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Fuzzy linear programming based on statistical confidence interval and interval-valued fuzzy set. (English) Zbl 0994.90143
A standard linear programming problem applied to a production process, with uncertain coefficients a ij and right-hand sides b i in the constraints, is considered. It is assumed that statistical confidence intervals of the uncertain a ij and b i for all i, j can be calculated. Each a ij , b i is substituted by a (1-α)-level fuzzy number, which is derived by making use of a statistical confidence interval. In this way, a fuzzy linear programming problem is obtained. Similarly two statistical confidence intervals are used to derive (1-α,1-β)-interval-valued fuzzy numbers, which are used as coefficients and right-hand sides in the constraints of an alternative fuzzy linear programming problem. The defuzzification of both fuzzy problems resulting in crisp linear programming problems is carried out using the theory presented at the beginning of the article and some known results from the literature. An illustrative numerical example is solved.
90C70Fuzzy programming
90C05Linear programming
62F25Parametric tolerance and confidence regions