ON THE GASTALDI – D’URSO FUZZY LINEAR REGRESSION

• Published in: Challenges of the Knowledge Society
• Main Authors: DANA-FLORENTA SIMION, DAN PETRU VASILIU, MIHAELA ILIESCU
• Format: Article
• Language: English
• Published: Nicolae Titulescu University Publishing House 2011-04-01
• Subjects: fuzzy linear regression; fuzzy metrics; Gastaldi - d’Urso equations; fuzzification; doubly linear adaptative fuzzy regression model.
• Online Access: http://cks.univnt.ro/uploads/cks_2011_articles/index.php?dir=02_economy%2F&download=cks_2011_economy_art_032.pdf

In the crisp regression models, the differences between observed values and calculates ones are suspected to be caused by random distributed errors, although these are due to observation errors and an unappropriate model structure. So, the fuzzy character of model prevails. The Fuzzy linear regression models (FLRM) are, roughly speaking, of two kinds: Fuzzy linear programming (FLP) based methods and Fuzzy least squares (FLS) methods. The FLP methods have been initiated by H.Tanaka (1982) and developed by H. Ishibuchi et al. The classical FLR model, Y=A0+A1X1+...+AkXk, has a explained Fuzzy triangular variable, Y, Fuzzy triangular coefficients {Aj} and crisp explanatory variables {Xj}: the parameters {Aj} of the model are estimated by minimizing the total indetermination of the model, so each data point lies within the limits of the response variable. In a large number of situations the prediction interval of the FLR model were much less than the interval obtained applying classical the Multiple linear regression model (see V.M. Kandala – 2002, 2003). However, this approach is somehow heuristic; on the other side, the LP model complexity overmuch increases as the number of data points increases. The FLS approach (P. Diamond; Miin-Shen Yang, Hsien-Hsiung Liu – 1988 et al) is an extension of the classical OLS method, using various metrics defined on the space of the fuzzy numbers. A significant number of recent works (McCauley- Bell (1999), J. deA. Sanchez and A. T. Gomez (2003) who used FLS to estimate the term structure of interest rates) deals with models with a fuzzy output, fuzzy coefficients and a crisp input vector. All the fuzzy components are symmetric triangular fuzzy numbers: the main idea of the method is to minimize the total support of the fuzzy coeficients. Sometimes, different restrictions occur. In our paper, we intend to build some examples for the P. d’Urso and T. Gastaldi models, that allow a comparative study on various options. (Pierpaolo d’Urso & Tommaso Gastaldi in: A least square approach to fuzzy linear regression, Comp. Stat. & Data Analysis 2000)