Research Of Order Relation Based On Pansystems Theory And Measures

In this paper, based on the research work of set theory and rough set theory, we do many deep and extensive researches on order relation at the theoretical level. From the recognition of the material world to the pansystem measure, from the change of measure to the change of order relation, we deeply discussed the essential of the order and its root in the material world. Furthermore, on the knowledge of order relation, we generalize and summarize the basic sorting method in computer science. We get a new recognition of these sorting methods from the systematic transformation and system formation's point of view and lay the foundation for new algorithm's further research. The main work and contribution of this paper are as follows:First, we strengthen the body-shadow essential of set theory, the composition and transformation between the part-whole relation and body-shadow relation. Strengthen the concept to re-recognize set theory from the body-shadow relation's perspective, to re-recognize the set's operation from composition and transformation between the part-whole and body-shadow relations. All these are the pansystem's extension on set theory.Second, from the pansystem ontology and epistemology's perspective, we introduce the pansystem measure theory and the innate measure characteristic of the material world. Furthermore, we interpret the essential of transformation between the partial order and the semi-partial order;deepen the essential of sort operation from the systematic theory.In the end, based on the research work which has been done on the pansystem measure theory and order relation, we summarize the basic sorting algorithm in the computer science such as insertion sort, exchange sort and radix sort and give their corresponding pansystem models. From the pansystem system transformation's perspective, we get a new recognition of sorting operation in computer science. We also provide the new point of view of which we view the transformation between the binary tree and B-tree an instance of the transformation between the partial order and semi-partial order. These new recognition of data structure which based on the systematic level provide us the foundation for further study and design of new algorithm.