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Abstract:

The problem of imperfect knowledge under uncertain environments has been tackled for a long time by philosophers, logicians and mathematicians. Rough set theory proposed by Zdzislaw Pawlak [1] has attracted attention of many researchers and practitioners all over the world, and has a fast growing group of researchers interested in this methodology. Fuzzy set theory proposed by Lotfi Zadeh [2] helps to understand and manipulate imperfect knowledge. Fuzzy sets are defined by partial membership, in contrast to crisp membership used in classical definition of a set. Rough set theory, expresses vagueness, not by means of membership, but employing a boundary region of a set. The back bone of rough set theory is the approximation space and lower and upper approximations of a set. The approximation space is a classification of the domain of interest into disjoint categories. The lower approximation is a description of the domain objects which are known with certainty to belong to the subset of interest, whereas the upper approximation is a description of the objects which possibly belong to the subset. Any subset defined through its lower and upper approximations is called a rough set. The main advantage of rough set theory is that it does not need any preliminary or additional information about data – like probability in statistics, grade of membership in fuzzy set and so on. Readers may consult the International Rough Set Society Web page [3] for more

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