Application of Fuzzy Clustering in Continuous Classification: A Case study

Document Type : Original Article

Authors

1 Ph.D. in Hydrology, Ministry of Energy, Iran

2 M.Sc. in Geology, Schlumberger Oilfield Services Co., Iran

Abstract

Using continuous classification (specifically zonation in this study) it is possible to save continuity of changes in natural phenomena while representing them. Fuzzy Sets Theory is a proper tool to study and represent this continuity. As a case study in application of Continuous Zonation, fuzzy clustering among many other pattern recognition methods was applied to study erodability of Tajan river watershed. The results have been compared with traditional PSIAC method and have been represented as continuous erodability maps by using pixels value combination method. The maps show that even in area that a class is dominant, changes in erodability are visible . Also classes, which do not really exist and are only the artifacts of crisp boundary classification, are omitted. Transitional changes can be modeled similar to real gradual ones in nature.

Keywords


حسنی پاک. ع. ا.، شرف‌الدین. م. (1380)، تحلیل داده‌های اکتشافی، دانشگاه تهران، 987 صفحه.
رفاهی، حسینقلی. (1379)، فرسایش آبی و کنترل آن، انتشارت دانشگاه تهران، 551 صفحه.
مرکز تحقیقات منابع آب (تماب)، (1375)، گزارش تلفیق مطالعات منابع آب حوزة رودخانه‌های مازندران، جلد دوم، بررسیها و مشخصات عمومی، 217 صفحه.
مرکز تحقیقات منابع آب (تماب)، (1376)، گزارش تلفیق مطالعات منابع آب حوزة رودخانه‌های مازندران، جلد سوم، تجزیه وتحلیل آمار و اطلاعات بیلان آبهای سطحی و رسوب، 157 صفحه.
وزارت نیرو، (1373)، استانداردهای مهندسی آب، فرسایش و رسوب، نشریه شماره 93، 95صفحه.
Bezdek. J. C. (1973), Fuzzy Mathematics in Pattern Classification, ph. D Dissertation, Cornell University Ithaca, NY.
Bezdek. J. C. and Pal. S. K. (1992), Fuzzy Models for Pattern Recognition, IEEE  Press, NewYork, 539p.
Burrough, P. A. (1986), Principles of Geographical Information Systems for Land Resources Assessment,  Monograph on Soil and Land Resources Survey, No,12, Oxford University Press, Oxford, Great Britain. 194p.
Burrough. P. A., van Gaana, P.F.M. and Hootamans, R. (1997), Continuous Classification in Soil Survey: Spatial Correlation, Confusion and Boundries, GEODERMA, Volume 77, pp. 115-135.
Chiu, S. (1994), Fuzzy Model Identification Based on Cluster Estimation, Proceedings of 3rd International Conference on Fuzzy Systems, Ed: Brenji et al.,  pp.1240-1245, IEEE, Orlando, USA
De Gruijiter, J. J., Walvoort, D. J. J. and Van Gaans, P.F.M. (1997), Continuous Soil Maps – a Fuzzy Set Approach to Bridge Aggregation Levels of Process and Distribution Models, GEODERMA, Volume 77, pp. 169-195.
Gath, I. and Geva, A. B. (1989), “Unsupervised Optimal Fuzzy Clustering”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7): pp. 773–781.
Grima, M. A. (2000), Neureo-Fuzzy Modeling in Engineering Geology, A. A. Balkema, Brookfield, pp. 244.
Gustafson D. E. and Kessel W. C. (1979), Fuzzy Clustering with a Fuzzy Covariance Matrix. Proceedings of the IEEE, San Diego, CA, USA, Vol.6, 761p.
Kaufman, A. (1975), Introduction to the Theory of Fuzzy Subsets, Academic Press, NewYork.
Kaymak, U. and Babusœka R. (1995), Compatible cluster merging for fuzzy modeling, Proceedings FUZZ-IEEE/IFES'95, Yokohama, Japan,  pp. 897-904.
Krishnapuram, R. and Freg, C-P. (1992), Fitting an unknown number of lines and planes to image data through, compatible cluster merging. Pattern Recognition, 25(4): pp. 385-400.
Lagacherie, P., Gazemier, D. R., Van Gaans, P.F.M. and Burrough, P. A. (1997), “Fuzzy k-means Clustering of Fields in an Elementary Catchment and Extrapolation to a Large Area”, GEODERMA, Volume 77, pp.197-216.
 MathWorks Co., Fuzzy Logic Toolbox for use with MATLAB, User’s Guide (2001), MathWorks, (online version), 217p.
McBratney, A. B. and De Gruijiter, J. J. (1992), A Continium Approach to Soil Classification by Modified Fuzzy k-means with Extragrades. J. Soil Sci, Vol.43, pp. 159-176
McBratney, A. B. and Odeh, I. O. A. (1997), Application of Fuzzy Logic Sets in Soil Science: Fuzzy Logic, Fuzzy Measurement and Fuzzy Decisions, GEODERMA, Volume 77, pp. 85-113.
 Mitra, B., Scott, H. D., Dixon, J. C. and McKimmey,  J. M. (1998), Applications of Fuzzy Logic to the Prediction of Soil Erosion in a Large Watershed, GEODERMA, Volume 86, pp.183-209
 Nisar Ahamed, T. R., Gopal Rao, K. and Murthy, J.S.R. (2000), Fuzzy Class Membership Approach to Soil Erosion Modeling, AGRICULTURAL SYSTEMS, Volume 63, pp.97-110.
Schwab, G. O., Fangemeier, D. D., Elliot, W. J. and Frevert, R. K. (1993), Soil and Water Conservation Engineering, Fourth Edition, Wiley and sons, 507p.
Setnes, M. (1999), Supervised Fuzzy Clustering for Rule Extraction. Proceedings of FUZZIEEE’ 99, pp. 1270–1274, Seoul, Korea.
Yager, R. R. and Filev, D. P. (1994), Essentials of Fuzzy Modling and Control, John Wiley and sons, Newyork, USA, 388p.
Zadeh, L. A. (1965), Fuzzy Sets, Information & Control, Vol. 8, pp. 338-353
Zadeh, L. A. (1968), Fuzzy Algorithms, Information & Control, Vol 12, pp 94-102