A relative tolerance relation of rough set with reduct and core approach, and application to incomplete information systems

Data mining concepts and methods can be applied in various fields. Many methods have been proposed and one of those methods is the classical 'rough set theory' which is used to analyze the complete data. However, the Rough Set classical theory cannot overcome the incomplete data. The simplest method for operating an incomplete data is removing unknown objects. Besides, the continuation of Rough Set theory is called tolerance relation which is less convincing decision in terms of approximation. As a result, a similarity relation is proposed to improve the results obtained through a tolerance relation technique. However, when applying the similarity relation, little information will be lost. Therefore, a limited tolerance relation has been introduced. However, little information will also be lost as limited tolerance relation does not take into account the accuracy of the similarity between the two objects. Hence, this study proposed a new method called Relative Tolerance Relation of Rough Set with Reduct and Core (RTRS) which is based on limited tolerance relation that takes into account relative similarity precision between two objects. Several incomplete datasets have been used for data classification and comparison of our approach with existing baseline approaches, such as the Tolerance Relation, Limited Tolerance Relation, and NonSymmetric Similarity Relations approaches are made based on two different scenarios. In the first scenario, the datasets are given the same weighting for all attributes. In the second scenario, each attribute is given a different weighting. Once the classification process is complete, the proposed approach will eliminate redundant attributes to develop an efficient reduce set and formulate the basic attribute specified in the incomplete information system. Several datasets have been tested and the rules generated from the proposes approach give better accuracy. Generally, the findings show that the RTRS method is better compared to the other methods as discussed in this study

A rough set approach for the discovery of classification rules in interval-valued information systems

A novel rough set approach is proposed in this paper to discover classification rules through a process of knowledge induction which selects optimal decision rules with a minimal set of features necessary and sufficient for classification of real-valued data. A rough set knowledge discovery framework is formulated for the analysis of interval-valued information systems converted from real-valued raw decision tables. The optimal feature selection method for information systems with interval-valued features obtains all classification rules hidden in a system through a knowledge induction process. Numerical examples are employed to substantiate the conceptual arguments

Vision-based neural network classifiers and their applications

A thesis submitted for the degree of Doctor of Philosophy of University of LutonVisual inspection of defects is an important part of quality assurance in many fields of production. It plays a very useful role in industrial applications in order to relieve human inspectors and improve the inspection accuracy and hence increasing productivity. Research has previously been done in defect classification of wood veneers using techniques such as neural networks, and a certain degree of success has been achieved. However, to improve results in tenus of both classification accuracy and running time are necessary if the techniques are to be widely adopted in industry, which has motivated this research. This research presents a method using rough sets based neural network with fuzzy input (RNNFI). Variable precision rough set (VPRS) method is proposed to remove redundant features utilising the characteristics of VPRS for data analysis and processing. The reduced data is fuzzified to represent the feature data in a more suitable foml for input to an improved BP neural network classifier. The improved BP neural network classifier is improved in three aspects: additional momentum, self-adaptive learning rates and dynamic error segmenting. Finally, to further consummate the classifier, a uniform design CUD) approach is introduced to optimise the key parameters because UD can generate a minimal set of uniform and representative design points scattered within the experiment domain. Optimal factor settings are achieved using a response surface (RSM) model and the nonlinear quadratic programming algorithm (NLPQL). Experiments have shown that the hybrid method is capable of classifying the defects of wood veneers with a fast convergence speed and high classification accuracy, comparing with other methods such as a neural network with fuzzy input and a rough sets based neural network. The research has demonstrated a methodology for visual inspection of defects, especially for situations where there is a large amount of data and a fast running speed is required. It is expected that this method can be applied to automatic visual inspection for production lines of other products such as ceramic tiles and strip steel

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Data classification based on tolerant rough set

This paper proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Similarity measure between two data is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value. The determination of optimal similarity threshold value is very important for the accurate classification. So, we determine it optimally by using the genetic algorithm (GA), where the goal of evolution is to balance two requirements such that (1) some tolerant objects are required to be included in the same class as many as possible and (2) some objects in the same class are required to be tolerable as much as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and the data set is grouped into the lower and upper approximation set depending on the coincidence of their classes. We propose a two-stage classification method that all data are classified by using the lower approximation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. The validity of the proposed classification method is tested by applying it to the IRIS data classification and its classification performance and processing time are compared with those of other classification methods such as BPNN, OFUNN, and FCM. (C) 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.X1138sciescopu