Abstract
Techniques for ranking simple fuzzy numbers are abundant in the literature. However, we lack efficient methods for comparing complex fuzzy numbers that are generated by fuzzy engineering economic analyses. In this chapter a probabilistic approach is taken instead of the usual fuzzy set manipulations. The Mellin transform is introduced to compute the mean and the variance of a complex fuzzy number. The fuzzy number with the higher mean is to be ranked higher. Two fuzzy cash flow analyses and a fuzzy multiple attribute decision analysis are illustrated in order to demonstrate the suitability of the probabilistic approach. A real beauty of the approach is that it can accommodate all types of fuzzy numbers such as uniform, triangular, or trapezoidal simultaneously, and all computations are easily calculated in the spreadsheet.
This chapter was adapted from the author’s article: Yoon KP (1996) A probabilistic approach to rank complex fuzzy numbers. Fuzzy Sets and Systems 80: 167-176.
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Yoon, K.P. (2008). A Probabilistic Approach to Fuzzy Engineering Economic Analysis. In: Kahraman, C. (eds) Fuzzy Engineering Economics with Applications. Studies in Fuzziness and Soft Computing, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70810-0_13
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DOI: https://doi.org/10.1007/978-3-540-70810-0_13
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