Application of a new fuzzy logic model known as "SMRGT" for estimating flow coefficient rate

Year 2024, Volume: 8 Issue: 1, 46 - 55, 19.01.2024

Ayşe Yeter Günal , Ruya Mehdi

https://doi.org/10.31127/tuje.1225795

Cited By: 2

Abstract

Since we all have our own set of limitations when it comes to perceiving the world and reasoning profoundly, we are constantly met with uncertainty as a result of a lack of information (lexical impression, incompleteness), as well as specific measurement inaccuracies. It has been found that uncertainty, which shows up as ambiguity, is the root cause of complexity, which is everywhere in the real world. Most of the uncertainty in civil engineering systems comes from the fact that the constraints (parameters) are hard to understand and are described in a vague way. The ambiguity comes from a number of sources, including physical arbitrariness, statistical uncertainty due to using limited information to estimate these characteristics, and model uncertainty due to using overly simplified methods and idealized depictions of actual performances. Thus, it is better to combine fuzzy set theory and fuzzy logic. Fuzzy logic is well-suited to modelling the indeterminacy and ambiguity that results from multiple factors and a lack of data. In order to improve upon a previous predictive model, this paper uses a smart model built on a fuzzy logic system (FLS). Precipitation, temperature, humidity, slope, and land use data were all taken into account as input variables in the fuzzy model. Toprak's original explanation of the simple membership function and fuzzy rules generation technique (SMRGT) was based on the fuzzy-Mamdani methodology and used the flow coefficient as its output. The model's results were compared to available data. The following factors were considered in the comparison: 1) The maximum, minimum, mean, standard deviation, skewness, variation, and correlation coefficients are the seven statistical parameters. 2) Four types of error criteria: Mean Absolute Relative Error (MARE), Mean Square Error (MSE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE). 3) Scatter diagram.

