Rough Mereological Reasoning in Rough Set Theory: Recent Results and Problems

摘要

This article comes up a couple of months after the death of Professor Zdzislaw Pawlak who created in 1982 the theory of rough sets as a vehicle to carry out Concept Approximation and a fortiori, Decision Making, Data Mining, Knowledge Discovery and other activities. At the roots of rough set theory, was a deep knowledge of ideas going back to Frege, Russell, Lukasiewicz, Popper, and others. Rough sets owe this attitude the intrinsic clarity of ideas, elegant simplicity (not to be confused with easy triviality), and a fortiori a wide spectrum of applications. Over the years, rough set theory has been enriched with new ideas. One of those additions has been rough mereology, an attempt at introducing a regular form of tolerance relations on objects in an information system, in order to provide a more flexible scheme of relating objects than indiscernibility. The theory of mereology, proposed long ago (1916) by S. Lesniewski, proved a valuable source of inspiration. As a result, a more general theory has emerged, still far from completion. Rough mereology, operating with so called rough inclusions, allows for definitions of a class of logics, that in turn have applications to distributed systems, perception analysis, granular computing etc. etc. In this article, we give a survey of the present state of art in the area of rough mereological theory of reasoning, as we know it, along with comments on some problems.