-Wolska K.,Borzymek P.,Kosiński W.: Evolutionary algorithm in fuzzy data problem, in Evolutionary Algorithms. Eisuke Kita (Ed.), In Tech, Publ., April2011,pp.201–218.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-50c56091-48b7-4e9a-88d8-e9cbdb539295