Capital Budgeting Techniques Using Discounted Fuzzy Cash Flows

  • Cengiz Kahraman
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 76)


In an uncertain economic decision environment, an expert’s knowledge about dicounting cash flows consists of a lot of vagueness instead of randomness. Cash amounts and interest rates are usually estimated by using educated guesses based on expected values or other statistical techniques to obtain them. Fuzzy numbers can capture the difficulties in estimating these parameters. In this chapter, the formulas for the analyses of fuzzy present value, fuzzy equivalent uniform annual value, fuzzy future value, fuzzy benefit-cost ratio, and fuzzy payback period are developed and given some numeric examples. Then the examined cash flows are expanded to geometric and trigonometric cash flows and using these cash flows fuzzy present value, fuzzy future value, and fuzzy annual value formulas are developed for both discrete compounding and continuous compounding.


Membership Function Cash Flow Fuzzy Number Ordinary Number Triangular Fuzzy Number 
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  1. [1]
    Zadeh, L.A. (1965) Fuzzy Sets, Information and Control, Vol. 8, pp. 338–353.Google Scholar
  2. [2]
    Buckley, J.U. (1987) The fuzzy mathematics of finance, Fuzzy Sets and Systems, Vol. 21, pp. 257–273.CrossRefGoogle Scholar
  3. [3]
    Chiu, C.Y., Park, C.S. (1994) Fuzzy cash flow analysis using present worth criterion, The Engineering Economist, Vol. 39, No. 2, pp. 113–138.CrossRefGoogle Scholar
  4. [4]
    Ward, T.L. (1985) Discounted fuzzy cash flow analysis, in 1985 Fall Industrial Engineering Conference Proceedings, pp. 476–481.Google Scholar
  5. [5]
    Blank, L.T., Tarquin, J.A. (1987) Engineering Economy, Third Edition, McGraw-Hill, Inc.Google Scholar
  6. [6]
    Chang, W. (1981) Ranking of fuzzy utilities with triangular membership functions, Proc. Int. Conf. of Policy Anal. and Inf. Systems, pp. 263–272.Google Scholar
  7. [7]
    Dubois, D., Prade, H. (1983) Ranking fuzzy numbers in the setting of possibility theory, Information Sciences, Vol. 30, pp. 183–224.CrossRefGoogle Scholar
  8. [8]
    Jain, R. (1976) Decision making in the presence of fuzzy variables, IEEE Trans. on Systems Man Cybernet, Vol. 6, pp. 698–703.CrossRefGoogle Scholar
  9. [9]
    Kaufmann, A., Gupta, M. M. (1988) Fuzzy Mathematical Models in Engineering and Management Science, Elsevier Science Publishers B. V.Google Scholar
  10. [10]
    Yager, R.R. (1980) On choosing between fuzzy subsets, Kybernetes, Vol. 9, pp. 151–154.CrossRefGoogle Scholar
  11. [11]
    Kahraman, C., Ulukan, Z. (1997) Continuous compounding in capital budgeting using fuzzy concept, in the Proceedings of 6`h IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’97), Bellaterra-Spain, pp. 14511455.Google Scholar
  12. [12]
    Kahraman, C., Ulukan, Z. (1997) Fuzzy cash flows under inflation, in the Proceedings of Seventh International Fuzzy Systems Association World Congress (IFSA’97), University of Economics, Prague, Czech Republic, Vol. IV, pp. 104–108.Google Scholar
  13. [13]
    Zimmermann, H.-J. (1994) Fuzzy Set Theory and Its Applications, Kluwer Academic Publishers.Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2001

Authors and Affiliations

  • Cengiz Kahraman
    • 1
  1. 1.Department of Industrial Engineeringİstanbul Technical UniversityİstanbulTurkey

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