×

Application of possibility theory to investment decisions. (English) Zbl 1136.91365

Summary: C. Carlson and R. Fullér [Fuzzy Sets Syst. 122, 315–326 (2001; Zbl 1016.94047)] introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see [S. Bodjanova, Inf. Sci. 172, 73–89 (2005; Zbl 1074.03018)] for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.

MSC:

91B06 Decision theory
91B28 Finance etc. (MSC2000)
03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Appadoo, S. S. (2006). Pricing financial derivatives with fuzzy algebraic models: A theoretical and computational approach. Ph.D. Thesis, Department of Business Administration, University of Manitoba, Winnipeg, Manitoba, Canada.
[2] Appadoo, S. S., Bector, C. R., & Sharma, V. N. (2000). Net present value under fuzzy data. Administrative Sciences Association of Canada (ASAC), University of Quebec at Montreal (UQUAM), Canada.
[3] Bector, C. R., Bhatt, S. K ., & Appadoo, S. S. (2003). Capital asset pricing model under fuzzy information. Administrative Sciences Association of Canada (ASAC), Nova Scotia, Canada.
[4] Bector C.R., Chandra S. (2005). Fuzzy mathematical programming and fuzzy matrix Games. Springer-Verlag, Berlin · Zbl 1078.90071
[5] Bodjanova S. (2005). Median value and median interval of a fuzzy number. Information Sciences 172, 73–89 · Zbl 1074.03018 · doi:10.1016/j.ins.2004.07.018
[6] Brealey R.A., Myers S.C. (1999). Principle of corporate finance. McGraw Hill, New York
[7] Buckley J.J. (1987). The fuzzy mathematics of finance. Fuzzy Sets and Systems 21, 257–273 · Zbl 0613.90017 · doi:10.1016/0165-0114(87)90128-X
[8] Buckley J.J. (1992). Solving fuzzy equations in economics and finance. Fuzzy Sets and Systems 48, 28996 · Zbl 0769.90023 · doi:10.1016/0165-0114(92)90344-4
[9] Calzi M.L. (1990). Toward a general setting for the fuzzy mathematics of finance. Fuzzy Sets and Systems 35, 265–280 · Zbl 0703.90002 · doi:10.1016/0165-0114(90)90001-M
[10] Carlsson C., Fuller R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 · Zbl 1016.94047 · doi:10.1016/S0165-0114(00)00043-9
[11] Carlsson, C., & Fuller, R. (2002). Fuzzy reasoning in decision making and optimization. Physica-Verlag. · Zbl 1016.68111
[12] Carlsson C., Fuller R. (2003). A fuzzy approach to real option valuation. Fuzzy Sets and Systems 139, 297–312 · Zbl 1055.91019 · doi:10.1016/S0165-0114(02)00591-2
[13] Chiu C.U., Park C.S. (1994). Fuzzy cash flow analysis using present worth criterion. The Engineering Economist 39, 113–138 · doi:10.1080/00137919408903117
[14] Choobineh F., Behrens A. (1992). Use of intervals and possibility distribution in economic analysis. Journal of Operations Research Society 43, 907–918 · Zbl 0825.90058
[15] Dubois D., Prade H. (1979). Fuzzy real algebra: Some results. Fuzzy Set and Systems 2, 327–348 · Zbl 0412.03035 · doi:10.1016/0165-0114(79)90005-8
[16] Dubois D., Prade H. (1980). Fuzzy sets and systems: Theory and applications. Academic Press, New York · Zbl 0444.94049
[17] Esogbue A.O., Hearnes W.E. (1998). On replacement models via a fuzzy set theoretic framework. IEEE Transactions on Systems, Man, and Cybernetics-Part C, Applications and Reviews 28, 549–58 · Zbl 0929.90011 · doi:10.1109/5326.725341
[18] Fuller R., Majlender P. (2003). On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Set and Systems 136, 363–374 · Zbl 1022.94032 · doi:10.1016/S0165-0114(02)00216-6
[19] Goetschel R., Voxman W. (1986). Elementary fuzzy calculus. Fuzzy Set and Systems 18, 31–43 · Zbl 0626.26014 · doi:10.1016/0165-0114(86)90026-6
[20] Kahraman C., Ruan D., Tolga E. (2002). Capital budgeting techniques using discounted fuzzy versus probability cash flows. Information Sciences 142, 57–76 · Zbl 1037.91051 · doi:10.1016/S0020-0255(02)00157-3
[21] Karsak E.E., Tolga E. (2001). Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments. International Journal of Production Economics 69, 49–64 · doi:10.1016/S0925-5273(00)00081-5
[22] Kaufmann A., Gupta M.M. (1985). Introduction to fuzzy arithmetic theory and applications. USA: Von Nostrand Reinhold Company, New York · Zbl 0588.94023
[23] Kaufmann A., Gupta M.M. (1988). Fuzzy mathematical models in engineering and management science. Elsevier Science Publishers BV, Amsterdam · Zbl 0683.90024
[24] Kuchta D. (2000). Fuzzy capital budgeting. Fuzzy Sets and Systems 111, 367–85 · Zbl 1053.91505 · doi:10.1016/S0165-0114(98)00088-8
[25] Kuchta D. (2001). A fuzzy model for R&D project selection with benefit, outcome and resource interactions. The Engineering Economist 46, 164–180 · doi:10.1080/00137910108967571
[26] Medaglia A.L., Fang S.C., Nuttle H.L.W., Wilson J.R. (2002). An efficient and flexible mechanism for constructing membership functions. European Journal of Operational Research 139, 84–95 · Zbl 1010.03525 · doi:10.1016/S0377-2217(01)00157-6
[27] Medasani S., Kim J., Krishnapuram R. (2002). An overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning 19, 391–417 · Zbl 0947.68555 · doi:10.1016/S0888-613X(98)10017-8
[28] Thavaneswaran A., Thiagarajah K., Appadoo S.S. (2007). Fuzzy coefficient volatility (FCV) models with applications. Mathematical and Computer Modelling 45, 777–786 · Zbl 1165.91415 · doi:10.1016/j.mcm.2006.07.019
[29] Thiagarajah K., Appadoo S.S., Thavaneswaran, A. (2007). Option valuation model with adaptive fuzzy numbers. Computers & Mathematics with Applications 53, 831–841 · Zbl 1213.91145 · doi:10.1016/j.camwa.2007.01.011
[30] Ward, T. L. (1985). Discounted fuzzy cash flow analysis. Industrial Engineering Conference, Institute of Industrial Engineers. 476–481
[31] Ward T.L. (2005). European option pricing under fuzzy environments. Internatioanl Journal of Intelligence Systems 20, 89–102 · Zbl 1079.91045 · doi:10.1002/int.20055
[32] Zadeh L.A. (1965). Fuzzy set. Information and Control 8, 338–353 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[33] Zadeh, L. A. (1996). Fuzzy Sets, fuzzy logic, and fuzzy systems by Lotfi A. Zadeh, Edited and with a preface by George J. Klir and Bo Yuan. Advances in fuzzy systems-applications and theory. River Edge, NJ: World Scientific Publishing Co., Inc. · Zbl 0873.01048
[34] Zimmermann H.J. (2001). Fuzzy sets theory and its applications, 4th Ed. Kluwer Academic Publishers, Nowell, MA, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.