Analyze the effect of number of fuzzy rules on fuzzy model performance in simulating soil water movement

Document Type : Original Article

Authors

1 Ph.D. Candidate of Irrigation and Drainage, Department of Water Engineering, Ferdowsi University of Mashhad

2 Professor, Department of Water Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

3 Professor, Department of Water Engineering, Ferdowsi University of Mashhad

Abstract

Fuzzy methods in simulating water flow in to the soil has attracted the attention of researchers because of the possibility of considering the uncertainty and variability of the parameters in this methods. The sensitivity of the fuzzy model is to find the balance between the accuracy of the fuzzy model and its speed of execution, which depends on the number of fuzzy rules. Therefore, our goal in this research is to investigate the effect of the number of fuzzy rules on the accuracy of the model. In order to achieve this, the fuzzy model for predicting water movement in unsaturated soil was evaluated by considering fuzzy sets with different supports and consequently different rule numbers. The rules of the fuzzy model were derived from the large training sets obtained by numerical solution of Richards equation by using HYDRUS-1D model. The results showed that increasing the number of fuzzy rules initially increased the accuracy of the model (NRMSE value decreased from 4.3 to 3.1 and maximum error value from 0.128 to 0.09 for fuzzy model with 9 and 49 rules, respectively but by increasing the number of input fuzzy sets and increasing the rules to 81, the accuracy of the fuzzy model was reduced. The reason for the reduced efficiency of the fuzzy model is rules overlap.

Keywords

References

خرمی، م و قهرمان، ب. 1396. بررسی عدم قطعیت پارامترهای خاک بر عدم قطعیت پروفیل رطوبتی با استفاده از نظریه‌ی مجموعه‌های فازی. تحقیقات منابع آب ایران. شماره 1. 126-138.
خرمی، م،. قهرمان، ب و داوری،ک. 1398. ارائه یک مدل فازی برای مدل سازی نفوذ آب در خاک. نشریه پژوهش‌های خاک (علوم خاک و آب). شماره 33. جلد 3. 275-287.
کوره پزان دزفولی، ا. 1386 . اصول و تئوری مجموعه‌های فازی و کاربرد آن در مدلسازی مسایل مهندسی آب. انتشارات جهاد دانشگاهی واحد صنعتی امیر کبیر.
Bardossy. A. and M.Disse. 1993. Fuzzy Rule-Based Models for Infiltration. Water Resources Research. VOL.29.NO2.PAGES 373-382.FEBRURY 1993.
Bardossy. A., Bronster. A and Merz. B. 1995. 1-,2- and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach, Advances in Water Resources, Vol. 18, No. 4, pp. 237-251.
Farthing, M, W and Ogden, F. L. 2017. Numerical Solution of Richards’ Equation: A Review of Advances and Challenges. SSSAJ. V81. N 6. 1257-1269.
Ishibuchi, H., Sotani, T and Murata, T. 2002. Tradeoff between the performance of fuzzy rule-based classification systems and the number of fuzzy if-then rules. 18th International conference of the north American Fuzzy information processing society. NAFIPS.
Liviu-Cristian, D., Gilles, M and Philippe, B. 2018. A Fast and Accurate Rule-Base Generation Method for Mamdani Fuzzy Systems. IEEE Transactions on Fuzzy Systems, Institute of Electrical and Electronics Engineers, 2018, pp.715-733.
Ozkan, I and Turksen, I.B. 2014. Uncertainty and Fuzzy Decisions, Chapter 2. Springer Science, Busines Media Dordrecht 2014.
Richards, L. A. 1931. Capillary conduction of liquids through porous media, Physics, I, 318-33, 1931.
Schulz, k and Huwe, B. 1997. Water flow modeling in the unsaturated zone with imprecise parameters using a fuzzy approach. Journal of Hydrology 201 (1997) 211-229.
Schulz, K and Huwe, B .1999. Uncertainty and sensitivity analysis of water transport modelling in a layered soil profile using fuzzy set theory. Journal of Hydroinformatics. 01. 2. 1999.
Simunek, J,. Van Genuckten, M. Th and Sejna, M. 2006. The Hydrus Software Package for Simulating the Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably – Saturated Media. Technical Manual.
Verma, P, Singh, P. George, K. V. Sing, H. V. Devotta, S and Singh, R.N.  2009. Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory. Applied Mathematical Modelling 33 (2009) 770-782.
Wan, F,. Shang, H,. Wang, L, X and Sun, Y, X. 2005. How to Determine the Minimum Number of Fuzzy Rules to Achieve Given Accuracy: A Computational Geometric Approach to SISO Case. Fuzzy Set and Systems 150 (2005). 199-209.
Wu, Q and Mencer, O. 2009. Evaluation Sampling Based Hotspot Detection. 2009. Architecture of Computing Systems– ARCS. Lecture Notes in Computer Science, vol 5455. Springer, Berlin, Heidelberg.  
Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 338-353, 1965.
Iranian Journal of Irrigation & Drainage
Volume 14, Issue 3 - Serial Number 81
July and August 2020
Pages 957-966

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