Three Approaches to Data Analysis - Test Theory, Rough Sets and Logical Analysis of Data

The book Three Approaches to Data Analysis [1] presents three approaches to data analysis: (1) Test Theory (TT), founded by Sergei V. Yablonskii; (2) Rough Sets (RS), founded by Zdzislaw I. Pawlak and (3) Logical Analysis of Data (LAD), founded by Peter L. Hammer. These three approaches have much in common. They all are related to Boolean functions and Boolean reasoning. All three data analysis approaches use decision tables for data representation. The first part of the book, written by Igor Chikalov, Mikhail Moshkov and Beata Zielosko, is devoted to Test Theory. Authors present three main areas of TT: (i) theoretical results related to tests, (ii) applications to control and diagnosis of faults, and (iii) applications to pattern recognition. This chapter consists of seven sections. The first three sections include theoretical results on tests, trees and rules. The following three sections deal with applications of TT. The second part of this book, written by Hung Son Nguyen and Andrzej Skowron, is dedicated to rough sets as a tool to deal with imperfect data, in particular, with vague concepts. This chapter presents vague concepts, indiscernibility and discernibility relations, approximation of concepts, rough sets, decision rules, dependencies, reducts, discernibility and Boolean reasoning and rough membership functions. Some comments on relationships of rough sets and logic are discussed. Some challenging issues for rough sets are included in the last section. The third part of the book was written by Vadim Lozin and Irina Lozina and is devoted to LAD. This chapter is divided into three sections: Theory, Methodology and Applications. The first section presents partially defined Boolean function, pattern and discuss various problems associated with these notions. This section contains binarization, attribute selection, pattern generation, model construction and validation. In the section devoted to applications; authors illustrate LAD methodology with a number of particular examples.