Concept Approximation in Mathematics and Computer Science. An Essay in Homage to Zdzisław Pawlak

Issue title: New Frontiers in Scientific Discovery – Commemorating the Life and Work of Zdzislaw Pawlak

Article type: Research Article

Authors: Polkowski, Lech

Affiliations: Polish-Japanese Institute of Information Technology, Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland. E-mail: [email protected]

Abstract: This article is conceived as a homage to the life and work of Professor Zdzisław Pawlak. Intended as a mark to His 80th birthday, it turns out to be a homage to His memory. On such occasions, one is drawn into a whirl of memories, in this case reaching back to about 92', when the author met Zdzisław because of being interested in rough sets. That theory was created in 1982 by Zdzisław Pawlak as a vehicle to carry out Concept Approximation and a fortiori, Decision Making, Data Mining, Knowledge Discovery and other activities. The creation of rough set theory, in my opinion then and now, was a single act, ignited and facilitated by Zdzisław's deep knowledge of ideas going back to Frege, Russell, Łukasiewicz, Popper, and others. This attitude to the tradition, was certainly a strong factor that attracted to Him creative folks. 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. This essay is intended as a panoramic view also on those applications. Any creation of a theory that gains recognition, many followers, and enters the standard repertoire of researchers is, in itself, an event worthy of analysis. Such analysis is not the subject of this essay; we are satisfied with presenting some views on the nature of Concept Approximation, and with outlining against this background the main features of rough sets and their extensions. In words of Cyprian Kamil Norwid: "� a few ideas that are not new �." This essay owes much to a lecture presented by the author at the Lateran University in Rome in January 2005 at the Conference Series: Scienza e Fede sull;Interpretazione del Reale; in that lecture main ideas exposed in this essay were presented. In the present exposition, some metaphysical ideas discussed in the original lecture were omitted. Nevertheless, the author takes liberty of the essay form in order to encapsulate in this text some more refined ideas than those usually inserted in technical works. The author is grateful to Professors Giandomenico Boffi and Alberto Pettorossi for invitation to Rome. On this occasion the author wishes also to invoke with personal gratitude the memory of the late Professor Helena Rasiowa who, in addition to many deep results, created much of the logical theory of rough sets.

Journal: Fundamenta Informaticae, vol. 75, no. 1-4, pp. 435-451, 2007