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An extension of rough set approximation to flow graph based data analysis
(2010-12-01)
Chitcharoen, Doungrat
;
Pattaraintakorn, Puntip
This paper concerns some aspects of mathematical flow graph based data analysis. In particular, taking a flow graph view on rough sets' categories and measures leads to a new methodology of inductively reasoning form data. This perspective shows interesting relationships and properties among rough set, flow graphs and inverse flow graphs. A possible car dealer application is outlined and discussed. Evidently, our new categories and measures assist and alleviate some limitations in flow graphs to discover new patterns and explanations. © 2010 Springer-Verlag Berlin Heidelberg.
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Novel matrix forms of rough set flow graphs with applications to data integration
(2010-11-01)
Chitcharoen, Doungrat
;
Pattaraintakorn, Puntip
Pawlak's flow graphs have attracted both practical and theoretical researchers because of their ability to visualize information flow. In this paper, we invent a new schema to represent throughflow of a flow graph and three coefficients of both normalized and combined normalized flow graphs in matrix form. Alternatively, starting from a flow graph with its throughflow matrix, we reform Pawlak's formulas to calculate these three coefficients in flow graphs by using matrix properties. While traditional algorithms for computing these three coefficients of the connection are exponential in l, an algorithm using our matrix representation is polynomial in l, where l is the number of layers of a flow graph. The matrix form can simplify computation, improve time complexity, alleviate problems due to missing coefficients and hence help to widen the applications of flow graphs. Practically, data sets often reside at different sources (heterogeneous data sources). Their individual analysis at each source is inadequate and requires special treatment. Hence, we introduce a composition method for flow graphs and corresponding formulas for calculating their coefficients which can omit some data sharing. We provide a real-world experiment on the Promotion of Academic Olympiads and Development of Science Education Foundation (POSN) data set which illustrates a desirable outcome and the advantages of the proposed matrix forms and the composition method. © 2010 Elsevier Ltd. All rights reserved.
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Entropy measures of flow graphs with applications to decision trees
(2009-08-27)
Pattaraintakorn, Puntip
Entropy is a fundamental principle in many disciplines such as information theory, thermodynamics, and more recently, artificial intelligence. In this article, a measure of entropy on Pawlak's mathematical flow graph is introduced. The predictability and quality of a flow graph can be derived directly from the entropy. An application to decision tree generation from a flow graph is examined. In particular, entropy measures on flow graphs lead to a new methodology of reasoning from data and shows rigorous relationships between flow graphs, entropy and decision trees. © 2009 Springer Berlin Heidelberg.
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Knowledge discovery by rough sets mathematical flow graphs and its extension
(2008-12-01)
Chitchareon, Doungrat
;
Pattaraintakorn, Puntip
Mathematical rough set theory has attracted both practical and theoretical researchers. A significant extension of rough set theory is called flow graphs. It is a knowledge representation in the form of information flow. Flow graph is a promising approach to analyze data flow, decision trees, decision rules, probability learning, etc. In this article, we present their connections to pertinent techniques and propose a new extension to association rules. Two new propositions are used to reveal the relationship between flow graphs and association rules. We conduct experiment on real-world data collected from POSN with the evaluation. We discuss some important properties of flow graphs, with examples throughout.
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Towards theories of fuzzy set and rough set to flow graphs
(2008-01-01)
Chitcharoen, Doungrat
;
Pattaraintakorn, Puntip
Mathematical rough set theory and fuzzy set theory have attracted both practical and theoretical researchers from their efficiently and effectively to analyze real-world data. A novel and significant extension is called flow graphs. In this paper, we Introduced how to calculate certainty, coverage and strength coefficients of decision rules from fuzzy attributes in a flow graph. Furthermore, we relax concept of mutual exclusion and introduced four new propositions of certainty and coverage coefficients for decision rules extracted from flow graph. An example calculation of these coefficients is provided. We also demonstrate real-world experiment on POSN data set. Several case studies illustrate a desirable outcome. © 2008 IEEE.

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