The Rough Method for Spatial Data Subzone Similarity Measurement

Author(s)
Weihua Liao

ABSTRACT

There are two methods for GIS similarity measurement problem, one is cross-coefficient for GIS attribute similarity measurement, and the other is spatial autocorrelation that is based on spatial location. These methods can not calculate subzone similarity problem based on universal background. The rough measurement based on membership function solved this problem well. In this paper, we used rough sets to measure the similarity of GIS subzone discrete data, and used neighborhood rough sets to calculate continuous data’s upper and lower approximation. We used neighborhood particle to calculate membership function of continuous attribute, then to solve continuous attribute’s subzone similarity measurement problem.

There are two methods for GIS similarity measurement problem, one is cross-coefficient for GIS attribute similarity measurement, and the other is spatial autocorrelation that is based on spatial location. These methods can not calculate subzone similarity problem based on universal background. The rough measurement based on membership function solved this problem well. In this paper, we used rough sets to measure the similarity of GIS subzone discrete data, and used neighborhood rough sets to calculate continuous data’s upper and lower approximation. We used neighborhood particle to calculate membership function of continuous attribute, then to solve continuous attribute’s subzone similarity measurement problem.

Cite this paper

W. Liao, "The Rough Method for Spatial Data Subzone Similarity Measurement,"*Journal of Geographic Information System*, Vol. 4 No. 1, 2012, pp. 37-45. doi: 10.4236/jgis.2012.41006.

W. Liao, "The Rough Method for Spatial Data Subzone Similarity Measurement,"

References

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[15] Q. H. Hu, D. R. Yu and Z. X. Xie, “Numerical Attribute Reduction Based on Neighborhood Granulation and Rough Approximation,” Journal of Software, Vol. 19, No. 3, 2008, pp. 640-649. doi:10.3724/SP.J.1001.2008.00640

[16] H. Xie, H. Z. Cheng and D. X. Niu, “Discretization of Continuous Attributes in Rough Sets Theory Based on Information Entropy,” Chinese Journal of Computers, Vol. 28, No. 9, 2005, pp. 1570-1574.

[17] R. Jensen and Q. Shen, “Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches,” IEEE Transactions on Knowledge and Data Engineering, Vol. 16, No. 12, 2004, pp. 1457-1471. doi:10.1109/TKDE.2004.96

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[20] D. S. Yeung, D. G. Chen, et al., “On the Generalization of Fuzzy Rough Sets,” IEEE Transactions on Fuzzy Systems, Vol. 13, No. 3, 2005, pp. 343-361. doi:10.1109/TFUZZ.2004.841734

[21] Q. H. Hu, D. R. Yu and Z. X. Xie, “Information-Pr- eserving Hybrid Data Reduction Based on Fuzzy Rough Techniques,” Pattern Recognition Letters, Vol. 27, No. 5, 2006, pp. 414-423. doi:10.1016/j.patrec.2005.09.004

[22] R. Slowinski and D. Vanderpooten, “A Generalized Definition of Rough Approximations Based on Similarity,” IEEE Transactions on Knowledge and Data Engineering, Vol. 12, No. 2, 2000, pp. 331-336. doi:10.1109/69.842271

[23] T. Y. Lin, “Data Mining and Machine Oriented Modeling: A Granular Computing Approach,” Applied Intelligence, Vol. 13, No. 2, 2000, pp. 113-124. doi:10.1023/A:1008384328214

[24] R. M. Wu and X. H. Zhang, “A Research on the Difference Measures of Rough Fuzzy Sets,” Journal of Southwest University for Nationalities (Natural Science Edition), Vol. 35, No. 6, 2009, pp. 1139-1142.

[25] Y. Y. Guan and H. K. Wang, “Measures of Rough Similarity between Sets,” Fuzzy Systems and Mathematics, Vol. 20, No. 1, 2006, pp. 134-139.

[26] W. X. Zhang, W. Z. Wu and J. Y. Liang, “Rough Set Theory and Method,” Science Press, Beijing, 2005.

[27] X. P. Geng, X. C. Du and P. Hu, “Spatial Clustering Method Based on Raster Distance Transform for Extended Objects,” Acta Geodaetica et Cartographica Sinica, Vol. 38, No. 2, 2009, pp. 162-168.

