Mihir Chakraborty (U of Calcutta, India)

TITLE: Algebras and Logics of Rough Sets

DATE: May 14, 3:50pm-4:40pm

ABSTRACT: The first part of the talk will deal with various definitions of rough set and various types of algebraic operations (union, intersection, and complementation) imposed upon rough sets. Different algebraic structures thus emerged shall be looked into and their interconnections indicated. A special mention shall be made of the approaches by Pagliani and by Chakraborty & Banerjee. The second part of the talk will touch upon various generalizations. Yao’s work in this regard shall be specially emphasized. In the third part implication lattices shall be introduced. This is a lattice arising out of rough set structure with respect to set-inclusion relation. This lattice was published in Fundamenta Informaticae in the context of rough dialogue. The forth part of the talk shall deal with various logics arising out of rough sets. Interrelations of these logics with the above mentioned algebraic structures in the part one of the talk shall be discussed. In the fifth part I intend to introduce so called "Rough Logics", developed recently by Bunder, Banerjee & Chakraborty, and which are intimately related with implication lattices. The talk will conclude with the mention of some open directions of research.

Wojciech Ziarko (U of Regina, Canada)

TITLE: Pawlak's Rough Sets and Beyond

DATE: May 15, 9:00am-9:50am

ABSTRACT: The original rough set theory introduced by Zdzislaw Pawlak provides solid fundamentals for extensions and growth of the rough set paradigm. It is similar, in this role, to the classical set theory as an underlying basis for probability theory, number theory etc. Several extensions of the rough set theory have been proposed in the past. The primary motivation was to bring the theory closer to "real life" problems, to take advantage of its results on problems not applicable to its original formulation. In particular, the probabilistic extension of the rough set approach seems to gain some prominence. Interesting applications in such general areas as machine learning, data mining, market research and pattern classification start to emerge. It turns out that by enriching the Pawlak's rough set theory with the notion of the probability function and some related probabilistic measures, a full generalization of the original theory can be achieved while vastly expanding the scope of possible applications. The probabilistic generalization preserves basic concepts of the original approach, such as the idea of set approximations, the idea of attribute dependency and reduct. The generalization enables to handle problems which previously belonged to the "boundary area", and as such, were intractable with rough set tools. The main focus of this brief tutorial will be on introduction of the basic elements of rough set theory in conjunction with their extensions in the probabilistic setting. The participants of the tutorial will acquire a good grasp of the original rough set approach, of its probabilistic extension, the connection between these two and of the potential applications. The tutorial is intended primarily for researchers working in the areas of machine learning, data mining and rough set applications.