. The present state of rough set theory and its applications is presented by articles in this collection as well as by research papers listed in APPENDIX 1 to which we refer the reader. We would like to discuss here some directions for further research as well as to point to some recent results not mentioned earlier which seem to us to be of importance for development of rough set theory and its applications. In our discussion we will be guided by the following three main topics: (i) Rough Sets in Knowledge Representation; (ii) Rough Sets in Approximate Reasoning about Knowledge; (iii) New Applications and New Hardware/Software. 1 A view on extended rough set theory New applications demand new ideas and their implementations. We would like to point to important new extensions of the nowadays rough set theory. 1.1 Concept Approximation The central theme in our discussion on the lines of the first two topics is that of Concept Approximation. It does involve a description process of ...