Study On Several Rough Set Models And Their Algorithms Based On Logical Combinations Of Precision And Grade

Variable precision rough set model and graded rough set model are two important expanding rough set models, and have expanded classical rough set model by precision and grade. Precision and grade are two important quantitative indexes of data, and related to the relative and absolute quantitative information respectively. According to the logical combinations of precision and grade, this paper aims to construct several new rough set models and explore their algorithms, properties and applications. The new models are expected to make composite descriptions of precision and grade quantitative indexes, and completely or partially expand variable precision rough set model, graded rough set model and classical rough set model.Based on the practical logical requirements of precision and grade, four kinds of new models are proposed by the common"logical or","logical and"and"logical difference"combinations of precision and grade parameters, which are rough set model based on"logical or"of precision and grade, rough set model based on"logical and"of precision and grade, rough set model based on"logical difference"of precision and grade, rough set model based on"logical difference"of grade and precision. In each model, related to precision and grade indexes the meanings of the upper and lower approximations are studied first, and then the complete rough set region system which classifies the universe more precisely is defined by extending positive region, negative region and boundary region of classical rough set model. Next, the basic structures and properties are investigated, and precise descriptions of rough set regions are obtained; Furthermore, macroscopic and microscopic algorithms are proposed and analyzed in order to calculate rough set regions, and an important conclusion is drawn that microscopic algorithm has more advantages in both time complexity and space complexity. Finally, a medical example is given to illustrate the models and algorithms, and mathematical properties of approximation operators, attribute approximate dependence and reduction are explored too, which are just a basis of deep research and applications of the new models. The four kinds of new models have partially expanded variable precision rough set model, graded rough set model and classical rough set model.Through this program that the upper and lower approximations make the"logical and"and"logical or"combinations of precision and grade respectively, the fifth new model is proposed and called rough set model based on"logical and"and"logical or"of precision and grade. In this new model, precise descriptions of rough set regions are obtained; macroscopic and microscopic algorithms are proposed and analyzed; many properties are obtained; an example is given. All these studies are similar to those of the previous four new models. Particularly, this new model has a perfect virtue that it has completely expanded variable precision rough set model, graded rough set model and classical rough set model in an ideal direction, so by its study results, precise descriptions of rough set regions, calculation algorithms and algorithm analyses, deep mathematical properties of approximation operators, all are obtained in variable precision rough set model, graded rough set model and classical rough set model.The several rough set models based on logical combinations of precision and grade, have logical connotations with respect to precision and grade indexes, and have expanded variable precision rough set model, graded rough set model and classical rough set model. Therefore, they have important value to theories and applications of rough set theory and model. At the same time, the concepts and optimal calculations of rough set regions play an important role in knowledge discovery related to precision and grade parameters.Besides, in introduction section, the relationship between the relative and absolute quantization, and the practical example where absolute quantitative information plays a leading role, both are explored. Furthermore, the important role of graded rough set model is analyzed, which could promote deep developments and applications of graded rough set model.The main innovative points of this paper are as follows:1. It explores the relationship between the relative and absolute quantization, and analyzes the importance of graded rough set model.2. In approximate space, it makes logical combinations of precision relative quantitative index and grade absolute quantitative index, and constructs composite description system of precision relative quantization and grade absolute quantization, and thus makes the composite descriptions of objective concepts of approximation space.3. It studies the relationship between variable precision rough set model and graded rough set model, and constructs five kinds of new rough set models. These new models have formed novel programs to make the composite relative and absolute quantitative description of approximate space, and have completely or partially expanded variable precision rough set model, graded rough set model and classical rough set model.4. Extending the usual concepts of classical rough set model: positive region, negative region and boundary region, it proposes the primitive concept in approximate space, which is the complete rough set system: upper and lower approximations, positive and negative regions, upper and lower boundary regions, boundary region. These rough set regions have composite meanings related to precision and grade indexes, and can classify the universe more precisely, so they lay the foundations of knowledge discovery such as rule extraction and uncertainty reasoning.5. It obtains precise descriptions of rough set regions of the five new models and the three old models (variable precision rough set model, graded rough set model and classical rough set model). It proposes two algorithms: macroscopic and microscopic algorithms, and by algorithm analyses and comparisons a conclusion is drawn that microscopic algorithm is more optimal in usual cases. Furthermore, by the complete expansion property of the new models, precise descriptions of rough set regions, calculation algorithms and algorithm analyses are obtained in variable precision rough set model, graded rough set model and classical rough set model.6. It studies basic properties and two-level power action properties of approximation operators in the five new models. Furthermore, the deep mathematical properties of variable precision approximation operators, grade approximation operators and classical approximation operators are obtained by the complete expansion property of the new models.7. It studies attribute approximate dependence and reduction in the new models, which lays the foundations of both knowledge discovery and deep applications.