Polish Journal of Management Studies
 ISSN 2081-7452
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Mazurek J.

Abstract: The rough set theory, which originated in the early 1980s, provides an alternative approach to the fuzzy set theory, when dealing with uncertainty, vagueness or inconsistence often encountered in real-world situations. The fundamental premise of the rough set theory is that every object of the universe is associated with some information, which is frequently imprecise and insufficient to distinguish among objects. In the rough set theory, this information about objects is represented by an information system (decision table). From an information system many useful facts and decision rules can be extracted, which is referred as knowledge discovery, and it is successfully applied in many fields including data mining, artificial intelligence learning or financial investment. The aim of the article is to show how hidden knowledge in the real-world data can be discovered within the rough set theory framework. After a brief preview of the rough set theorys basic concepts, knowledge discovery is demonstrated on an example of baby car seats evaluation. For a decision rule extraction, the procedure of Ziarko and Shan is used.

: information system, knowledge discovery,
1 rough sets, rule extraction, uncertainty.


The rough set theory was proposed by a Polish computer scientist Zdislaw I. Pawlak in 1982; see e.g. [8], [9] or [10]. It is a mathematical tool for handling uncertainty and vagueness in decision making processes. The theory is based on an assumption that every object of the universe is associated with some information, such as price, quantity or durability in economics. However, some objects might be indiscernible when they are associated with the same information. Thats why a set of such objects cannot be defined precisely (as a crisp set), and is formally approximated by rough sets a pair of sets which give its lower and upper approximation.  
Since 1980s, the rough set theory was successfully applied to many fields ranging from data mining to artificial intelligence learning. The main benefits of a rough sets model according to Tay and Shen [14]:

It doesnt need any external information such as knowledge of probability distribution in statistics or a membership function in fuzzy set theory.
It allows both for quantitative and qualitative analysis.
It enables to discover fact hidden in a database and to express them as decision rules.
It eliminates redundant information of original data.
The decision rules are supported by real examples contained in the data.
Results of the rough set model are easy to understand and interpret.
In economics, rough sets models such as RSES, LERS, DataLogic, TRANCE or ProbRough are used for [14]:
Business failure prediction, see e.g. [13] or [2],
Database marketing, see e.g. [11],
Financial investment, see e.g. [16].

After its introduction in early 1980s, the rough set theory was studied intensively by a large number of experts and was extended into (group) multicriteria decision analysis (see e.g. [4] or [5]), fuzzy sets ([3]), machine learning ([15]) and other fields of mathematics and computer science.

The aim of the article is to show how hidden knowledge in the real-world data can be discovered within the rough set theory framework. This might be helpful in managers work, as it can facilitate understanding of data and information in general. The paper is organized as follows: Section 2 provides a brief preview of the rough set theorys basic concepts, in Section 3 an example the evaluation of baby car seats is analyzed within the rough set theory and in Section 4 rule extraction from an information system in Section 3 is demonstrated. Conclusions close the article.    

more in full version


The aim of the article was to show how hidden knowledge in the real-world data can be discovered within the rough set theory framework. For knowledge discovery the approach of Ziarko and Shan was applied to the baby car seat evaluation with four condition attributes (safety, handling, comfort and maintenance) and three decision attributes (good, satisfactory and unsatisfactory) presented in the newspaper Mladá Fronta Dnes. From decision matrices decision rules listed in the previous section were extracted, furthermore, it was learned that one of condition attributes, namely handling, was redundant. This example demonstrated that the rough set approach can be useful also in a management, as knowledge acquisition is an important part of manager
s work.


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Streszczenie: Teoria zbiorów przybliżonych, która powstała w roku 1980, oferuje alternatywne podejście do teorii zbiorów rozmytych, gdy ma się do czynienia ze zjawiskiem niepewności, niejasności i niekonsekwencji, często spotykanym w rzeczywistych sytuacjach. Podstawowym założeniem teorii zbiorów przybliżonych jest to, że każdy obiekt wszechświata jest związany z pewnymi informacjami, które są często nieprecyzyjne i niewystarczające do rozróżnienia między obiektami. W teorii zbiorów przybliżonych, informacje o obiektach są reprezentowane przez system informacyjny (tabela decyzyjna). System informacyjny dostarcza wiele przydatnych faktów i reguł, które są określane jako odkrywanie wiedzy, która z powodzeniem jest stosowana w wielu dziedzinach, w tym w ekstrakcji danych, sztucznej inteligencji czy przy inwestycjach finansowych. Cele artykułu jest pokazanie, w jaki sposób wiedza ukryta w rzeczywistych danych, mogą zostać odkryte w trudnych ramach teorii mnogości. Po krótkim przedstawieniu podstawowych pojęć teorii zbiorów przybliżonych, na przykładzie ocen fotelików samochodowych, przedstawiono zjawisko odkrywania wiedzy. W celu wydobycia reguły decyzyjnej zastosowano procedurę Ziarko i Shan.

Słowa kluczowe: System informacyjny, odkrywanie Widzy, zbiory przybliżone, ekstrakcja zasad, niepewność  

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