Abstract
The experimental design can be generated by using the replicated measures of responses in multi-response experiments. In the modeling of this kind of designs, observed response values, which are obtained differently in each replication of the experiment, cannot be correctly represented with a single numerical quantity. In this case, it will be more proper to define a quantity which expresses the vagueness and complexity on the responses. Fuzzy numbers can be employed to represent the repeated responses. In this work, fuzzy modeling is performed by considering observed repeated response values as triangular fuzzy numbers in the case of the input values are crisp. Triangular fuzzy model parameters are estimated by using fuzzy least squares (FLS) method. The proposed fuzzy modeling approach is implemented on a data set defined in the literature.
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References
Bashiri M, Hosseininezhad SJ (2009) A fuzzy programming for optimizing multi response surface in Robust Designs. J Uncertain Syst 3:163–173
Diamond P (1988) Fuzzy least squares. Inf Sci 46:141–157
Hejazi TH, Bashiri M, Diaz-Garcia JA, Noghondarian K (2012) Optimization of probabilistic multiple response surfaces. Appl Math Modell 36:1275–1285
Khuri AI, Cornell M (1996) Response surfaces. Marcel Dekker, New York
Kim KJ, Lin DKJ (1998) Dual response surface optimization: a fuzzy modeling approach. J Qual Technol 30(1):1–10
Myers RH, Montgomery DC (2002) Response surface methodology: process and product optimization using designed experiments, 2nd edn. Wiley, New York
Pignatiello JJ (1993) Strategies for robust multiresponse quality engineering. IIE Trans 25:5–15
Shapiro AF (2005) Fuzzy regression models. ARC USA, pp 1–17
Türkşen Ö, Apaydın A (2012) Modeling and optimization of multi-response surface problems with fuzzy approach. Anadolu Univ J Sci Technol 13(1):65–79
Xu R, Dong Z (2006) Fuzzy modeling in response surface method for complex computer model based design optimization. In: Proceedings of the 2nd IEEE/ASME international conference on mechatronic and embedded systems and applications, pp 1–6
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
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Türkşen, Ö., Apaydın, A. (2014). A Modeling Approach Based on Fuzzy Least Squares Method for Multi-Response Experiments with Replicated Measures. In: Banerjee, S., Erçetin, Ş. (eds) Chaos, Complexity and Leadership 2012. Springer Proceedings in Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7362-2_19
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DOI: https://doi.org/10.1007/978-94-007-7362-2_19
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