广义差集矩阵和正交表——处理复杂系统的新思维系列之十七

Generalized Difference Matrix and Orthogonal Arrays——New Thinking of Dealing with Complex Systems Series Seventeen

本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。作为系列论文的第十七篇,介绍了广义差集矩阵和混合正交表以及普通差集的等价关系,利用广义差集矩阵构造了正交表和普通差集,同时也利用正交表构造了广义差集矩阵。

This series of articles, based on ＂Multilateral Matrix Theory＂ and inspired by the Eastern holistic thinking,are trying to provide and improve a set of powerful mathematical tools to handle multi- target local issues, non-uniformity problems and nonlinear problems of complex system ranging from the whole to the part with rigorous theoretical analysis and proof. As the seventeenth paper of the series, the equivalence relation of the generalized difference matrix, mixed orthogonal arrays and usual difference matrix have been introduced. It turned out that the generalized difference matrix could construct the mixed orthogonal arrays and usual difference matrix, which in turn was constructed by means of mixed orthogonal arrays.