Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.

Rough sets

W: Bulletin of the European Association for Theoretical Computer Science (EATCS), 24:94-109, 1984

On rough sets

Rough set approach to multi-attribute decision analysis

Knowledge Discovery and Data Mining is a very dynamic research and development area that is reaching maturity. As such, it requires stable and well-defined foundations, which are well understood and popularized throughout the community. This survey presents a historical overview, description and future directions concerning a standard for a Knowledge Discovery and Data Mining process model. It presents a motivation for use and a comprehensive comparison of several leading process models, and discusses their applications to both academic and industrial problems. The main goal of this review is the consolidation of the research in this area. The survey also proposes to enhance existing models by embedding other current standards to enable automation and interoperability of the entire process.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0269888906000737

A survey of Knowledge Discovery and Data Mining process models

A rough set theory is a new mathematical tool to deal with uncertainty and vagueness of decision system and it has been applied successfully in all the fields. It is used to identify the reduct set of the set of all attributes of the decision system. The reduct set is used as preprocessing technique for classification of the decision system in order to bring out the potential patterns or association rules or knowledge through data mining techniques. Several researchers have contributed variety of algorithms for computing the reduct sets by considering different cases like inconsistency, missing attribute values and multiple decision attributes of the decision system. This paper focuses on the review of the techniques for dimensionality reduction under rough set theory environment. Further, the rough sets hybridization with fuzzy sets, neural network and metaheuristic algorithms have also been reviewed. The performance analysis of the algorithms has been discussed in connection with the classification.

Review: Dimensionality reduction based on rough set theory: A review

An application of a methodology for discovering strong probabilistic rules in data is presented. The methodology is based on an extended model of rough sets called variable precision rough sets model incorporated in DATALOGIC/R knowledge discovery tool from Reduct Systems Inc. It has been applied to analyze monthly stock market data collected over a ten year period. The objective of the analysis was to identify dominant relationships among fluctuations of market indicators and stock prices. For the purpose of comparison, both precise and imprecise, strong and weak rules were discovered and evaluated by a domain expert, a stock broker. The evaluation revealed that the strong rules (supported by many cases) essentially confirm the expert's experiences whereas weak rules are often difficult to interpret. This suggests the use of rule strength as the primary criteria for the selection of potentially useful predictive rules.

/pdf/an-application-of-datalogic-r-knowledge-discovery-tool-to-132tr08o27.pdf

An application of DATALOGIC/R knowledge discovery tool to identify strong predictive rules in stock market data

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.

A methodology for stock market analysis utilizing rough set theory

A methodology for the discovery of temporal rules in stock market data is presented. The two types of temporal rules defined are snapshot and aggregate. Snapshot temporal rules are formulated by associating a current decision attribute instance to the relevant past condition attribute instances. Aggregate temporal rules are formulated by associating a current decision attribute instance to the total change of relevant past condition attribute instances. Any chronologically based data can be disretized in this manner to produce snapshot and aggregate temporal rules. The knowledge discovery tool, Datalogic/R+, was used from Reduct Systems which applies the concepts of Rough Set Theory for pattern recognition in data. Monthly stock market data through the 80’s representing 120 cases containing 32 stock and economic indicators are analyzed. The main objective is to discover relationships with a company’s stock price change to stock and economic indicators over a time lapse of six months. Relationships were derived by the discovery of snapshot and aggregate temporal rules. The temporal rules discovered are consistent and confirm one another.

Temporal Rules Discovery Using Datalogic/R+ with Stock Market Data

Accurate risk measurement is important for making and assessing investment decisions Recently, directional change representations of returns are proposed as a new method for analyzing and forecasting intra-day price movements and for creating investment strategies This paper presents an FGARCH model for intraday Value-at-Risk (IVaR) estimation, for assessing risk properties in time series represented as directional change events, and for predicting the market risk for investment strategies based on directional changes We apply the proposed method to 5-minute intraday data and report the time-varying risk based on IVaR estimates We study the accuracy of these estimates and report the robustness of the risk estimates to the choice of the threshold parameter for directional change representations Furthermore, we apply the proposed methodology to compare the risk properties of two investment strategies based on directional changes with a baseline moving window investment strategy For these data, we find that the directional change strategies lead to higher returns but no substantial increase in risk compared to the baseline strategy The proposed methodology is applicable to other intra-day data frequencies and it is generalizable to other risk metrics

Intraday value-at-risk estimation for directional change events and investment strategies

Methods to accurately analyze financial risk have drawn considerable attention in financial institutions. One difficulty in financial risk analysis is the fact that banks and other financial institutions invest in several assets which show time-varying volatilities and hence time-varying financial risk. In addition, these assets are typically correlated and the correlation between different assets may change over time. Such changes in the multivariate volatility structure of the assets lead to substantial changes in the financial risk of a portfolio held by the financial institution. Therefore analyzing changes in the volatility of assets in a multivariate setting is essential to document changing risk properties of financial institutions. In this paper we propose a Probabilistic Fuzzy System (PFS) to model the unobserved time-varying correlation between a large set of financial returns. We define a parsimonious PFS where the current pairwise correlations between assets depend on two antecedent variables, namely the minimum and maximum past correlation in the market. We exemplify the proposed PFS model in six pairwise correlations for four industry portfolios in the US and show that the proposed method captures time-varying pairwise correlations while keeping the antecedent space parsimonious. Furthermore, we show that a portfolio investor that invests in these US industries calculates a lower risk for his/her portfolio when time-varying correlation estimates are not taken into account.

Multivariate time-varying volatility modeling using Probabilistic Fuzzy Systems

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