Study On Rough Sets Theory And Its Applications

Rough set theory, initialized by Professor Pawlak in early 1980's, has been proved to be an excellent mathematical tool dealing with uncertain and vague description of objects, whose basic idea is to derive classification rules of conception by knowledge reduction with the ability of classification unchanged. It can find the hiding and potential rules, that is knowledge, from the data without any preliminary or additional information. In recent years, as an important part of soft computing, rough set theory has been widely used in many areas, especially in the area of pattern recognition, machine learning, decision analysis, knowledge discovery and knowledge acquisition etc. In this dissertation, the focus is on rough sets theory and vague sets theory with their applications in group decision making problems, information retrieval and fuzzy multi-criteria decision making problems. The main contributions and original ideas included in the dissertation are summarized as follows.1. A novel definition of entropy is introduced for tolerant rough set theory, on the basis of which the relation between knowledge and entropy is constructed. We prove that the entropy of knowledge decreases monotonously as the granularity of information becomes smaller. Then a new reduction algorithm in tolerant rough set is presented. Another attribute reduction algorithm is developed for a general type of fuzzy data by using a resemblance relation based on pseudometric. A novel rough set model based on concordance relation is presented, which relaxing the indiscernibility and tolerance between objects on the basis of classical and tolerant rough sets. We make an analysis of the relation between roughness of concordance relation and entropy. An example is shown to illustrate the newly proposed model.2. A rough set approach to group decision making is presented with respect to the decision making problems with linguistic assessment information. A pairwise comparison table is constructed by using a little outranking information, then decision rules are extracted from this table in terms of dominance rough set theory. Finally, we use a score function to sort all the alternatives and select the best one. An example shows that the method is effective.3. A novel information retrieval model based on generalized rough sets calledconditional probability rough sets is presented in this paper. We construct conditional probability relation and fuzzy conditional probability relation between terms. Three kinds of information retrieval method are studied for crisp document feature sets and crisp documents and query, crisp document feature sets and fuzzy documents and query and fuzzy document feature sets and fuzzy documents and query, respectively. Simulation results show that these methods are effective and practical.4. We construct the lower and upper approximation operators of a vague set in the universe, which is partitioned by an indiscernibility relation. Furthermore, a parameterized roughness measure of a vague set is given followed by an analysis of its properties. We apply vague set theory to fuzzy multiple objective decision making problem, in which we obtain vague evaluation of each alternative by computing the sets of objectives being in favor, against and neutral, respectively. We develop an extension of TOPSIS to fuzzy multicriteria decision-making (MCDM) based on vague set theory, where the characteristics of the alternatives are presented by vague sets. The vague positive-ideal solution (VPIS) and vague negative-ideal solution (VNIS) are determined using a score function and the distance of different alternatives versus VPIS and VNIS is computed in terms of the weighted distance measure between two vague values. Finally, the relative closeness values of various alternatives to the positive-ideal solution are ranked to determine the best alternative. An example is shown to illustrate the procedure of the proposed method.