Searching for the complete cover of a compatible relation on non-empty finite sets plays an important role in data mining and management decision-making. In this paper, the complete cover theory of a compatible relation is discussed, and the relevant theorem of merging compatible classes into complete cover is put forward and proved, and a generating algorithm of the complete cover of a compatible relation is proposed, and apply it to find the optimal solution for resource scheduling and allocating and so on. The application results show that the algorithm has the close efficiency to dynamic programming method, and the practical application is simple, feasible and steady.

Considering the limitation of AHP-fuzzy comprehensive evaluation method on the isomorphism and mutual exclusion of comment sets, it is difficult to use this method to evaluate actual cases with different dimension comment sets or check comment grades. This paper propounded an improved AHP-fuzzy comprehensive evaluation method with heterogeneous and check comment set, and the proposed method was further applied to the comprehensive evaluation of the evaluation state of collegiate teaching quality. Results illustrated that the improved method excelled not only in analysing and comparing the membership degree of each evaluation grade of the ultimate evaluation factors, but also in examining and evaluating the expected compliancedegree of each evaluation factor. The evaluation results were demonstrated to be more objective, accurate and applicable in a much wider scope.

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The minimum set covering problem with a wide application background is a classical NP problem in the combinatorial optimization and theoretical computing, which defect is at exponential time complexity. Therefore, based on the compatible relations in set theory，this paper constructed the minimum set cover search model, designed an exact algorithm (MSCPT) to solve the minimum set cover on the maximum simple cover, and conducted its time complexity analysis, proof and time performance test. Finally, MSCPT is applied to the optimal location of express service points. The test results show that the MSCPT with sub exponential time complexity can effectively solve the exact solution in small-scale set cover, and its practical application is simple, feasible and steady.