Introduction
In this chapter we first discuss different ways to generate sequences of “random” numbers in some interval [a,b]. Usually the random numbers are first produced in [0,1] and then we perform a linear transformation to get them into [a,b]. Next we consider making sequences of random non-negative integers. We wish to produce sequences of random vectors v = (x 1,...,x n ) where the x i are real numbers, and the randomness here means that the v will uniformly fill the space [a,b]n. These random vectors will be used in the next chapter to generate sequences of random fuzzy numbers.
Subsequently, vectors of so-generated random fuzzy numbers are used for streams to feed fuzzy Monte Carlo optimization. As is shown in Chapter 4, with a 5-tuple we can generate a fuzzy number with quadratic membership functions. In some cases we evaluate using a vector of two or three fuzzy numbers generated from 5-tuples. In Chapters 6 and 9, we generate pairs of fuzzy numbers from Sobol quasi-random 10-tuples. In Chapters 7 and 8, vectors of three fuzzy numbers generated from Sobol 15-tuples are used. Other applications are in Chapters 10-16.
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Buckley, J.J., Jowers, L.J. (2007). Crisp Random Numbers and Vectors. In: Monte Carlo Methods in Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76290-4_3
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