On Fuzzy Least-squares Regression Analysis
The data used in regression analysis may be inexact or uncertain. Uncertainty of data comes from randomness and from fuzziness. Statistical regression has many applications. But problems can occur, for instance, if the data set is too small, or there is difficulty verifying distribution assumptions. The standard econometric estimation is used when both the independent and dependent variables are given as real numbers. However, in many real-life situations only fuzzy data is available. The statistical techniques can be extended to include ambiguity of events. Fuzzy linear regression is a modelling techniques based on fuzzy set theory. It is applied to different areas such as finance, business administration and so on. The regression model with fuzzy data has been treated from diffferent points of view. Models where the variables are fuzzy or models where the relation of the variables is fuzzy may be considered. Significant amount of research has been conducted on fuzzy regression models. One can consider models with fuzzy observations and crisp parameters, crisp observations and fuzzy parameters, fuzzy observations and fuzzy parameters, In this paper, we apply calculus of variations methods in fuzzy regression analysis. The fuzzy regression model is considered to be fuzzy outputs, fuzzy inputs and crisp parameters. In order to include fuzzy constant term into regression model, we solve the calculus of variations problem. The results show that the regression model with fuzzy constant term has better performance than the regression model with crisp constant term.