Ordered fuzzy numbers approach to an investment project evaluation

• Autorzy: Kosiński W. K. , Kosiński W. , Kościeński K.
• Języki publikacji: EN

Abstrakty

EN

Aim of the paper is to propose a new tool for a decision supporting system concerning the financial project evaluation. It is based on the determination of the internal rate of return (IRR) of a investment project in which all expenditure and anticipated incomes are vague, and described by Ordered Fuzzy Numbers (OFNs). It means that the probabilistic approach is neglected in this paper and the use of the well developed arithmetics of OFNs is made to find a positive fuzzy root of a fuzzy polynomial representing the fuzzy net present value of the project. Since in the space of OFNs a partial order relation is defined together with a number of defuzzification functionals, the authors can construct a decision support system for investors helping them in acceptance procedure of most profitable investment projects.

Słowa kluczowe

EN

internal rate of return; IRR; net present value; NPV; Ordered Fuzzy Number; OFN; root of fuzzy polynomial; defuzzification functional

• Wydawca: Production Engineering Committee of the Polish Academy of Sciences ; Polish Association for Production Management
• Czasopismo: Management and Production Engineering Review
• Rocznik: 2013
• Tom: Vol. 4, No. 2
• Strony: 50--62
• Opis fizyczny: Bibliogr. 48 poz., tab., wykr.

Twórcy

autor

Kosiński W. K.

• Polish-Japanese Institute of Information Technology, Department of Computer Science, Poland

autor

Kosiński W.

• Polish-Japanese Institute of Information Technology, Department of Computer Science, Koszykowa 86, 02-008 Warsaw, Poland, phone: [phone]
• Kazimierz-Wielki University, Institute of Mechanics and Applied Computer Science, Poland

autor

Kościeński K.

• Kazimierz-Wielki University, Institute of Mechanics and Applied Computer Science, Poland

