Tolerance Granular Space And Its Applications

The basic idea of granular computing is the using of granules during problem solving.Information granules always exist in our true-life, and they are the abstraction of the reality.The granulation is to construct the concepts depending on the context effectively and is useroriented. Besides, it is also for the simplification of our understanding of the physical andvirtual world.As computing units, granules can decompose a complex problem into some simple orsmall problems, so that the computing costs are reduced, a problem can be understood better,and the trivial can be avoided during problem solving. The research on granular computingmainly focuses on two parts: the construction of granules and the computing with granules.The former considers the generation, description and explanation of granules, and the latterdiscusses the using of granules during computing. In general, granular computing is aproblem describing and solving method, which depends on the abstraction of the reality bygranules, the relations among granules, the composition and decomposition of granules, andthe transformation among granules or granule sets.This thesis proposes a new granular computing model, tolerance granular space model.The basic idea of the model is based on the human ability that is, people can abstract orsynthetize the knowledge and data related to special tasks to different degrees or sizesgranules, and accomplish the tasks with the helps of the granules and relations among them.The main researches and contributions are fourfold: Propose the model of tolerance granular spaces. The model is constructed based ontolerance relations, and it is composed with four parts: object set system, tolerancerelation system, transformation function and nested tolerance covering system. The mainfeatures of the model focus on the definition of granules and the problem solvingmethods with the help of the hierarchical and nested structure of tolerance granularspaces. In this part, we mainly discuss the issues about the definition of tolerancegranules, the relations among granules, the composition and decomposition of granules,the formulating of the models, model constructing methods, and the features andproperties of tolerance granular models, etc.Develop a tolerance granular space based information classification method. In thisapplication, our model is used as a knowledge extraction tool and a classifier. Based onthe theory of tolerance granular space and related knowledge of informationclassification, the tolerance granular space modeling algorithm TGM and the tolerancegranular space based classification algorithm TGLC are developed. Simulation resultsshow that our algorithms have higher classification rates and better robust thancomparing algorithms.Propose a new bilevel decision model. Bilevel decision addresses the problem in whichtwo levels of decision makers, each tries to optimize their individual objectives underconstraints, act and react in an uncooperative, sequential manner. However, bileveldecision making may involve many uncertain factors in a real world problem. Thereforeit is hard to determine the objective functions and constraints of the leader and thefollower when building a bilevel decision model. To deal with this issue, this studyexplores the use of tolerance granule sets generated from tolerance granular space toformat a bilevel decision problem by establishing a tolerance granule sets based model.In this part, we present the definition of the tolerance granule sets based bilevel decisionmodel, the modeling algorithm and the decision algorithm, etc. An application shows theeffectiveness of the model and algorithms.Develop a new tolerance granular space based image texture recognizing algorithm. Inthis application, the model is used as a texture feature extraction tool, and with theextracted features, images are distinguished with each other. With the experiments, theeffectiveness and efficiency of our methods are testified and the application alsoindicates that tolerance granular space is an effective tool to solve some problems inimage processing fields. Then , we summarize above applications, analyze the methodsand its perspectives of the model's application in data mining, and develop the generaltolerance granular space based problem modeling and solving methods.Based on above fruits, we have a conclusion about the theory and applications oftolerance granular spaces. Besides, some problems in the model and our future worksare proposed.