On rough definability and types of approximation of classifications

• Autorzy: Tripathy B.K. , Ojha J , Mohanty D. , Kumar Ch M.S.
• Języki publikacji: EN

Abstrakty

EN

The study of rough definability of classifications was initiated by Busse [3]. Classifications are of great interest, as in the process of learning from examples, rules are derived from classifications generated by single decisions. It was established by him that not all concepts associated with rough definability of sets can be extended to classifications. Four propositions were established in [3] and used in defining types of classifications. In this article we extend these propositions to obtain necessary and sufficient type theorems from which several results besides the above four results of Busse could be derived. We interpret and illustrate each of these results through examples. It is found that there are 11 possible types of classifications. Out of which only 5 which are basic in nature were considered by Busse without stating any reason for doing so. However, in this paper we shall establish that the other six types reduce to these five considered by him, either directly or transitively. In this paper, we prove a general theorem which provides a complete picture of the types of elements in a classification and introduce an algorithm to generate these classifications, given the number of elements in the classification. In fact, this result establishes the statement of Pawlak [9] that the notions of complement for sets and that for classifications are different. Also, we shall establish some properties of the parameters of measures of uncertainty; the accuracy of approximation and the quality of approximation of classifications.

Słowa kluczowe

EN

rough set; classification; R-definable; R-lower approximation; R-upper approximation; Typel; type 2; Type 3; Type 4

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2010
• Tom: Vol. 35, No. 3
• Strony: 197--215
• Opis fizyczny: Bibliogr. 13

Twórcy

autor

Tripathy B.K.

autor

Ojha J

autor

Mohanty D.

autor

Kumar Ch M.S.

• School of Computing Science and Engineering, VIT University, Vellore - 632 014, Tamil Nadu, India

Bibliografia

• [1] C.C Chan and J. Grzymala-Busse. Rough-set boundaries as a tool for learning rules from examples. In Proc. of the ISMIS-89, 4th Int. Symposium on Methodologies for intelligent Systems, pages 281-288, 1989.
• [2] C.C. Chan and J. Grzymala-Busse. On the attribute redundancy and the learning programs ID3, PRISM and LEM 2. Department of Computer Science, University of Kansas, TR-91-14, 20 December, 1991.
• [3] J. Grzymala-Busse. Knowledge acquisition under uncertainty - a rough set approach. Journal of Intelligent and Robotics Systems, 1:3-16, 1988.
• [4] Z. Pawlak. Rough sets, Basic notions, Institute comp. Sci. Polish Acad. Sci., Rep. No.431, Warsaw. 1981.
• [5] Z. Pawlak. Classification of objects by means of attributes, Institute comp. Sci. Polish Acad. Sci., Rep. No.431, Warsaw. 1981.
• [6] Z. Pawlak. Rough sets. International Journal of Information and Computer Science, pages 341-356, 1982.
• [7] Z. Pawlak. Rough classifications. International Journal of Man Machine studies, 20:469-483, 1983.
• [8] Z. Pawlak. Rough sets and fuzzy sets. Fuzzy sets and systems, 17:99-102, 1985.
• [9] Z. Pawlak. Rough sets, Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers. 1991.
• [10] Z. Pawlak and A. Skowron. Rudiments of rough sets. Information Sciences, 177:3-27, 2007.
• [11] Z. Pawlak and A. Skowron. Rough sets: some extensions. Information Sciences, 177:28-40, 2007.
• [12] Z. Pawlak and A. Skowron. Rough sets and boolean reasoning. Information Sciences, 177:41-73, 2007.
• [13] B.K. Tripathy and A. Mitra. Topological properties of rough sets and their applications. Accepted for publication in Int. Jour, of Granular Computing Rough Sets and Intelligent Systems, 2009.