Abstract
This paper is dealing with the upper and lower approximation models for representing the given phenomenon in a fuzzy environment. Based on the given data, the upper and lower approximation models can be derived from upper and lower directions, respectively where the inclusion relationship between these two models holds. Thus, the inherent fuzziness existing in the given phenomenon can be represented by the upper and lower models. The modalities of the upper and lower models have been illustrated in regression analysis and also in the identification methods of possibility distributions. The comparison of the concepts of possibility data analysis and rough sets is shown. A measure similar to the accuracy measure of rough sets is used to clarify the difference between the data structure and the assumed model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dubois, D. and Prade, H. (1988) Possibility Theory. Plenum Press, New York
Guo, P. and Tanaka, H. (1998) Possibilistic data analysis and its application to portfolio selection problems. Fuzzy Economic Review 3 /2, 3–23
Pawlak, Z. (1982) Rough sets. Int. J. Information and Computer Sciences 11, 341–356
Pawlak, Z. (1984) Rough classification. Int. J. Man-Machine Studies 20, 469–483
Tanaka, H., Guo, P. and Turksen B. (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy sets and Systems 111, 387–397
Tanaka, H., Hayashi, I. and Watada, J. (1989) Possibilistic linear regression analysis for fuzzy data. European J. of Operational Research 40, 389–396
Tanaka, H. and Ishibuchi, H. (1991) Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters. Fuzzy sets and Systems 41, 145–160
Tanaka, H.and Guo, P. (1999) Portfolio selections based on upper and lower exponential possibility distributions. European J. of Operational Research 114 (1999) 115–126
Tanaka, H. and Guo, P. (1999) Possibilistic Data Analysis for Operations Research. Physica-Verlag, Heidelberg; New York
Tanaka, H. and Ishibuchi, H. (1993) Evidence theory of exponential possibility distributions. Int. J. of Approximate Reasoning 8, 123–140
Tanaka H. and Lee, H. (1998) Interval regression analysis by quadratic programming approach. IEEE Transaction on Fuzzy Systems 6, 473–481
Tanaka, H., Lee H. and Guo, P. (1998) Possibility data analysis with rough set concept. Proceeding of Sixth IEEE International Conference on Fuzzy Systems 117–122
Zadeh, L. A. (1977) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tanaka, H., Guo, P. (2002). Possibilistic Data Analysis and Its Similarity to Rough Sets. In: Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds) Data Mining, Rough Sets and Granular Computing. Studies in Fuzziness and Soft Computing, vol 95. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1791-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1791-1_26
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2508-4
Online ISBN: 978-3-7908-1791-1
eBook Packages: Springer Book Archive