Image segmentation-oriented tolerance granular computing model

A tolerance granular space model, written as a 4-tuple (OS, TR, FG, NTC), is presented in this paper. From the perspective of philosophy, The basic idea of the model is based on the human ability, that is, people can abstract or synthetize the knowledge and data relating with special tasks to different degrees or sizes granules, and accomplish the tasks with the helps of the granules and relations among them. From the perspective of technology and theory, TGrC consists of four parts: object set system, tolerance relation system, transformation function and nested tolerance covering system. The main features of the model focus on the definition of granules and the problem solving methods with the help of the hierachical and nested structure of tolerance granular spaces. In this paper, we mainly discuss the issues about the definition of tolerance granules, the relations among granules, the composition and decomposition of granules, the formulating of the models, model constructing methods, and the features and properties of tolerance granular models, etc. At last, we give an example to the principle and validity of the proposed model.