Special issue on Hybrid Intelligence using rough sets

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 online resources, publications etc. The Third International Conference on Hybrid Intelligent Systems (HIS’03) gathered individual researchers who see the need for synergy between various intelligent techniques. This special issue comprising of four papers is focused on hybrid intelligence using rough set theory and its applications. Papers were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed. The papers are organized as follows. In the first paper, Polkowski proposes a framework for hybridizing rough, fuzzy and neural computational models. The concept is based on rough mereology and by having rough inclusions that are logical connectives of rough mereology it is possible to construct granules of knowledge that constitute elementary objects for calculi merging rough, fuzzy and neurocomputing schemes. The idea of rough inclusions provide a bridge between rough and fuzzy theories linking them across the gap resulting from distinct approaches to model uncertainty of knowledge.