The article reviews the basics of the variable precision rough set and the Bayesian approaches to data dependencies detection and analysis. The variable precision rough set and the Bayesian rough set theories are extensions of the rough set theory. They are focused on the recognition and modelling of set overlap-based, also referred to as probabilistic, relationships between sets. The set-overlap relationships are used to construct approximations of undefinable sets. The primary application of the approach is to analysis of weak data co-occurrence-based dependencies in probabilistic decision tables learned from data. The probabilistic decision tables are derived from data to represent the inter-data item connections, typically for the purposes of their analysis or data value prediction. The theory is illustrated with a comprehensive application example illustrating utilization of probabilistic decision tables to face image classification.

This paper reports our experiences with the application of the hierarchy of probabilistic decision tables to face recognition. The methodology underlying the classifier development for our experiments is the variable precision rough sets, a probabilistic extension of the rough set theory. The soft-cut and probabilistic distance-based classifier method, the related theoretical background, including the feature extraction technique based on the principal component analysis, and some experimental results are presented. © 2011 Wiley Periodicals, Inc.

This paper is a presentation of results obtained in experiments in which rough set theory's methods and techniques were applied in the identification and analysis of data dependencies and relationships on an empirical data. The data used pertains to the biological control of the Leafy Spurge weed in the prairies of Western Canada. The project used an agent beetle known as Aphthona nigriscutis (A. n.). The rough set theory was applied to the data in order to identify and analyze the different factors affecting the success of the biological control of the host weed. Discovery and confirmation of meaningful patterns and the computation of a set of rules for the critical application of agent beetle in the control of the host weed were very encouraging.

Abstract: The paper is concerned with the creation of predictive models from data within the framework of the variable precision rough set model. It is focused on two aspects of the model derivation: computation of uncertain, in general, rules from information contained in probabilistic decision tables and forming hierarchies of decision tables with the objective of reduction or elimination of decision boundaries in the resulting classifiers. A new technique of creation of a linearly structured hierarchy of decision tables is introduced and compared to tree‐structured hierarchy. It is argued that the linearly structured hierarchy has significant advantages over tree‐structured hierarchy.

The paper is concerned with the creation of predictive models from data within the framework of the variable precision rough set model. The article is focused on two aspects of the model derivation: computation of uncertain, in general, rules from information contained in probabilistic decision tables and forming hierarchies of decision tables with the objective of reduction or elimination of decision boundary in the resulting classifiers. A new technique of creation of linearly structured hierarchy of decision tables is introduced and compared to tree structured hierarchy. It is argued that the linearly structured hierarchy has significant advantages over tree structured hierarchy.

The Variable Precision Rough Set Model (VPRS) is an extension of the original rough set model. This extension is directed towards deriving decision table‐based predictive models from data with parametrically adjustable degrees of accuracy. The imprecise nature of such models leads to quite significant modification of the classical notion of decision table. This is accomplished by introducing the idea of approximation region‐based, or probabilistic decision table which is a tabular specification of three, in general uncertain, disjunctive decision rules corresponding to rough approximation regions: positive, boundary and negative regions. The focus of the paper is on the extraction of such decision tables from data, their relationship to conjunctive rules and probabilistic assessment of decision confidence with such rules.

This paper presents an approach to incremental concept learning in attribute-value systems. The main characteristic feature of this approach is adaptive creation of a complete decision table rather than classification rules. The approach involves gra

A method for finding all deterministic and maximally general rules for a target classification is explained in detail and illustrated with examples. Maximally general rules are rules with minimal numbers of conditions. The method has been developed within the context of the rough sets model and is based on the concepts of a decision matrix and a decision function. The problem of finding all the rules is reduced to the problem of computing prime implicants of a group of associated Boolean expressions. The method is particularly applicable to identifying all potentially interesting deterministic rules in a knowledge discovery system but can also be used to produce possible rules or nondeterministic rules with decision probabilities, by adapting the method to the definitions of the variable precision rough sets model.

