两种结构的商空间模型比较研究

摘要

本文提出了多粒度计算的一般架构，即自顶向下的分解和自底而上的综合。结构在商空间理论中扮演着举足轻重的角色，不同结构下商空间模型会有所差异。在合成方面，具有拓扑结构的不同商空间的合成拓扑不是商拓扑，而具有代数结构的不同商空间的合成运算是商运算。在分解方面，定义了问题等价和可逆分解的概念后，得出了两种结构的分解都是可链式化的，即链式分解和直接分解是等价的，以及代数结构的商空间模型中正交分解是可逆分解，而对于拓扑结构的商空间模型类似结论不一定成立。%A multi-granular computing architecture ,namely a top-down decomposition and bottom-up synthesis is proposed . The structure plays a very important role in quotient space model (QSM ) ,and the QSMs with different structures generally vary . With respect to composition ,a composition of topologies of different quotient spaces is generally not a quotient topology ,while a op-erator composition of operators of different quotient spaces is a quotient operator .As for decomposition ,it acquires the two important conclusions when defining the concepts of problem equivalence and reversible decomposition .One is that the granulation for two structures by means of either chained or directed are equivalent ,the other is that an orthogonal decomposition in QSM with a alge-braic structure is reversible ,but a similar conclusions is not true in QSM with a topological structure .