[28] X. F. Li and J. Li, “Data Mining and Knowledge Discovery,” Higher Education Press, Beijing, 2003.

[29] Y. Zhou, H. Lin and Y. B. Cui, “The Study under Rough Relation and It’s Neighbor Relation,” Computer Science, Vol. 31, No. 10A, 2004, pp. 61-63.

[30] F. C. Liu, “Similarity Measure and Similarity Direction between Fuzzy Rough Sets,” Computer Engineering and Applications, Vol. 35, 2005, pp. 63-66.

[31] H. K. Wang, Y. Y. Guan and K. Q. Shi, “Measure of Similarity between Rough sets and Its Application,” Computer Engineering and Applications, Vol. 31, 2004, pp. 39-40.

[32] Z. H. Shi and Y. P. Lian, “Measure of Similarity between Rough Sets Based on Inclusion,” Research of Mathematic Teaching-Learning, Vol. 2, 2008, pp. 53-54.

[1] W. R. Tobler, “A Computer Movie Simulating Urban Growth in the Detroit Region,” Economic Geography, Vol. 46, No.2, 1970, pp. 234-240. doi:10.2307/143141

[2] A. D. Cliff and J. K. Ord, “Spatial Autocorrelation,” Pion, London, 1973.

[3] J. F. Wang, L. F. Li and Y. Ge, “A Theoretic Framework for Spatial Analysis,” Acta Geographica Sinica, Vol. 55 No.1, 2000, pp. 92-103.

[4] F. Chen and D. S. Du, “Application of the Integration of Spatial Statistical Analysis with GIS to the Analysis of Regional Economy,” Geomatics and Information Science of Wuhan University, Vol. 27 No. 4, 2002, pp. 391-396.

[5] L. Anselin, “Local Indicators of Spatial Association: LI- SA,” Geographical Analysis, Vol. 27, No. 2, 1995, pp. 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x

[6] D. Y. Li and C. Y. Liu, “Artificial Intelligence with Uncertainty,” Journal of Software, Vol. 15, No. 11, 2004, pp. 1583-1594.

[7] Z. Pawlak, ”Rough Sets,” International Journal of Computer and Information Sciences, Vol. 11, 1982, pp. 341- 356.

[8] Z. Pawlak, “Rough Sets Theoretical Aspects of Reasoning about Data,” Kluwer Academic Publishers, Dordre- cht, 1991.

[9] Z. Pawlak, “Rough Set Theory and Its Application to Data Analysis,” Cybernetics and Systems, Vol. 29, No. 9, 1998, pp. 661-668. doi:10.1080/019697298125470

[10] R. Slowinski, “A generalization of the in Discernibility Relation for Rough Sets Analysis of Quantitative Information,” Decisions in Economics and Finance, Vol. 15, No. 1, 1992, pp. 65-78. doi:10.1007/BF02086527

[11] P. Srinivasan, “The Importance of Rough Approximations for Information Retrieval,” International Journal of Man-Machine Studies, Vol. 34, No. 5, 1991, pp. 657-671. doi:10.1016/0020-7373(91)90017-2

[12] T. Beaubouef, F. Petry and B. Buckles, “Extension of the Relational Database and Its Algebra with Rough Sets Techniques,” Computational Intelligence, Vol. 11, No. 2, 1995, pp. 233-245. doi:10.1111/j.1467-8640.1995.tb00030.x

[13] X. B. Yang, D. J. Yu and J. Y. Yang, “Dominance-Based Rough Set Approach to Incomplete Interval-Valued Information System,” Data & Knowledge Engineering, Vol. 68, No. 11, 2009, pp. 1331-1347. doi:10.1016/j.datak.2009.07.007

[14] T. Beaubouef, F. E. Petry and R. Ladner, “Spatial Data Methods and Vague Regions: A Rough Sets Approach,” Applied Soft Computing, Vol. 7, No. 1, 2007, pp. 425-440. doi:10.1016/j.asoc.2004.11.003

[15] Q. H. Hu, D. R. Yu and Z. X. Xie, “Numerical Attribute Reduction Based on Neighborhood Granulation and Rough Approximation,” Journal of Software, Vol. 19, No. 3, 2008, pp. 640-649. doi:10.3724/SP.J.1001.2008.00640

[16] H. Xie, H. Z. Cheng and D. X. Niu, “Discretization of Continuous Attributes in Rough Sets Theory Based on Information Entropy,” Chinese Journal of Computers, Vol. 28, No. 9, 2005, pp. 1570-1574.