Keywords

Fuzzy system, SMRGT, Flow Coefficient, Mamdani theory, Ambiguity

References

• Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
• Erdem, F. (2022). Risk assessment with the fuzzy logic method for Ankara OIZ environmental waste water treatment plant. Turkish Journal of Engineering, 6(4), 268-275. https://doi.org/10.31127/tuje.975623
• Öztürk, A., Allahverdi, N., & Saday, F. (2022). Application of artificial intelligence methods for bovine gender prediction. Turkish Journal of Engineering, 6(1), 54-62. https://doi.org/10.31127/tuje.807019
• Freksa, C. (1992). Temporal reasoning based on semi-intervals. Artificial intelligence, 54(1-2), 199-227. https://doi.org/10.1016/0004-3702(92)90090-K
• Mamdani. (1977). Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE transactions on computers, 100(12), 1182-1191. https://doi.org/10.1109/TC.1977.1674779
• Sen, Z. (2009). Fuzzy logic and hydrological modeling. CRC Press. ISBN: 978-1-4398-0939-6
• Zadeh, L. A. (1971). Quantitative fuzzy semantics. Information sciences, 3(2), 159-176. https://doi.org/10.1016/S0020-0255(71)80004-X
• Toprak, Z. F. (2009). Flow discharge modeling in open canals using a new fuzzy modeling technique (SMRGT). CLEAN–Soil, Air, Water, 37(9), 742-752. https://doi.org/10.1002/clen.200900146
• Kissi, M., Ramdani, M., Tollabi, M., & Zakarya, D. (2004). Determination of fuzzy logic membership functions using genetic algorithms: application to structure–odor modeling. Journal of molecular modeling, 10, 335-341. https://doi.org/10.1007/s00894-004-0200-2
• Kim, J. W., Kim, B. M., & Kim, J. Y. (1998). Genetic algorithm simulation approach to determine membership functions of fuzzy traffic controller. Electronics Letters, 34(20), 1982-1983. https://doi.org/10.1049/el:19981369
• Mondelli, G., Castellano, G., Attolico, G., & Distante, C. (1998, April). Parallel genetic evolution of membership functions and rules for a fuzzy controller. In International Conference on High-Performance Computing and Networking (pp. 922-924). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0037234
• Chen, S. M., & Chen, Y. C. (2002). Automatically constructing membership functions and generating fuzzy rules using genetic algorithms. Cybernetics &Systems, 33(8), 841-862. https://doi.org/10.1080/01969720290040867
• Wu, C. J., & Liu, G. Y. (2000). A genetic approach for simultaneous design of membership functions and fuzzy control rules. Journal of Intelligent and Robotic Systems, 28, 195-211. https://doi.org/10.1023/A:1008186427312
• Wu, S., Er, M. J., & Gao, Y. (2001). A fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks. IEEE transactions on fuzzy systems, 9(4), 578-594. https://doi.org/10.1109/91.940970
• Inoue, H., Kamei, K., & Inoue, K. (1998). Automatic generation of fuzzy rules using hyper-elliptic-cone membership functions by genetic algorithms. Journal of Intelligent & Fuzzy Systems, 6(1), 65-81.
• Kim, M. W., Ryu, J. W., Kim, S., & Lee, J. G. (2003). Optimization of fuzzy rules for classification using genetic algorithm. In Advances in Knowledge Discovery and Data Mining: 7th Pacific-Asia Conference, PAKDD 2003, Seoul, Korea, April 30–May 2, 2003 Proceedings 7 (pp. 363-375). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-36175-8_36
• Pal, T., Pal, N. R., & Pal, M. (2003). Learning fuzzy rules for controllers with genetic algorithms. International Journal of Intelligent Systems, 18(5), 569-592. https://doi.org/10.1002/int.10104
• de Castro, P. A., & Camargo, H. A. (2004). A study of the reasoning methods impact on genetic learning and optimization of fuzzy rules. In Advances in Artificial Intelligence–SBIA 2004: 17th Brazilian Symposium on Artificial Intelligence, Sao Luis, Maranhao, Brazil, September 29-Ocotber 1, 2004. Proceedings 17 (pp. 414-423). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-28645-5_42
• Rutkowska, D. (1998). On generating fuzzy rules by an evolutionary approach. Cybernetics & Systems, 29(4), 391-407. https://doi.org/10.1080/019697298125669
• Lin, C. J., & Ho, W. H. (2005). An asymmetry-similarity-measure-based neural fuzzy inference system. Fuzzy Sets and Systems, 152(3), 535-551. https://doi.org/10.1016/j.fss.2004.11.001
• Kim, J. H., Seo, J., & Kim, G. C. (1996). Estimating membership functions in a fuzzy network model for part-of-speech tagging. Journal of Intelligent & Fuzzy Systems, 4(4), 309-320.
• Leng, G., McGinnity, T. M., & Prasad, G. (2005). An approach for on-line extraction of fuzzy rules using a self-organising fuzzy neural network. Fuzzy sets and systems, 150(2), 211-243. https://doi.org/10.1016/j.fss.2004.03.001
• Besada-Juez, J. M., & Sanz-Bobi, M. A. (2002). Extraction of fuzzy rules using sensibility analysis in a neural network. In Artificial Neural Networks—ICANN 2002: International Conference Madrid, Spain, August 28–30, 2002 Proceedings 12 (pp. 395-400). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-46084-5_64
• Jin, Y., & Sendhoff, B. (2003). Extracting interpretable fuzzy rules from RBF networks. Neural Processing Letters, 17, 149-164. https://doi.org/10.1023/A:1023642126478
• Simon, D. (2002). Sum normal optimization of fuzzy membership functions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10(04), 363-384. https://doi.org/10.1142/S0218488502001533
• Singpurwalla, N. D., & Booker, J. M. (2004). Membership functions and probability measures of fuzzy sets. Journal of the American statistical association, 99(467), 867-877. https://doi.org/10.1198/016214504000001196
• Dempster, A. P. (2004). Membership functions and probability measures of fuzzy sets: comment. Journal of the American Statistical Association, 99(467), 882-885.
• Zadeh, L. A. (2004). Membership functions and probability measures of fuzzy sets: comment. Journal of the American Statistical Association, 99(467), 880-882.
• Lindley, D. V. (2004). Membership functions and probability measures of fuzzy sets: comment. Journal of the American Statistical Association, 99(467), 877-880.
• Laviolette, M. (2004). Membership functions and probability measures of fuzzy sets: comment. Journal of the American Statistical Association, 99(467), 879-881.
• Singpurwalla, N. D., & Booker, J. M. (2004). Membership functions and probability measures of fuzzy sets. Journal of the American statistical association, 99(467), 867-877. https://doi.org/10.1198/016214504000001196
• Sancho‐Royo, A., & Verdegay, J. L. (1999). Methods for the construction of membership functions. International Journal of Intelligent Systems, 14(12), 1213-1230. https://doi.org/10.1002/(SICI)1098-111X(199912)14:12<1213::AID-INT3>3.0.CO;2-5
• Chen, J. E., & Otto, K. N. (1995). Constructing membership functions using interpolation and measurement theory. Fuzzy Sets and systems, 73(3), 313-327. https://doi.org/10.1016/0165-0114(94)00322-X
• Altas, E., Aydin, M. C., & Toprak, Z. F. (2017). Determination of Water Surface profile in Open Canal Using a New Fuzzy Modeling Technique (SMRGT), International Conference on Water Resource and Environmental (WRE 2107), July 26 – 29, 2017, Qingdao – China.
• Coskun, C. (2014). Automated fuzzy model generation and an analysis of the proposed method. International Journal of Open Problems in Computer Science and Mathematics, 238(1397), 1-13.
• Toprak, Z. F., Songur, M., Hamidi, N., & Gulsever, H. (2013). Determination of losses in water-networks using a new fuzzy technique (SMRGT). AWERProcedia Information Technology & Computer Science, 3(2013), 833-840.
• Karakaya, D. (2018). Modelling of flow coefficient with fuzzy SMGRT method. Master’s Thesis, Dicle University
• Yalaz, S., Atay, A., Toprak, Z. F. (2013). Fuzzy Linear Regression for Time-Related Data with Fuzzy SMRGT Method, Mathematics Symposium, Diyarbakır, 1-7.
• Bayri, G., (2018). Classification of Soils with Simple Membership Functions and Fuzzy Rules Generation Technique (SMRGT). Master’s Thesis, Bitlis Eren University.
• Şevgin, F., & fuat TOPRAK, Z. (2021). Meteorolojik Akış Katsayısının Bulanık SMRGT Yöntemi ile Belirlenmesi: Murat Havzası Örneği. Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, 12(2), 401-409. https://doi.org/10.24012/dumf.844325
• Toprak, Z. F. (2004). Determination of Longitudinal Dispersion Coefficients in Natural Channel Using Fuzzy Logic Method. PhD Thesis, Istanbul Technical University
• Toprak, Z. F. (2017). The Advantages of SMRGT Method In Modelling Hydrological Events. International Conference on Water Resource and Environment (WRE 2017), July 26 – 29, Qingdao – China