We present a generalization of the original idea of rough sets as introduced by Pawlak. The generalization, called the Variable Precision Rough Sets Model with Asymmetric Bounds, is aimed at modeling decision situations characterized by uncertain inf

Quants are aiding brokers and investment managers for stock market analysis and prediction. The Quant's black magic stems from many of the evolving artificial intelligence (AI) techniques. Extensive literature exists describing attempts to use AI techniques, and in particular neural networks, for analyzing stock market variations. The main problem with neural networks, however is the tremendous difficulty in interpreting the results. The neural nets approach is a black box approach in which no new knowledge regarding the nature of the interactions between the market indicators and the stock market fluctuations is extracted from the market data. Consequently, there is a need to develop methodologies and tools which would help in increasing the degree of understanding of market processes and, at the same time, would allow for relatively accurate predictions. The methods stemming from the research on knowledge discovery in databases (KDD) seem to provide a good mix of predictive and knowledge acquisition capabilities for the purpose of market prediction and market data analysis. This paper describes the methodology of rough sets while citing two applications which apply rough set theory (BST) for stock market analysis using Datalogic/R+. This is based on the variable precision model of rough sets (VPRS) to acquire new knowledge from market data.

One of the most important problems in the application of knowledge discovery systems is the identification and subsequent updating of rules. Many applications require that the classification rules be derived from data representing exemplar occurrences of data patterns belonging to different classes. The problem of identifying such rules in data has been researched within the field of machine learning, and more recently in the context of rough set theory and knowledge discovery in databases. In this paper we present an incremental methodology for finding all maximally generalized rules and for adaptive modification of them when new data become available. The methodology is developed in the context of rough set theory and is based on the earlier idea of discernibility matrix introduced by Skowron.

The Vector Space Model (VSM) has been adopted in information retrieval as a means of coping with inexact representation of documents and queries, and the resulting difficulties in determining the relevance of a document relative to a given query. The major problem in employing this approach is that the explicit representation of term vectors is not known a priori. Consequently, earlier researchers made the assumption that the vectors corresponding to terms are pairwise orthogonal. Such an assumption is clearly unrealistic. Although attempts have been made to compensate for this assumption by some separate, corrective steps, such methods are ad hoc and, in most cases, formally inconsistent. In this paper, a generalization of the VSM, called the GVSM, is advanced. The developments provide a solution not only for the computation of a measure of similarity (correlation) between terms, but also for the incorporation of these similarities into the retrieval process. The major strength of the GVSM derives from the fact that it is theoretically sound and elegant. Furthermore, experimental evaluation of the model on several test collections indicates that the performance is better than that of the VSM. Experiments have been performed on some variations of the GVSM, and all these results have also been compared to those of the VSM, based on inverse document frequency weighting. These results and some ideas for the efficient implementation of the GVSM are discussed.

The study of independence (dependence) between the condition and decision attributes is an important issue in decision theory. Most important applications in artificial intelligence are non-deterministic. It is shown that algebraic dependence is not adequate in these situations, and probabilistic independence provides a correct measure of information uncertainty for expert system design.

We demonstrate in this paper that the principles of inductive learning can be precisely formulated and hopefully better understood based on the theory of rough sets introduced by Pawlak. We discuss some statistical aspects of evaluating and forming decision rules from examples of expert decisions. We also suggest a method of comparing decision rules inferred by different learning algorithms from the same set of samples.

An information retrieval model, named the Generalized Vector Space Model (GVSM), is extended to handle situations where queries are specified as (extended) Boolean expressions. It is shown that this unified model, unlike currently available alternatives, has the advantage of incorporating term correlations into the retrieval process. The query language extension is attractive in the sense that most of the algebraic properties of the strict Boolean language are still preserved. Although the experimental results for extended Boolean retrieval are not always better than the vector processing method, the developments here are significant in facilitating commercially available retrieval systems to benefit from the vector based methods. The proposed scheme is compared to the p-norm model advanced by Salton and coworkers. An important conclusion is that it is desirable to investigate further extensions that can offer the benefits of both proposals.

In information retrieval, it is common to model index terms and documents as vectors in a suitably defined vector space. The main difficulty with this approach is that the explicit representation of term vectors is not known a priori. For this reason, the vector space model adopted by Salton for the SMART system treats the terms as a set of orthogonal vectors. In such a model it is often necessary to adopt a separate, corrective procedure to take into account the correlations between terms. In this paper, we propose a systematic method (the generalized vector space model) to compute term correlations directly from automatic indexing scheme. We also demonstrate how such correlations can be included with minimal modification in the existing vector based information retrieval systems. The preliminary experimental results obtained from the new model are very encouraging.