EUSFLAT 2017, IWIFSGN 2017: Advances in Fuzzy Logic and Technology 2017 pp 509-520

# Real Option Analysis with Interval-Valued Fuzzy Numbers and the Fuzzy Pay-Off Method

• József Mezei
• Mikael Collan
• Pasi Luukka
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

## Abstract

This paper presents an extension of the fuzzy pay-off method for real option valuation using interval-valued fuzzy numbers. To account for a higher level of imprecision that can be present in many applications, we propose to use triangular upper and lower membership functions as the basis of real option analysis. In the paper, analytical formulas are derived for the triangular case by calculating the possibilistic mean of truncated interval-valued triangular fuzzy numbers. A numerical example of a cash-flow analysis is presented to illustrate the use of the proposed approach.

## Keywords

Real option valuation Fuzzy pay-off Interval-valued fuzzy numbers Possibilistic mean

## References

1. 1.
Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Set. Syst. 122, 315–326 (2001)
2. 2.
Carlsson, C., Fullér, R., Mezei, J.: Project selection with interval-valued fuzzy numbers. In: Proceedings of the Twelfth IEEE International Symposium on Computational Intelligence and Informatics (CINTI 2011), Budapest, Hungary, pp. 23–26. IEEE (2011)Google Scholar
3. 3.
Collan, M., Fullér, R., Mezei, J.: A fuzzy pay-off method for real option valuation. J. Appl. Math. Decis. Sci. 2009 (2009). Advances in Decision Sciences, Article ID 238196, 14 pagesGoogle Scholar
4. 4.
Datar, V., Mathews, S.: A practical method for valuing real options: the boeing approach. J. Appl. Corp. Fin. 19, 95–104 (2007)
5. 5.
Dubois, D., Prade, H.: Interval-valued fuzzy sets, possibility theory and imprecise probability. In: Proceedings of the International Conference in Fuzzy Logic and Technology, Barcelona, Spain, pp. 314–319 (2005)Google Scholar
6. 6.
Ho, S.-H., Liao, S.H.: A fuzzy real option approach for investment project valuation. Exp. Syst. Appl. 38, 15296–15302 (2011)
7. 7.
Liu, P.: Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans. Fuzzy Syst. 22, 83–97 (2014)
8. 8.
Mathews, S., Salmon, J.: Business engineering: a practical approach to valuing high-risk, high-return projects using real options. In: Gray, P. (ed.) Tutorials in Operations Research: Informs (2007)Google Scholar
9. 9.
Muzzioli, S., De Baets, B.: Fuzzy approaches to option price modelling. IEEE Trans. Fuzzy Syst. doi:
10. 10.
Ozen, T., Garibaldi, J.M.: Effect of type-2 fuzzy membership function shape on modelling variation in human decision making. In: Proceedings of Thee IEEE International Conference on Fuzzy Systems, Budapest, Hungary, pp. 971–976. IEEE (2004)Google Scholar
11. 11.
Pedrycz, W.: Why triangular membership functions. Fuzzy Set. Syst. 64, 21–30 (1994)
12. 12.
Wang, G., Li, X.: The applications of interval-valued fuzzy numbers and interval-distribution numbers. Fuzzy Set. Syst. 98, 331–335 (1998)
13. 13.
Wang, Z., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Set. Syst. 118, 375–385 (2001)
14. 14.
Wu, J., Chiclana, F.: A social network analysis trustconsensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowl. Based Syst. 59, 97–107 (2014)
15. 15.
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
16. 16.
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)
17. 17.
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Set. Syst. 1, 3–28 (1978)
18. 18.
Zmeškal, Z.: Generalised soft binomial American real option pricing model (fuzzystochastic approach). Eur. J. Oper. Res. 207, 1096–1103 (2010)