Research On Hierarchy Granular Computing Theory And Its Application

In the field of computational intelligence, granular computing (GrC) is a new method for simulating human thinking and solving complicated problems. It may be regarded as an umbrella covering the theories, methodologies and techniques of granularity. It is a powerful tool for solving complicated problems, mining massive data sets, and dealing with fuzzy information. The basic idea of granular computing is solving complicated problems in different granularity levels, and the method indicates human intelligence in some degree when people solve the complicated problems. With the development of granular computing theory, different granular computing theoretic models are developed with different viewpoints. Fuzzy set (computing with words), rough set and quotient space are three basic granular computing models.Although each granular computing model has its own method or tool to solve complicated problems, they have a common characteristic that a problem space will be divided into many subspaces which consist of a hierarchical structure before solving the problem. That is, a hierarchical knowledge granularity space is constructed at first when solving a complicated problem, and then partial solutions are obtained in different granularity levels in top-bottom manner and a global solution of the original problem is composed from these partial solutions in bottom-top way until a satisfied solution is resulted. So, a structural granular computing model (it is called hierarchy granular computing model in this thesis) is a very important granular computing model, and the research work about hierarchy granular computing model is an important issue. This research work will contribute to pushing the development of granular computing theory, and is very useful for establishing a uniform granular computing frame.In this thesis, we summarize the granular computing related researches at first. Then, we study several key issues of the hierarchical granular computing theory in detail, such as constructing a hierarchical knowledge granularity space, measuring the uncertainty of a hierarchical knowledge granularity space, analyzing the uncertainty of a rough set in a hierarchical knowledge granularity space, and acquiring knowledge from an information system based on a hierarchical structure, and so on. The most important contributions of this thesis are listed as follows:A new method for hierarchically constructing normalized isosceles distance function between different quotient spaces is proposed based on the fuzzy quotient space with a threshold of 1, and a fuzzy quotient space theory with arbitrary threshold is extended. In this thesis, a recursive method for constructing a fuzzy equivalence relation based on a hierarchical structure is proposed. In this way, both a hierarchical structure and a fuzzy equivalence relation can be transformed into each other. And the operations of quotient space decomposition and composition can be realized through the intersection and combination operations among fuzzy equivalence relations. These results extend the fuzzy quotient space based granular computing theory. (Chapter 2)In order to measure the uncertainty of a hierarchical quotient space, information entropy sequence of a hierarchical quotient space is proposed based on information entropy theory. It is found that the information entropy sequence is a increasing monotonously with the decreasing of knowledge granularity. The concept of isomorphism among hierarchical quotient spaces is also defined, and the isomorphism principle among hierarchical quotient spaces is proved, that is, the necessary and sufficient condition of hierarchical quotient spaces, isomorphism is that they have same division sequence and same information entropy sequence. The relationship among information entropy sequence, hierarchical quotient space, fuzzy equivalence relation and fuzzy similarity relation is discovered, and it indicates that the information entropy sequence is a better tool to measure the uncertainty of a hierarchical quotient space than the other methods. These results provide a good foundation for measuring the uncertainty of a hierarchical quotient space. (Chapter 3)A new method for measuring the fuzziness of rough set is proposed based on information entropy, and the fuzziness measured by the new method is proved to be decreasing monotonously with the refining of knowledge granularity in a hierarchical knowledge granularity space. Roughness, rough entropy, fuzziness, and fuzzy entropy are major methods for measuring the uncertainty of rough set, and in some knowledge granularity level these methods can indicate the uncertainty of rough set, but in different granularity levels the uncertainty measured with these methods may be inconsistent with human cognition. The fuzziness of rough set measured by new method proposed in this thesis will not change when the granules in positive region and negative region are divided into finer granules, or when the granules in boundary region are divided into finer granules proportionately, and the fuzziness will decrease strictly when the graunles are divided in other ways. These results are consistent with human cognition, and they overcome the limitations of existing measuring methods of uncertainty of rough set. (Chapter 4)A new method for building hierarchical knowledge granularity space in an incomplete information system is proposed according to hierarchy granular computing model. A new method for hierarchically acquiring knowledge from fuzzy decision information systems is proposed. The granularity principle of attribute reduction in information systems is studied in the viewpoint of granular computing. A rule generating algorithm based on maximal granule (RGABMG) is proposed. In this algorithm, rules can be acquired from an information system directly without attribution reduction, and the simulation experiments'results show the algorithm's advantages in rule extraction. These results further push the application of hierarchy granular computing theory. (Chapter 5)...