A Fuzzy Modeling Approach for Replicated Response Measures Based on Fuzzification of Replications with Descriptive Statistics and Golden Ratio

Some of the experimental designs can be composed of replicated response measures in which the replications cannot be identified exactly and may have uncertainty different than randomness. Then, the classical regression analysis may not be proper to model the designed data because of the violation of probabilistic modeling assumptions. In this case, fuzzy regression analysis can be used as a modeling tool. In this study, the replicated response values are newly formed to fuzzy numbers by using descriptive statistics of replications and golden ratio. The main aim of the study is obtaining the most suitable fuzzy model for replicated response measures through fuzzification of the replicated values by taking into account the data structure of the replications in statistical framework. Here, the response and unknown model coefficients are considered as triangular type-1 fuzzy numbers (TT1FNs) whereas the inputs are crisp. Predicted fuzzy models are obtained according to the proposed fuzzification rules by using Fuzzy Least Squares (FLS) approach. The performances of the predicted fuzzy models are compared by using Root Mean Squared Error (RMSE) criteria. A data set from the literature, called wheel cover component data set, is used to illustrate the performance of the proposed approach and the obtained results are discussed. The calculation results show that the combined formulation of the descriptive statistics and the golden ratio is the most preferable fuzzification rule according to the well-known decision making method, called TOPSIS, for the data set.

Anahtar Kelimeler:

Replicated response measures, Fuzzy least squares; Triangular type-1 fuzzy numbers; Golden ratio

PDF

___

[1] Zadeh, L.A. 1965. Fuzzy sets. Information Control, 338-353.
[2] Tanaka, H., Uejima, S., Asai, K. 1982. Linear Regression Analysis With Fuzzy Model. IEEE Transactions On Systems, Man, And Cybernetics, 12(6), 903-907.
[3] Diamond, P. 1988. Fuzzy least squares. Information Sciences, 46, 141-157.
[4] Ubale, A.B., Sananse, S. L. 2015. Fuzzy Regression Model and Its Application: A Review. International Journal of Innovative Research in Science, Engineering and Technology, 4(11), 10853-10860.
[5] Bashiri, M., Hosseininezhad, S.J. 2009. A Fuzzy Programming for Optimizing Multi Response Surface in Robust Designs. Journal of Uncertain Systems, 3(3), 163-173.
[6] Bashiri, M., Hosseininezhad, S.J. 2012. Fuzzy Development of Multiple Response Optimization. Group Decision and Negotiation, 21(3), 417-438.
[7] Türkşen, Ö., Apaydın, A. 2014. A Modeling Approach Based on Fuzzy Least Squares Method for Multi-Response Experiments with Replicated Measures. Chaos, Complexity and Leadership 2012 Springer Proceedings in Complexity, Springer Netherlands, 153-158.
[8] Türkşen, Ö., Güler, N. 2015. Comparison of fuzzy logic based models for the multi-response surface problems with replicated response measures. Applied Soft Computing, 37, 887-896.
[9] Türkşen, Ö., Kocadağlı, O. 2015. Fuzzy Modeling for Replicated Response Measures by Using Type-2 Fuzzy Numbers. The 4th International Fuzzy Systems Symposium Proceedings Book, 5-6 November 2015, 464-468.
[10] Türkşen, Ö. 2016. Analysis of Response Surface Model Parameters with Bayesian Approach and Fuzzy Approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24(1), 109−122.
[11] Mendel, J.M. 2017. Type-1 Fuzzy Sets and Fuzzy Logic. Uncertain Rule-Based Fuzzy Systems, Springer International Publishing AG, 25-99.
[12] Dunlap, R.A. 1997. The Golden Ratio and Fibonacci Numbers. World Scientific Publishing, London. 157s.
[13] Harper, D., Kosbe, M., Peyton, L. 1987. Optimization of Ford Taurus Wheel Cover Balance. Fifth Symposium on Taguchi Methods, 527-539.
[14] Chen, S.J., Hwang, C.L. 1992. Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin, 536s.