Dominik Ślȩzak

Stable rule extraction and decision making in rough non-deterministic information analysis

Rough Non-deterministic Information Analysis (RNIA) is a rough set-based data analysis framework for Non-deterministic Information Systems (NISs). RNIA-related algorithms and software tools developed so far for rule generation provide good characteristics of NISs and can be successfully applied to decision making based on non-deterministic data. In this paper, we extend RNIA by introducing stability factor that enables to evaluate rules in a more flexible way and by developing a question-answering functionality that enables decision makers to analyze data gathered in NISs in case there are no pre-extracted rules that may address specified conditions.

Approximate Bayesian networks

We introduce the notion of an approximate Bayesian network, which almost keeps the information entropy of data and encodes knowledge about approximate dependencies between features. Presented theoretical results, as well as relationships to fundamental concepts of the rough set theory, provide a novel methodology of applying the Bayesian net models to the real life data analysis.

A Mathematical Extension Of Rough Set-Based Issues Toward Uncertain Information Analysis

Rough set theory was originally proposed for analyzing data gathered in data tables, often referred to as information systems. The lower and upper approximations introduced within this theory are known as the very useful concepts. The theory as a whole now becomes a recognized foundation for granular computing. This paper investigates the rough set-based issues for analyzing table data with uncertainty. In reality, tables with non-deterministic information are focused on instead of tables with deterministic information, and several mathematical properties are examined. Especially, decision rule generation from tables with non-deterministic information is highlighted. This investigation is also applied to tables with uncertain numerical data. As a result, a new mathematical framework for analyzing tables with uncertain information is formalized.

Bireducts with tolerance relations

Abstract Reducing the number of attributes by preventing the occurrence of incompatibilities and eliminating existing noise in the original data is an important goal in different frameworks, such as in those focused on modelling and processing incomplete information in information systems. Bireducts were introduced in Rough Set Theory (RST) as one of successful solutions for the problem aimed at achieving a balance between elimination of attributes and characterization of objects that the remaining attributes can still distinguish. This paper considers bireducts in a general framework in which attributes induce tolerance relations over the available objects. In order to compute the new reducts and bireducts a characterization based on a general discernibility function is given.

Professor Zdzisław Pawlak (1926-2006): Founder of the Polish School of Artificial Intelligence

This chapter is dedicated to the memory of Professor Zdzislaw Pawlak, founder of the Polish school of Artificial Intelligence and one of the pioneers in Computer Engineering and Computer Science with worldwide influence.

Ordered Fuzzy Numbers: Definitions and Operations

We outline basic notions and assumptions related to the Ordered Fuzzy Number (OFN) model. Definitions of mathematical operations, several interpretations of their results, as well as additional OFN parameters are presented. Some of them, such as inclination or order, are specific to OFNs, whereas others are equivalent to those present in the well-known convex fuzzy number model. An important aspect of this part is also a discussion of algebraic properties of the OFN model.

Ordered Fuzzy Numbers: Sources and Intuitions

Most emerging methodologies, before they become well settled, stem from careful analysis of previous solutions. In that respect, this chapter refers to the roots of the Ordered Fuzzy Number (OFN) model. First, we outline some drawbacks of the most popular fuzzy number representations, which inspired us to search for a new approach. Then we discuss the idea of looking at fuzzy numbers from an alternative viewpoint. This leads towards formulation of the OFN model comprising three conceptual steps: (1) representing membership functions of fuzzy numbers as the pairs of increasing/decreasing components; (2) for each of two components treated as a locally defined function, inverting the meanings of its domain and its set of values; and finally (3) treating the obtained pairs of components as the ordered pairs. By introducing arithmetic operations on such ordered pairs, we obtain the framework, which is in many cases equivalent to the previous approaches but it also enables the representation of new information aspects.

Erratum: Rough Sets and Current Trends in Computing

The title of this book has been corrected. As small number of books were printed with the title “Rough Sets and Current Trends in Soft Computing”. The word “Soft” has been removed.

Special issue: Rough and Fuzzy Methods for Data Mining

This special issue of International Journal of Hybrid Intelligent Systems (IJHIS) published by IOS Press contains a selection of papers presented initially at the RSFDGrC’09 Conference (Rough Sets, Fuzzy Sets, Data Mining and Granular Computing) held in IIT Delhi, India, on December 16–20, 2009. RSFDGrC is the series of international scientific conferences spanning over last 15 years. It investigates the meeting points among the four major areas outlined in its title, with respect to foundations and applications. Five papers included in this special issue are devoted to various aspects of rough sets, fuzzy sets, data mining and granular computing, with a special emphasis on hybrid methodologies for solving theoretical problems and dealing with practical challenges of representing and mining compound data. The first paper, “Facilitating Efficient Mars Terrain Image Classification with Fuzzy-Rough Feature Selection” by Changjing Shang, Dave Barnes and Qiang Shen, presents an application study of exploiting fuzzyrough feature selection (FRFS) techniques in aid of efficient and accurate Mars terrain image classification. The employment of FRFS allows for the induction of low-dimensionality feature sets from sample descriptions of feature vectors of a much higher dimensionality. Supported with comparative studies, the work demonstrates that FRFS helps to enhance both the ef-

Toward Rough Sets Based Rule Generation from Tables with Uncertain Numerical Values

Rough sets based rule generation from tables with uncertain numerical values is presented. We have already focused on two topics, i.e., rule generation from tables with non-deterministic information and rule generation from tables with numerical values. For non-deterministic information, we have extended the typical rough sets to rough sets based on uncertain information. For numerical values, we have defined numerical patterns with two symbols ’@’ and ’#’, and have introduced the equivalence classes depending upon the figures. This paper employs intervals for uncertain numerical values, as well as rules with intervals. By using a real example, we show that it is possible to handle such rules according to the same method as the one already developed for non-deterministic information.