Bibliografia

• [1] Buckley J.J., The fuzzy mathematics of finance, Fuzzy Sets and Systems, 21, 257-274, 1987.
• [2] Chen Guanrong, Pham Trung Tat, Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems, CRS Press, Boca Raton, London, New York,Washington, D.C., 2001.
• [3] Buckley James J., Eslami E., An Introduction to Fuzzy Logic and Fuzzy Sets, Physica-Verlag, Springer-Verlag, Heidelberg, 2005.
• [4] Duboi D., Prade H., Operations on fuzzy numbers, Int. J. System Science, 9 (6), 613-626, 1978.
• [5] Klir G.J., Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems, 91, 165-175, 1997.
• [6] Zadeh L.A., Fuzzy sets, Information and Control, 8, 338–353, 1965.
• [7] Zadeh L.A., The concept of a linguistic variable and its application to approximate reasoning, Part I, Information Sciences, 8, 199-249, 1975.
• [8] Buckley J.J., Solving fuzzy equations in economics and finance, Fuzzy Sets and Systems, 48, 289-296, 1992.
• [9] Kosiński W., On soft computing and modelling, Image Processing Communications, An International Journal with special section: Technologies of Data Transmission and Processing, held in 5th International Conference INTERPOR 2006, 11 (1), 71-82, 2006.
• [10] Chwastyk A., Kosiński W., Fuzzy calculus with applications [in Polish: Rachunek rozmyty z aplikacjami ], Matematyka Stosowana, 15/56, 2013, in print.
• [11] Dobija M., Administrating Accounting and Controlling [in Polish: Rachnkowość Zarząadcza i Controlling], Wydawnictwo Naukowe PWN, Warszawa, 1999.
• [12] Jarugowa A., Nowak W.A., Szychta A., Administrating Accounting [in Polish: Rachunkowość Zarządcza], Absolwent, Gdańsk, 1999.
• [13] Nahotko S., Efectiveness and risc in innovation processes [in Polish: Efektywność i ryzyko w procesach innowacyjnych], TNOiK, Bydgoszcz, 1999.
• [14] Ju Y.J., Kim C.E., Shim J.-C., Genetic-based fuzzy models: interest rate forecasting problem, Computers and Industrial Engineering, 33 (3-4), 561-564, 1997.
• [15] Kingham M., Mohammadia M., Financial modelling and prediction of interest rate using fuzzy logic and genetic algorithms, in: Proceed. of the 1996 Australina-New Zeland Conf., on Intelligent Information Systems, IEEE, New York, pp. 233-266, 1996.
• [16] Kuchta D., A step towards fuzzy accounting, Badania Operacyjne i Decyzje, 1, 75-84, 2000.
• [17] Kosiński W., Prokopowicz P., Ślęzak D., Fuzzy numbers with algebraic operations: algorithmic approach, in: Intelligent Information Systems 2002, M. Kłopotek, S.T. Wierzchoń, M. Michalewicz [Eds.], Proc. IIS’2002, Sopot, June 3-6, 2002, Poland, Physica Verlag, pp. 311-320, 2002.
• [18] Kosiński W., Prokopowicz P., D. Ślęzak, Drawback of fuzzy arithmetics - new intutions and propositions, in: Proc. Methods of Aritificial Intelligence, T. Burczyński, W. Cholewa, W. Moczulski [Eds.], PACM, Gliwice, Poland, 2002, pp. 231-237, 2002.
• [19] Kosiński W., Prokopowicz P., Ślęzak D., On algebraic operations on fuzzy numbers, in: Intelligent Information Processing and Web Mining, Proc. of the International IIS: IIPWM’03 Conference held in Zakopane, Poland, June 2-5, 2003), M. Kłopotek, S.T.Wierzchoń, K. Trojanowski [Eds.], Physica Verlag, Heidelberg, pp. 353-362, 2003.
• [20] Kosiński W., Prokopowicz P., Ślęzak D., Ordered fuzzy numbers. Bulletin of the Polish Academy of Sciences, S´er. Sci. Math., 51 (3), 327-338, 2003.
• [21] Kosiński W., Prokopowicz P., Algebra of fuzzy numbers [in Polish: Algebra liczb rozmytych], Matematyka Stosowana, 5/46, 37-63, 2004.
• [22] Kosiński W., Prokopowicz P., Ślęzak D., Calculus with fuzzy numbers in: Proc. Intern. Workshop on Intelligent Media for Communicative Intelligence, Warszawa, September, 2004, L.Bolc, T. Nishida, Z. Michalewicz,(eds), LNCS, vol. 3490, pp. 21-28 Springer, Heidelberg, (2005).
• [23] Kuchta D., Soft Mathematics in Managament. Application of interval and fuzzy numbers in administrating accounting [in Polish: Miękka matematyka w zarządzaniu. Zastosowanie liczb przedziałowych i rozmytych w rachunkowości zarządczej ], Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław, 2001.
• [24] Koleśnik R., Kosiński W., Prokopowicz P., Frischmuth K., On algebra of ordered fuzzy numbers, in: Soft Computing - Foundations and Theoretical Aspects, K.T. Atanassov, O. Hryniewicz, J. Kacprzyk [Eds.], Akademicka Oficyna Wydawnicza EXIT, Warszawa, pp. 291-302, (2004).
• [25] Nguyen H.T.. A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64, 369-380, 1978.
• [26] Goetschel R. Jr., VoxmanW., Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1), 31-43, 1986.
