Preface

摘要

Professor Zdzistaw Pawlak's fundamental papers connected with rough sets theory were published in 1982. Roman Slowinski highlighted the crucial importance of the original rough set theory: "This theory helps to find answers to many basic questions in mathematics, computer science, artificial intelligence, decision theory, conflict theory, machine learning, knowledge discovery and control theory. This theory is founded on an observation that knowledge about objects from a real or abstract world is granular. Indeed, objects described by the same information are indiscernible and create elementary sets, which are knowledge granules for that world. When willing to express a concept, referring to a given set of objects, in terms of knowledge about the world the objects come from, one encounters a situation in which in general, the concept is not expressible exactly by the available granules; in other words, the union of elementary sets having non-empty intersection with our set, does not coincide with the set. This set - a concept - may, however, be expressed roughly, using sets called lower and upper approximations -lower approximation containing elementary sets (granules) which are wholly included in our set, and upper approximation containing also those sets which are partly included in our set. The difference between those approximations is called a boundary of a set, and contains ambiguous objects, for which one cannot claim with certainty, whether they do or do not belong to our set. Differentiating between definite knowledge represented by lower approximation and approxi-mate knowledge represented by the boundary of a set has a fundamental impact on the deduction process. Rough set theory complements fuzzy set theory and soft computing, with which it now delivers the best tools for reasoning about data bearing different types of "im-perfections", such as ambiguity, inaccuracy, inconsistency, incompleteness, and uncertainty."'