Operations Research with Fuzzy Data

Often in real-case problems, all the numerical data are not precisely known and the nature of the uncertainty is possibilistic14 rather than probabilistic. Then, the data are said fuzzy. The adaptation of an ordinary algorithm (appropriate to precise data) to fuzzy data is not always straightforward. Theoretically, the direct application of the extension principle of fuzzy set theory solves this problem, but not generally in a computationally attractive manner. Practically, the case of forecasting algorithms, where the result may be fuzzy is different from this of decision algorithms where the result must be precise. For an illustrative purpose, we successively deal with the PERT, assignment, travelling salesman and transportation problems. Using results about the algebraic manipulation of fuzzy numbers, computationally attractive algorithms for fuzzy data are provided.