Saturday, March 18, 2006

Rough Set 理論について

The operation of contemporary computers and software systems is based on the underlying classical set theory with its associated binary-valued, true/false Boolean logic. This approach, although extremely successful in many application areas, is revealing its limitations when it comes to some "tough" problems such as, for example, speech or image recognition, machine learning, data mining, some forms of control etc. This is due to the fact that the implicit assumption of the "classical" approach is that in there is always sufficient, perfect knowledge about the state of an object or a system to make a unique determination of a recognition or processing decision. Unfortunately, the fact of life is that more often than not the underlying knowledge is much less than perfect. One can argue that with except of "pure" artificial systems, such as existing computer systems, the knowledge about majority of most natural systems or phenomena appearing in physics, chemistry, biology, markets etc. is limited, often allowing only for uncertain predictions rather than unique decisions. These limitations of knowledge are not modeled by the fundamental mathematics behind today's computational devices and, in fact, there is no knowledge model at all in the underlying logic. The theory of rough sets can be viewed as an extension of the "classical" set theory by incorporating the model of knowledge into its formalism, thus allowing for representing sets approximately in terms of the available context knowledge. Such a representation, in general, leads to approximate decision logics in which uncertainty is its natural component, reflecting the imperfections of the context knowledge. The incorporation of the knowledge model into fundamental set theory opens up new possibilities in machine learning, pattern classification, control systems, data mining, medical diagnosis and in variety of other areas dealing with complex objects, systems or natural phenomena. The elementary nature of the rough set theory will lead to significant impact on the applicability and on the fundamentals of computing science, comparable to the influence the classical set theory had on the basics of contemporary computing systems. It is expected that research projects undertaken by researchers affiliated with RSTL will constitute an essential contribution to the general impact in terms of the growth of rough set theory and its applications.


Post a Comment

<< Home