Research On Some Issues Of Rough Sets Theory And Its Applications

Rough sets theory is an effective mathematical approach to uncertain and vague data analysis proposed by Professor Pawlak in early 1980's. The next two decades did witness a substantial progress in developing this theory both theoretically and practically. Nowadays, as an important part of soft computing, Rough sets theory is widely used in many areas, including pattern recognition, machine learning, decision analysis, knowledge discovery in database, expert system, etc. In this dissertation, we focus on some issues of Rough sets theory and its applications. The main contributions and original ideas included in the dissertation are summarized as follows.·Approaches to knowledge reduction in inconsistent decision tables. At present, approaches to knowledge reduction for the distribution reduct, the maximum distribution reduct and the assignment reduct of an inconsistent decision table are based on discernibility matrixes, which are time-consuming when the dataset is large. To overcome this shortcoming, an approach is proposed to convert the computation for the three types of reducts of the original inconsistent decision table into the computation for the Pawlak reduct of three types of derived consistent decision tables. Thus, efficient heuristic knowledge reduction algorithms for the Pawlak reduct can be exploited to reduce computational costs.·Heuristic algorithm for knowledge reduction in incomplete decision tables. The Rough sets model based on the tolerance relation is the most cited one for incomplete decision tables. In this model, knowledge reduction for the generalized decision reduct is the commonly used type of knowledge reduction. At present, approaches to this type of knowledge reduction are based on discernibility matrixes, which means they are not applicable to large datasets. To deal with this problem, based on the analysis of the properties related to the generalized decision reduct, the significance of each attribute is proposed. Using it as heuristic information, a complete algorithm for knowledge reduction is proposed.·New definition of Variable Precision Fuzzy Rough sets. Like Rough sets, Fuzzy Rough sets are sensitive to noises in data. Inspired by the Variable Precision Rough sets model, the concept of Variable Precision Fuzzy Rough sets is proposed to deal with this problem. But the existing model of Variable Precision Fuzzy Rough sets does not possess some basic requirements which are possessed by Rough sets, Variable Precision Rough sets and Fuzzy Rough sets. To overcome this shortcoming, the concepts of theβ-lower andβ-upper approximations of a fuzzy set in a fuzzy approximation space are redefined. The definitions are proved to possess those basic requirements.·New crossover operator based on Rough sets theory. The commonly used crossover operators are likely to destroy useful schemata with high defining length or order. Inspired by the research results of human DNA, a new crossover operator based on Rough sets theory is proposed to overcome this shortcoming. By using this specialized crossover operator, useful schemata can be found and have a high probability of surviving recombination regardless of their defining length or order.·Two-stage tabu search algorithm based on Rough Sets Theory. Based on Rough sets theory, a two-stage tabu search algorithm is proposed for combinatorial optimization problems represented by TSP. In this approach, unlike other adaptive tabu search algorithms, the balance between intensification and diversification is not achieved by tuning tabu search parameters adaptively, but a two-stage search strategy. The first stage aims to diversification. In this stage, by stimulating the search area moving away from the initial solution, the solution space is explored in a certain degree. Then, the promising area decision table is constructed and the promising area is obtained by the knowledge reduction procedure. The second stage aims to intensification. This stage begins with the best solution contained in the promising area and exploits it. In the search procedure, some constrains are imposed flexibly on the selection of the current solution so as to utilize useful information obtained in the first stage.·Cluster validity index based on Rough sets theory. Combining basic ideas of two kinds of commonly used cluster validity indices, a new index is proposed for Fuzzy c-Means algorithm. The proposed index uses the distance between cluster centroids and the overlap between fuzzy clusters to evaluate the interclass difference. Furthermore, the concepts of Fuzzy Rough sets are introduced to quantify the consistency of the corresponding partition. Thus, the preferable fuzzy partition can be found. ·Pronominal anaphora resolution based on Rough sets theory. Aninstance-based learning approach combined with Fuzzy Rough sets to resolve pronominal anaphora within Chinese text is presented. The first phase of the presented approach is preprocessing. In this phase, the potential antecedents set is formed. Then, the attribute values of every noun phase in this set are computed according to an attributes set which only involves shallow syntactic and semantic knowledge. The second phase aims to select representative examples from the potential antecedents set and reduce redundant attributes to improve the generalization capability of these examples. The two tasks are done by using the concepts of Fuzzy Rough sets. The two phases above can be regarded as the learning phase. The last phase is using those examples to estimate whether a new noun phase is the antecedent of the pronominal anaphora.