A fuzzy software prototype for spatial phenomena: case study precipitation distribution

Yanar, Tahsin Alp
As the complexity of a spatial phenomenon increases, traditional modeling becomes impractical. Alternatively, data-driven modeling, which is based on the analysis of data characterizing the phenomena, can be used. In this thesis, the generation of understandable and reliable spatial models using observational data is addressed. An interpretability oriented data-driven fuzzy modeling approach is proposed. The methodology is based on construction of fuzzy models from data, tuning and fuzzy model simplification. Mamdani type fuzzy models with triangular membership functions are considered. Fuzzy models are constructed using fuzzy clustering algorithms and simulated annealing metaheuristic is adapted for the tuning step. To obtain compact and interpretable fuzzy models a simplification methodology is proposed. Simplification methodology reduced the number of fuzzy sets for each variable and simplified the rule base. Prototype software is developed and mean annual precipitation data of Turkey is examined as case study to assess the results of the approach in terms of both precision and interpretability. In the first step of the approach, in which fuzzy models are constructed from data, "Fuzzy Clustering and Data Analysis Toolbox", which is developed for use with MATLAB, is used. For the other steps, the optimization of obtained fuzzy models from data using adapted simulated annealing algorithm step and the generation of compact and interpretable fuzzy models by simplification algorithm step, developed prototype software is used. If the accuracy is the primary objective then the proposed approach can produce more accurate solutions for training data than geographically weighted regression method. The minimum training error value produced by the proposed approach is 74.82 mm while the error obtained by geographically weighted regression method is 106.78 mm. The minimum error value on test data is 202.93 mm. An understandable fuzzy model for annual precipitation is generated only with 12 membership functions and 8 fuzzy rules. Furthermore, more interpretable fuzzy models are obtained when Gath-Geva fuzzy clustering algorithms are used during fuzzy model construction.


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Citation Formats
T. A. Yanar, “ A fuzzy software prototype for spatial phenomena: case study precipitation distribution,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.