Preface
In our daily life there are many cases when observations of objects in a population are fuzzy, inaccurate. Fuzzy concepts have been introduced in order to model such vague terms as observed values of some physical or economical terms. Measured physical fields or observed economical parameters may be inaccurate, noisy or difficult to measure and to observe with an appropriate precision because of technical reasons.
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References
Buckley, J.J.: Solving fuzzy equations in economics and finance. Fuzzy Sets and Systems 48, 289–296 (1992)
Buckley, J.J., Eslami, E.: An Introduction to Fuzzy Logic and Fuzzy Sets. Physica-Verlag, Springer, Heidelberg (2005)
Chen, G., Pham, T.T.: Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems. CRS Press, Boca Raton (2001)
Czogała, E., Pedrycz, W.: Elements and Methods of Fuzzy Set Theory (in Polish). PWN, Warszawa (1985)
Drewniak, J.: Fuzzy numbers. In: Chojcan, J., Łȩski, J. (eds.) Fuzzy Sets and their Applications. In Polish: Zbiory rozmyte i ich zastosowania, pp. 103–129. WPŚ, Gliwice (2001)
Dubois, D., Prade, H.: Operations on fuzzy numbers. International Journal of Systems Science 9(6), 613–626 (1978)
Goetschel Jr., R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18(1), 31–43 (1986)
Kaucher, E.: Interval analysis in the extended interval space IR. Computing (suppl. 2), 33–49 (1980)
Kaufman, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold, New York (1991)
Kacprzyk, J.: Fuzzy Sets in System Analysis (in Polish). PWN, Warszawa (1986)
Klir, G.J.: Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems 91(2), 165–175 (1997)
Koleśnik, R., Prokopowicz, P., Kosiński, W.: Fuzzy Calculator – usefull tool for programming with fuzzy algebra. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 320–325. Springer, Heidelberg (2004)
Kosiński, W.: On soft computing and modelling. In: Image Processing Communications, An International Journal with special section: Technologies of Data Transmission and Processing, held in 5th International Conference INTERPOR, vol. 11(1), pp. 71–82 (2006)
Kosiński, W.: On defuzzyfication of ordered fuzzy numbers. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 326–331. Springer, Heidelberg (2004)
Kosiński, W.: On fuzzy number calculus. International Journal of Applied Mathematics and Computer Science 16(1), 51–57 (2006)
Kosiński, W.: Defuzzyfication functionals of ordered fuzzy numbers (submitted for publication, 2007)
Kosiński, W., Markowska-Kaczmar, U.: An evolutionary algorithm determining a defuzzyfication functional. Task Quarterly 11(1-2), 47–58 (2007)
Kosiński, W., Piechór, K., Prokopowicz, P., Tyburek, K.: On algorithmic approach to operations on fuzzy numbers. In: Burczyński, T., Cholewa, W. (eds.) Methods of Artificial Intelligence in Mechanics and Mechanical Engineering, pp. 95–98. PACM, Gliwice (2001)
Kosiński, W., Prokopowicz, P.: Algebra of fuzzy numbers (In Polish): Algebra liczb rozmytych. Matematyka Stosowana. Matematyka dla Społeczeństwa 5(46), 37–63 (2004)
Kosiński, W., Prokopowicz, P.: Fuzziness – Representation of Dynamic Changes, Using Ordered Fuzzy Numbers Arithmetic, New Dimensions in Fuzzy Logic and Related Technologies. In: Stepnicka, M., Novak, V., Bodenhofer, U. (eds.) Proceedings of the 5th EUSFLAT Conference I, Ostrava, Czech Republic, September 11-14, 2007, pp. 449–456. University of Ostrava (2007)
Kosiński, W., Prokopowicz, P., Kacprzak, D.: On the role of orientation in (for) order fuzzy numbers (submitted for publication, 2008)
Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Fuzzy numbers with algebraic operations: algorithmic approach. In: Kłopotek, M., Wierzchoń, S.T., Michalewicz, M. (eds.) Intelligent Information Systems, Proceedings IIS 2002, Sopot, Poland, June 3-6, 2002, pp. 311–320. Physica Verlag, Heidelberg (2002)
Kosiński, W., Prokopowicz, P., Ślȩzak, D.: On algebraic operations on fuzzy numbers. In: Kłopotek, M., Wierzchoń, S.T., Trojanowski, K. (eds.) Proceedings of the International IIS: IIPWM 2003 Conference, Zakopane, Poland, June 2-5, 2003, pp. 353–362. Physica Verlag, Heidelberg (2003)
Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Drawback of fuzzy arithmetics – new intuitions and propositions. In: Burczyński, T., Cholewa, W., Moczulski, W. (eds.) Proceedings Methods of Artificial Intelligence, pp. 231–237. PACM, Gliwice (2002)
Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Ordered fuzzy numbers. Bulletin of the Polish Academy of Sciences, Série des Sciences Mathematiques 51(3), 327–338 (2003)
Kosiński, W., Prokopowicz, P., Ślȩzak, D.: On algebraic operations on fuzzy reals. In: Rutkowski, L., Kacprzyk, J. (eds.) Proceedings of the Sixth International Conference on Neutral Networks and Soft Computing, Zakopane, Poland, June 11-15, 2002. Advances in Soft Computing, p. 54. Physica-Verlag, Heidelberg (2003)
Kosiński, W., Słysz, P.: Fuzzy numbers and their quotient space with algebraic operations. Bulletin of the Polish Academy of Sciences, Série des Sciences Mathematiques 41(3), 285–295 (1993)
Kosiński, W., Weigl, M.: General mapping approximation problems solving by neural networks and fuzzy inference systems. Systems Analysis Modelling Simulation 30(1), 11–28 (1998)
Leontief, W.W.: The Structure of American Economy, 2nd edn. Oxford University Press, New York (1951)
Łojasiewicz, S.: Introduction to the Theory of Real Functions. (In Polish): Wstȩp do teorii funkcji rzeczywistych (Biblioteka Matematyczna, Tom 46). PWN, Warszawa (1973)
Martos, B.: Nonlinear Programming – Theory and Methods. (Polish translation of the English original published by Akadémiai Kiadó, Budapest, 1975), Warszawa, Poland (1983)
Nguyen, H.T.: A note on the extension principle for fuzzy sets. Journal of Mathematical Analysis and Applications 64, 369–380 (1978)
Piegat, A.: Fuzzy Modelling and Control. (In Polish: Modelowanie i sterowanie rozmyte). Akademicka Oficyna Wydawnicza PLJ, Warszawa (1999)
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, Dymaczewo, Poland, June, pp. 349–354 (2005)
Prokopowicz, P.: Algorithmization of Operations on Fuzzy Numbers and its Applications. (In Polish: Algorytmizacja działań na liczbach rozmytych i jej zastosowania). Ph.D. Thesis, IPPT PAN, kwiecień (2005)
Prokopowicz, P.: Using Ordered Fuzzy Numbers Arithmetic. In: Cader, A., Rutkowski, L., Tadeusiewicz, R., Zurada, J. (eds.) Proceedings of the 8th International Conference on Artificial Intelligence and Soft Computing, Zakopane, Polska, June 25-29, 2004. Fuzzy Control in Artificial Intelligence and Soft Computing, pp. 156–162. Academic Publishing House EXIT, Warszawa (2006)
Sanchez, E.: Solutions of fuzzy equations with extended operations. Fuzzy Sets and Systems 12, 237–248 (1984)
Wagenknecht, M.: On the approximate treatment of fuzzy arithmetics by inclusion, linear regression and information content estimation. Fuzzy Sets and their Applications; (In Polish: Chojcan, J., Łȩski, J. (eds.): Zbiory rozmyte i ich zastosowania), Wydawnictwo Politechniki Śla̧skiej. Gliwice, Poland, pp. 291–310 (2001)
Wagenknecht, M., Hampel, R., Schneider, V.: Computational aspects of fuzzy arithmetic based on archimedean t-norms. Fuzzy Sets and Systems 123(1), 49–62 (2001)
Yager, R.R., Filev, D.P.: Basics of modelling and fuzzy control (Polish translation of the English original). WNT, Warszawa (1995)
Yoshida, K.: Functional Analysis, 6th edn. Springer, Heidelberg (1980)
Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part I. Information Sciences 8(3), 199–249 (1975)
Zadeh, L.A.: The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems 11(3), 199–227 (1983)
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Kosiński, W., Prokopowicz, P., Kacprzak, D. (2009). Fuzziness – Representation of Dynamic Changes by Ordered Fuzzy Numbers. In: Seising, R. (eds) Views on Fuzzy Sets and Systems from Different Perspectives. Studies in Fuzziness and Soft Computing, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93802-6_24
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