1 Possibilistic Regression in False-Twist Texturing S.M. TAHERI*, H. TAVANAI+, M. NASIRI+ *School of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156, IRAN (corresponding author), [email protected]+Department of Textile Engineering, Isfahan University of Technology, Isfahan 84156, IRAN Abstract: - A possibilistic linear regression, i.e. a linear regression with possibilistic coefficients, is explained. The application of such possibilistic regression method for modeling of twist liveliness of false twist textured nylon yarns as a function of percentage retraction has been studied, based on a few available data. It turns out that possibilistic regression method is superior to conventional statistical regression, when a very small number of observations are available. In such cases the basic assumptions, under which statistical regression analysis is valid, can not be investigated. Based on some criterions, such as the total vagueness of models and the mean of predictive capabilities, the optimum fuzzy model has been derived. Key-Words: - Possibilistic regression, Texturing, Predictive capability 1 Introduction and Background Statistical regression analysis is a widely used statistical tool to model the relationship among variables to describe and/or predict the phenomena. Statistical regression is useful in a non-vague environment where the relationship among variables is sharply defined. On the other hand, fuzzy regression analysis may be used wherever a relationship among variables is imprecise and/or data are inaccurate and/or the sample size is insufficient. In such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis. Fuzzy regression, for the first time, was introduced and investigated by Tanaka et al. in 1982 [10]. They, especially, considered the linear regression model with fuzzy coefficients, and used linear programming techniques to develop a model superficially resembling linear regression. (A survey about fuzzy regression can be found in [9]). As mentioned above, one of the application of fuzzy regression approaches is the cases in which only a small amount of data is available. It should be mentioned that classical statistical regression makes rigid assumptions about the statistical properties of the model; e.g., the normality of error terms and the independence of such errors [6]. These assumptions, as well as, the aptness of the model, are difficult to justify unless a sufficiently large data set is available. The violation of such basic assumptions could adversely affect the validity and performance of statistical regression analysis. Alternatively, in such cases, fuzzy regression analysis can be a useful tool [2]. After introducing and developing fuzzy set theory, many attempts have been made to use and apply this theory in textile researches. For example, Raheel and Liu used fuzzy comprehensive evaluation technique to predict fabric hand [8]. Fuzzy cluster analysis was used by Pan for fabric handle sorting [7]. Kokot and Jermini used fuzzy clustering for estimating cotton damage when treated with electro generated oxygen at different temperatures [4]. Mujionemi and Mantysalo tried to model the relationship between the dye absorption and dye concentration in dyeing leather with two dyestuffs by ANFIS [5], (see also [14]). Tavanai et al. [13] investigated a fuzzy regression approach for modeling of colour yield in polyethylene terepthalate dyeing. Proceedings of the 6th WSEAS Int. Conf. on Systems Theory & Scientific Computation, Elounda, Greece, August 21-23, 2006 (pp202-207)
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Possibilistic Regression in False-Twist Texturing
S.M. TAHERI*, H. TAVANAI+, M. NASIRI+
*School of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156, IRAN (corresponding author), [email protected]
+Department of Textile Engineering, Isfahan University of Technology, Isfahan 84156, IRAN
Abstract: - A possibilistic linear regression, i.e. a linear regression with possibilistic coefficients, is explained.
The application of such possibilistic regression method for modeling of twist liveliness of false twist textured
nylon yarns as a function of percentage retraction has been studied, based on a few available data.
It turns out that possibilistic regression method is superior to conventional statistical regression, when a very
small number of observations are available. In such cases the basic assumptions, under which statistical
regression analysis is valid, can not be investigated. Based on some criterions, such as the total vagueness of
models and the mean of predictive capabilities, the optimum fuzzy model has been derived.