Abstract
In rough set approach, the rough approximations called lower and upper ones have been discussed. This concept can be extended into a new research field of data analysis. The proposed approach to data modeling is to obtain dual mathematical models by using a similar concept to rough sets. The dual models called lower and upper models have an inclusion relation. In the other words, the proposed method can be described as two approximations to a phenomenon under consideration such that
Thus, the lower and upper models are obtained by the greatest lower bound and the least upper bound, respectively. This property is illustrated by interval regression models which are not crisp, but have an interval relationship between inputs and outputs. Generally, the lower and upper models are formulated by greatest lower and least upper bounds, respectively. The given phenomenon can be expressed by the pair (lower model, upper model) corresponding to rough approximations.
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References
Pawlak, P.: Rough Sets, Kluwer Academic, Dordrecht (1991).
Tanaka, H., Guo, P.: Possibilistic Data Analysis for Operations Research, Physica-Verlag, Heidelberg (1999).
Tanaka, H., Lee, H.: Interval regression analysis by quadratic programming approach, IEEE Trans. on Fuzzy Systems 66 (1998) 473–481.
Tanaka, H., Lee, H.: Interval Regression analysis with polynominal and its similarity to rough sets concept, Fundamenta Informaticae, IOS Press. 37 (1999) 71–87.
Sugihara, K., Tanaka, H.: Interval evaluations in the analytic hierarchy process by possibility analysis, An Int. J. of Computational Intelligence 173 (2001) 567–579.
Sugihara, K., Ishii, H., Tanaka, H.: On interval AHP, 4th Asian Fuzzy Systems Symposium — Proceedings of AFSS2000 — (2000) 251–254.
Guo, P., Tanaka, H., Zimmermann, H.J.: Upper and lower possibility distributions of fuzzy decision variables in upper level decision problems, Int. J. of Fuzzy Sets and Systems 111 (1999) 71–79.
Guo, P., Tanaka, H.: Possibilistic data analysis and its application to portfolio selection problems, Fuzzy Economic Review 3/2 (1998) 3–23.
Entani, T., Maeda, Y., Tanaka, H.: Dual models of interval DEA and its extension to interval data, European J. of Operational Research 136 (2002) 32–45.
Pawlak, Z.: Rough Classification, Int. J. of Man-Machine Studies 20 (1984) 469–483.
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© 2003 Springer-Verlag Berlin Heidelberg
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Tanaka, H. (2003). Dual Mathematical Models Based on Rough Approximations in Data Analysis. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_7
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DOI: https://doi.org/10.1007/3-540-39205-X_7
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