Introduction
Any sequence claimed to be random, real numbers or fuzzy numbers, must be tested for randomness. We first test our sequence of fuzzy random numbers, obtained from Sobol quasi-random numbers, for randomness using a run test and then a frequency test. We identified two types of triangular shaped fuzzy numbers from Chapter 4: (1) quadratic fuzzy numbers generated from 7-tuples; and (2) quadratic Bézier generated fuzzy numbers (QBGFNs). For reasons given there we direct our attention to QBGFNs. A run test depends on what definition of ≤ between fuzzy numbers we are using. So we do the run test three times on the Bézier fuzzy numbers; first using Buckley’s Method of ≤ (Section 2.6.1) next using Kerre’s Method of ≤ (Section 2.6.2) and lastly using Chen’s Method of ≤ (Section 2.6.3). We must also test our sequence of random fuzzy vectors for randomness. We have seen that sequences of random numbers can pass randomness tests but when they are used to build vectors the resulting sequence of vectors can fail randomness tests (Chapter 3). We will test our sequences of random vectors, whose components are all TFNs, for randomness using a chi-square test.
Actually, these randomness tests are not too important. We plan to use our sequences of random fuzzy numbers/vectors to generate approximate solutions to fuzzy optimizations problems. What is important is for our method to uniformly fill the search space to a fuzzy optimization problem. We argue that this is true in the last section in this chapter.
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Buckley, J.J., Jowers, L.J. (2007). Tests for Randomness. 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_5
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