Granular Lattice Matrix Space Model And Its Application Research

When people deal with problems in real world, they often analyze it in different levels. The strategy is described more accurately by granular computing. Therefore, granular computing is not only the sum of theory, method and tools, but also regarded as world view and methodology.Granular computing is studied in two respects, which are construction and computation of granules. The former deals with its form, description and interpretation. The latter focus on its applications in solving problem. All in one word, granular computing describes the problem by the relationship among granules, decomposition and composition of granules.One new granular computing model is proposed in the paper, which is granular lattice matrix space model. It not only has the merit of rough set and quotient space based on conception of division, but also solves the problem in fuzzy space, such as the way of fuzzy set. It sets up the bridge between granularity, matrix and image. Besides it, it provides a simple way to unite fuzzy set, rough set and quotient space to one model. The main researches and contributions involve four points as following.(1)Propose the model of granular lattice matrix space. It simulates the relationship of granules and granular layers by granular matrix and granular lattice matrix. It not only granulates knowledge and information into granules, but also reflects the relation among granular layer. The knowledge hierarchy structure helps to realize transition among granules and granular layer, which provides a new method to describe knowledge.(2)Develop knowledge discovery algorithm of incomplete and complete information system based on the model. Take incomplete and complete information system as research objects, we substitute matrix operation for general algorithms. It provides a new method different from traditional methods, and it is proved by theory analyze and examples.(3)Propose dynamic clustering algorithm based on the model. Firstly, we takes statistic variable F to decide granular layer. Secondly, we apply knowledge discovery algorithm based on the model to define distance formula. Finally, we adopt dynamic granularity to value sample points by coarser and finer granularity. The new algorithm not only improves clustering accuracy, but also testifies the new model in application.(4)Develop image segmentation algorithm based on the model. Based on the relation between image segmentation and granularity division, firstly we convert image into hierarchy knowledge structure, then construct unit granular layer, finally compose segmentations in each unit layer to acquire final effect. Experiments improve the algorithm has better effect in edge fining.The innovative achievements of the paper can be concluded as following.(1) Propose the model of granular lattice matrix space. It provides a simple way to unite fuzzy set, rough set and quotient space to one model(2) Taking complete information system as object, we develop knowledge discovery algorithm based on the model by granular matrix and granular lattice matrix.(3) Taking incomplete information system as object, we propose knowledge discovery algorithm based on the model by tolerance granules.(4) Adopting dynamic granularity, we propose dynamic clustering algorithm based on the model. It improves clustering accuracy while reducing time complexity.(5) Based on the coherence of granularity division and image, we develop image segmentation algorithm based on the model. It has better effects in edge fining than other algorithms.