• [27] Kaucher E., Interval analysis in the extended interval space IR, Computing Suppl., 2, 33-49, 1989.
• [28] Drewniak J., Fuzzy numbers [in Polish], in: Fuzzy Sets and their Applications, Zbiory rozmyte i ich zastosowania, Chojcan J., Łęski J. [Eds.], WPŚ, Gliwice, Poland, pp. 103-129, 2001.
• [29] Wagenknecht M., On the approximate treatment of fuzzy arithmetics by inclusion, linear regression and information content estimation, in: Fuzzy Sets and their Applications, Zbiory rozmyte i ich zastosowania, Chojcan J. Łęski J. [Eds.], Wydawnictwo Politechniki Śląskiej, Gliwice, pp. 291-310, 2001.
• [30] Kaufman A., Gupta M.M., Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York, 1991.
• [31] Prokopowcz P., Algoritmization of operations on fuzzy numbers and its applications [in Polish: Algorytmizacja działań na liczbach rozmytych i jej zastosowania], Ph.D. Thesis, IPPT PAN, Warszawa, 2005.
• [32] Kosiński W., On fuzzy number calculus, Int. J. Appl. Math. Comput. Sci., 16 (1), 51-57, 2006.
• [33] Czogała E., Pedrycz W., Elements and methods of fuzzy set theory [in Polish], PWN, Warszawa, 1985.
• [34] Piegat A., Fuzzy modelling and control [in Polish: Modelowanie i sterowanie rozmyte], Akademicka Oficyna Wydawnicza EXIT, Warszawa, 1999.
• [35] Kosiński W., On defuzzyfication of ordered fuzzy numbers, in: Artifical Intelligence and Soft Computing ICAISC 2004, Proc. of the 7th Intern. Conf. Zakopane, Poland, June 2004, Rutkowski L., Siekmann J., Tadeusiewicz R., Zadeh L.A. [Eds.], Springer, Berlin, pp. 326-333, 2004.
• [36] Alexiewicz A., Functional Analysis [in Polish: Analiza funkcjonala], PWN, Warszawa, 1969.
• [37] Dobrosielski W., Trangular extension - new defuzzification methods of Ordered Fuzzy Numbers [in Polish: Trojkątne Rozszerzanie, nowa metoda wyostrzania na skierowanych liczbach rozmytych], in: Proceedings of XIV International PhD Workshop OWD 2012, Conference Archives, PTETiS, 31, 328-333, 2012.
• [38] Kosiński W., Piasecki W., Wilczyńska-Sztyma D., On fuzzy rules and defuzzification functionals for Ordered Fuzzy Numbers, in: Proc. of AIMeth’2009 Conference, Nowvember, 2009, Burczyński T., Cholewa W., Moczulski W. [Eds.] AIMETH Series, pp. 161-178, Gliwice, 2009.
• [39] Kosiński W., Wilczyńska-Sztyma D., Defuzzification and implication within ordered fuzzy numbers, in: WCCI 2010 IEEE World Congress on Computational Intelligence July, 18-23, 2010 - CCIB, Barcelona, Spain, pp. 1073-1079, 2010.
• [40] Rosa A., Modelling with Ordered Fuzzy Numbers [in Polish: Modelowanie z wykorzystaniem skierownych liczb rozmytych], Engineering Thesis, WMFiT, Kazimierz-Wielki University, Bydgoszcz, 2011.
• [41] Wilczyńska D., On control aspects within ordered fuzzy numbers in MATLAB environment [in Polish], Master Thesis, WMFiT, Kazimierz-Wielki University, Bydgoszcz, 2007.
• [42] Kacprzak M., Kosiński W., On lattice structure and implications on ordered fuzzy numbers, In: Proc. of the 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT, Aix-les-Bains, France, July 18-22, 2011, Galichet Sylvie, Montero Javier, Mauris Gilles [Eds.], Atlantis Press, ISBN 978-90-78677-00-0, pp. 267-274, 2011.
• [43] Gruszczyńska A., Krajewska I., Fuzzy Calculator on Step Ordered Fuzzy Numbers [in Polish], Engineering Thesis, WMFiT, Kazimierz-Wielki University, Bydgoszcz, 2008.
• [44] Kościeński K., Modul of Step Ordered Fuzzy Numbers in Control of Material Point Motion [in Polish: Moduł schodkowych skierowanych liczb rozmytych w sterowaniu ruchem punktu materialnego], Engineering Thesis, PJWSTK, Warszawa, 2010.
• [45] Prokopowicz P., Using ordered fuzzy numbers arithmetic, in: Fuzzy Control in Artificial Intelligence and Soft Computing, Proc. of the 8th International Conference on Artificial Intelligence and Soft Computing Zakopane, Polska, 2004, June 25-29, 2006, Cader A., Rutkowski L., Tadeusiewicz R., Zurada J. [Eds.], Academic Publishing House EXIT, Warsaw, pp. 156-162, 2006.
• [46] Kosiński W., Prokopowicz P., Kacprzak D., Fuzziness - representation of dynamic changes by ordered fuzzy numbers, Chapter in: Views of Fuzzy Sets and Systems from Different Perspectives, Rudolf Seising [Ed.], Studies in Fuzziness and Soft Computing, Vol. 243, Springer, Berlin,Heidelberg, pp. 485-508, 2009.
• [47] Hazen G.B., A new perspective on multiple internal rates of return, The Engineering Economist, 48 (2), 31-51, 2003.
• [48] Hartman J.C., Schafrick I.C., (2004), The relevant internal rate of return, The Engineering Economist, 49 (2), 139-158.