[17] R. Jensen and Q. Shen, “Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches,” IEEE Transactions on Knowledge and Data Engineering, Vol. 16, No. 12, 2004, pp. 1457-1471. doi:10.1109/TKDE.2004.96

[18] D. Dubois and H. Prade, “Rough Fuzzy Sets and Fuzzy Rough Sets,” International Journal of General Systems, Vol. 17, No. 2, 1990, pp. 191-209. doi:10.1080/03081079008935107

[19] Q. H. Hu, D. R. Yu and Z. X. Xie, “Fuzzy Probabilistic Approximation Spaces and Their Information Measures,” IEEE Transactions on Fuzzy Systems, Vol. 14, No. 2, 2006, pp. 191-201. doi:10.1109/TFUZZ.2005.864086

[20] D. S. Yeung, D. G. Chen, et al., “On the Generalization of Fuzzy Rough Sets,” IEEE Transactions on Fuzzy Systems, Vol. 13, No. 3, 2005, pp. 343-361. doi:10.1109/TFUZZ.2004.841734

[21] Q. H. Hu, D. R. Yu and Z. X. Xie, “Information-Pr- eserving Hybrid Data Reduction Based on Fuzzy Rough Techniques,” Pattern Recognition Letters, Vol. 27, No. 5, 2006, pp. 414-423. doi:10.1016/j.patrec.2005.09.004

[22] R. Slowinski and D. Vanderpooten, “A Generalized Definition of Rough Approximations Based on Similarity,” IEEE Transactions on Knowledge and Data Engineering, Vol. 12, No. 2, 2000, pp. 331-336. doi:10.1109/69.842271

[23] T. Y. Lin, “Data Mining and Machine Oriented Modeling: A Granular Computing Approach,” Applied Intelligence, Vol. 13, No. 2, 2000, pp. 113-124. doi:10.1023/A:1008384328214

[24] R. M. Wu and X. H. Zhang, “A Research on the Difference Measures of Rough Fuzzy Sets,” Journal of Southwest University for Nationalities (Natural Science Edition), Vol. 35, No. 6, 2009, pp. 1139-1142.

[25] Y. Y. Guan and H. K. Wang, “Measures of Rough Similarity between Sets,” Fuzzy Systems and Mathematics, Vol. 20, No. 1, 2006, pp. 134-139.

[26] W. X. Zhang, W. Z. Wu and J. Y. Liang, “Rough Set Theory and Method,” Science Press, Beijing, 2005.

[27] X. P. Geng, X. C. Du and P. Hu, “Spatial Clustering Method Based on Raster Distance Transform for Extended Objects,” Acta Geodaetica et Cartographica Sinica, Vol. 38, No. 2, 2009, pp. 162-168.

[28] X. F. Li and J. Li, “Data Mining and Knowledge Discovery,” Higher Education Press, Beijing, 2003.

[29] Y. Zhou, H. Lin and Y. B. Cui, “The Study under Rough Relation and It’s Neighbor Relation,” Computer Science, Vol. 31, No. 10A, 2004, pp. 61-63.

[30] F. C. Liu, “Similarity Measure and Similarity Direction between Fuzzy Rough Sets,” Computer Engineering and Applications, Vol. 35, 2005, pp. 63-66.

[31] H. K. Wang, Y. Y. Guan and K. Q. Shi, “Measure of Similarity between Rough sets and Its Application,” Computer Engineering and Applications, Vol. 31, 2004, pp. 39-40.

[32] Z. H. Shi and Y. P. Lian, “Measure of Similarity between Rough Sets Based on Inclusion,” Research of Mathematic Teaching-Learning, Vol. 2, 2008, pp. 53-54.