The analysis and application for gray correlation theory

This world is often modeled in tenns of systems or environments, for examples: natural environment (or ecological system) and social environment. These environments and systems do not exist independently of each other. Some systems can be described as subsets of other larger systems or are dependent on other systems. One example is that the educational systems or demographic environments are within the context of a larger social environment or system. Systems and subsystems in a larger system exist many interrelationships. Changes in one system may be dependent or influenced by events in another systems. It is possible that, no isolated, independent systems exist in this world. The interrelationship of many systems are well known and understood, but some others' are poorly understood or even unknown. Methods are needed for analyzing and modeling relationships within systems. Gray system theory provides the necessary tools for creating models of systems and analyzing fuzzy relationships in those systems. This paper presents specific methods for finding measurable relationship between systems and their subsystems. The results from the California Test of Mental Maturity(CTMM) are used as independent variables in this paper, and the test scores of a midterm exams at a vocational technical school are used as dependent variables. The superiority analysis model from gray correlation theory will be used to detennine whether the two are related or not. One assumption is made from this result, that is if a significant change in one variable is followed by a similar significant change in another variable, a strong correlation exists. Conversely, if a significant change in one variable is followed, by a little change or no change in another variable, then there is no significant correlation. Therefore gray correlation theory can be used as a tool to measure changing distributions in dynamic systems.