| In operations research, management science, information science, systems science, computer science, engineering and many other areas, there is objective or artificial uncertainty. With these uncertainties, there are no doubt a lot of uncertainty optimization problems. However, for these decision problems with uncertainties, the classical optimization theory is often powerless. Therefore, the uncertain programming theory aroused more and more attention of scholars. In this paper, a more in-depth study was conducted to the scheduling problem of fuzzy numbers, the fuzzy linear programming of the uncertain programming and its duality theory.First, in the basis of fuzzy set theory, a distance measure and the fuzzy number weights area were introduced, a new index for ranking fuzzy numbers based on the divergence was established, which made up for past deficiencies in fuzzy scheduling problems, and its application of multi-attribute decision making in an uncertain environment was presented.Second, the paper described a fuzzy linear programming problem with fuzzy coefficients, introduced a new pair of dual fuzzy relations, on this basis, put forward a solution method of fuzzy linear programming, the structure of the solution was also given, and verified by an example to prove the feasibility, validity and practicability of the new method.The fuzzy linear programming duality theory has been also studied in this article; the related theorems corresponding to the duality theorems in classical linear programming were proposed and proved.In the end, after summarizing the whole paper, some problems to be further studied were pointed out.
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