Automated Discovery of Properties of Rough Sets

• Autorzy: Grabowski A.
• Języki publikacji: EN

Abstrakty

EN

The computer certification of rough sets (the translation in a way understandable by machines) seems to be far beyond the test phase. To assure the feasibility of the approach, we try to encode selected problems within rough set theory and as the testbed of already developed foundations – and in the same time as a payoff of the established framework – we shed some new light on the well-known question of generalization of rough sets and the axiomatization of approximation operators in terms of (various types of) binary relations. We show how much the human work can be enhanced with the use of automatic tools, without loosing too much time for the translation. Although the syntax is understandable by the computer, it offers relative flexibility and expressive power of the formal language.

Słowa kluczowe

EN

formalization of mathematics; generalized rough approximations; rough sets

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 128, nr 1-2
• Strony: 66--79
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Grabowski A.

• University of Białystok, Institute of Informatics, Akademicka 2, 15-267 Białystok, Poland

Bibliografia

• [1] Gomolińska, A.: On certain rough inclusion functions, Transactions on Rough Sets, 9, 35-55, 2008.
• [2] Grabowski, A.: Basic properties of rough sets and rough membership function, Formalized Mathematics, 12(1), 21-28, 2004; can be tracked also under http: //mizar. org/version/current/html/roughs_1. html.
• [3] Grabowski, A., Jastrzębska, M.: On the lattice of intervals and rough sets, Formalized Mathematics, 17(4), 237-244, 2009.
• [4] Grabowski, A., Korniłowicz, A., Naumowicz, A.: Mizar in a nutshell, Journal of Formalized Reasoning, 3(2), 153-245,2010.
• [5] Grabowski, A., Schwarzweller, Ch.: Rough Concept Analysis - theory development in the Mizar system, Lecture Notes in Computer Science, 3119, 130-144, 2004.
• [6] Grabowski, A., Schwarzweller, Ch.: Translating mathematical vernacular into knowledge repositories, Lecture Notes in Computer Science, 3863, 49-64, 2006.
• [7] Järvinen, J.: Lattice theory for rough sets, Transactions on Rough Sets VI, 400-498, 2007.
• [8] Pawlak, Z.: Automatyczne dowodzenie twierdzeń, Warsaw, PZWS, 1965 (Eng. Automated theorem proving, in Polish).
• [9] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, 1991.
• [10] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, 245-253,1996.
• [11] Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in Mizar, Lecture Notes in Computer Science, 6167, 132-146, 2010.
• [12] Wiedijk, F.: Formal proof - getting started, Notices of the American Mathematical Society, 55(11), 14081414, 2008.
• [13] Vigneron, L.: Automated deduction techniques for studying rough algebras, Fundamenta Informaticae, 33(1), 1998, pp. 85-103.
• [14] Yao, Y.Y.: Constructive and algebraic methods of theory of rough sets, Information Sciences, 109, 21-47, 1998.
• [15] Yao, Y.Y., Li, X.: Comparison of rough-set and interval-set models for uncertain reasoning, Fundamenta Informaticae, 27, 289-298, 1996.
• [16] Zhu, W.: Generalized rough sets based on relations, Information Sciences, 177, 4997-5011,2007.
• [17] Zhu, W.: Relationship between generalized rough sets based on binary relations and covering, Information Sciences, 178(21), 4105-4113, 2008.