Showing papers by "Zdzisław Pawlak published in 1996"

Rough sets, rough relations and rough functions

Abstract: The paper explores the concepts of approximate relations and functions in the framework of the theory of rough sets. The difficulties with the application of the idea of rough relation to general rough function definition are discussed. The definition of rough function for the domain of real numbers is introduced and its properties are investigated in detail including the generalization of the standard notion of function continuity known in the theory of real functions.

Why rough sets

Abstract: The problem of imperfect knowledge has been tackled for a long time by philosophers, logicians and mathematicians. Recently it became also a crucial issue for computer scientists, particularly in the area of artificial intelligence. There are many approaches to the problem of how to understand and manipulate the imperfect knowledge. The most successful one is, no doubt, fuzzy set theory proposed by Zadeh. Rough set theory is another attempt to this problem. The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. Rough set theory overlaps with many other theories, especially with fuzzy set theory, evidence theory and Boolean reasoning methods-nevertheless it can be viewed in its own rights, as an independent, complementary, and not competing discipline.

Rough sets and data analysis

Abstract: In this talk we are going to present basic concepts of a new approach to data analysis, called rough set theory. The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. Rough set theory overlaps with many other theories, especially with fuzzy set theory, evidence theory and Boolean reasoning methods, discriminant analysis-nevertheless it can be viewed in its own rights, as an independent, complementary, and not competing discipline. Rough set theory is based on classification. Consider, for example, a group of patients suffering from a certain disease. With every patient a data file is associated containing information like, e.g. body temperature, blood pressure, name, age, address and others. All patients revealing the same symptoms are indiscernible (similar) in view of the available information and can be classified in blocks, which can be understood as elementary granules of knowledge about patients (or types of patients). These granules are called elementary sets or concepts, and can be considered as elementary building blocks of knowledge about patients. Elementary concepts can be combined into compound concepts, i.e. concepts that are uniquely defined in terms of elementary concepts. Any union of elementary sets is called a crisp set, and any other sets are referred to as rough (vague, imprecise). With every set X we can associate two crisp sets, called the lower and the upper approximation of X. The lower approximation of X is the union of all elementary set which are included in X, whereas the upper approximation of X is the union of all elementary set which have non-empty intersection with X. In other words the lower approximation of a set is the set of all elements that surely belongs to X, whereas the upper approximation of X is the set of all elements that possibly belong to X. The difference of the upper and the lower approximation of X is its boundary region. Obviously a set is rough if it has non empty boundary region; otherwise the set is crisp. Elements of the boundary region cannot be classified, employing the available knowledge, either to the set or its complement. Approximations of sets are basic operation in rough set theory.

Rough control application of rough set theory to control

Abstract: The two most significant developments in the field of artificial intelligence (Al) since 1990 are real world practicality and diversification [14,15]. Fuzzy set theory, for example, has grown to become a major scientific technology, applied to a couple of thousand systems for everyday industrial and commercial settings worldwide [16]. The area of neural networks is another example where extensive practical applications are expected [27]. An interesting question would be determining what the next generation of new Al technologies are and their potentials for practical applications. Rough set theory is a relatively new mathematical and Al technique introduced in the early 1980's by Pawlak. The technique is particularly suited to reasoning about imprecise or incomplete data, and discovering relationships in this data. The main advantage of rough set theory is that it does not require any preliminary or additional information about data like probability in statistics, basic probability assignment in Dempster Shafer theory of evidence or the value of possibility in fuzzy set theory. Rough set theory overlaps, to some extend, with many other theories used to reasoning about data, in particular with Dempster Shafer theory and fuzzy set theory. Despite of these connections it can be viewed as an independent discipline in its own right. Recently there has been a growing interest in rough set theory among researchers in many Al related disciplines. The theory has found many real life applications in many areas. The primary application of rough sets so far have been in data and decision analysis, databases, knowledge based systems, and machine learning. Some information about application of the theory can be found in [20]. Although there has been some research on rough control [4,8,9,10,11,12,13,23,25,27,28,29] their number and domains have been relatively small, and they are all academic rather than real life applications. It is worthwhile to mention in this context however that two rough controllers have been implemented in hardware [4,13] displaying very attractive features. First of all their speed

Rough sets: Present state and further prospects

Abstract: W: Institute of Computer Science Report 49/94. Warsaw University of Technology, Poland, 00-665 Warsaw, Nowowiejska 15/19, 1994

Rough set and data mining

Abstract: W: Proceedings of the International Conference on Intelligent Processing and Manufacturing Materials, Gold Coast, Australia, 1997, pages 1-5, 1996

Rough sets: Present state and perspectives

Abstract: W: Proceedings of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 1996), vol 2, Granada, Spain, July 1-5, 1996, pages 1137-1145, 1996

Data versus logic a rough set view

Abstract: W: S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka, and A. Nakamura, editors, Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD'96), The University of Tokyo, November 6-8, 1996, pages 1-8, 1996

Helena Rasiowa and Cecylia Rauszer research on logical foundations of Computer Science

Abstract: W: Bulletin of the Section of Logic, 25(3-4):174-184, 1996. (special issue: Logic, Algebra and Computer Science, Helena Rasiowa and Cecylia Rauszer in Memoriam, A. Skowron (ed.))