Characterizing Solutions of Rough Programming Problem Based on a Boundary Region
[1]
Ebrahim Abdalla Youness, Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
[2]
Heba Gharieb Gomaa, Suez Institute for Management Information System, Suez, Egypt.
In this paper we introduce the concept of rough function and its convexity and differentiability based on its boundary region. Also a new kind of rough programming problem and its solutions are discussed according to the notion of boundary region.
Rough Function, Convexity, Differentiability, Boundary Region and Rough Programming Problems
[1]
T. Arciszewski, W. P. Ziarko, Adaptive expert system for preliminary design wind bracings in steel skeleton structure, Second Century of the Skyscraper, Van Nostrand Reinhold Company, New York, 1988, pp. 847-855.
[2]
D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal General Systems, 17, 1990, pp. 191-209.
[3]
J. Fibak, Z. Pawlak, K. Slowinski, Rough sets based decision algorithms for treatment of duodenal ulcer by HSV, Bulletin of PAS, 34, 1986, pp. 227-246.
[4]
T. Helmut, Fuzzy rough sets versus rough fuzzy sets-an interpretation and a comparative study using concepts of modal logics, in: Proceedings of 5th European Congress on Intelligent Techniques and Sift Computing (EUFIT 97) 9-11 September, Aachen, Germany, 1997, pp. 159-167.
[5]
W. Jin-Mao, Rough set based approach to selection of node, International Journal Computational Cognition 1, 2, 2003, 25-40.
[6]
T. Y. Lin, Neighborhood systems-a qualitative theory for fuzzy and rough sets, in: P. Wang (Ed.), Advances in Machine Intelligence and Soft Computing, vol. 4, 1997, pp. 132-155.
[7]
T. Munakata, Rough control: A perspective, Rough Sets and Data Mining Analysis of Imprecise Data, 1997, pp. 77-87.
[8]
S. Mitatha, K. Dejhan, F. Cheevasuvit, Kasemsht, Some experimental results of using rough sets for printed Thai characters recognition, International Journal of Computational Cognition 1, 4, 2003, pp. 109-121.
[9]
Z. Pawlak, K. Slowinski, R. Slowinski, Rough classification of patients after highly selective vagotomy for duodenal ulcer, International Journal of Man-Machine Studies, 24, 1986, pp. 413-433.
[10]
Z. Pawlak, rough Sets, Kluwer Academic Publishers, Dordrecht, 1991.
[11]
Z. Pawlak, Rough Sets, in: T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining Analysis of Imprecise Data. Kluwer Academic, Boston, MA, 1997, pp.38.
[12]
S. Qiang, C. Alexios, Combining rough sets and data-driven fuzzy learning for generation of classification rules. Pattern Recognition, 32, 1999, pp. 2073-2076.
[13]
R. Slowinski (Ed.), Intelligent Decision Support-Handbook of Advances and Applications of the Rough Set Theory, Kluwer Academic Publishers, Dordrecht, 1992.
[14]
Y. Y. Yao, S. K. Wong, T. Y. Lin, A review of rough sets models, in: T. Y. Lin, N. Cercone (Eds.), Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic, Boston, MA, 1997, pp. 47-76.
[15]
E. A. Youness, Characterizing solutions of rough programming problems, in: European Journal of Operational Research, 168, 2006, pp. 1019-1029.
