Keywords: prediction, fuzzy data, conventional regression analysis, fuzzy regression model.

Prediction is one of the most prevailing decision-making techniques in construction management. Conventional regression analysis is one of the widely recognized statistical tools by engineers to build a representative prediction equation from data collected for the entire population. The principle goal of the conventional regression analysis is to find a best fit mathematical model, so that a dependent variable can be forecast from independent variables. Essentially, ordinary regression analysis is used to handle numerical observed data rather than imprecise data or qualitative values. However, a great deal of observations, variables, and information associated with predicting and assessing casual interrelationships among the contributing inputs are often insufficient, imprecise or ambiguous. Also, when the collected data are insufficient which do not cover the entire information of interest, the experts' subjective measurement and opinion are often used as substitutes for unavailable data. For such data, ordinary regression analysis is not capable of coping with this problem.

Fuzzy regression analysis is more useful than ordinary regression analysis when imprecise data or human judgments are involved. A fuzzy regression model provides a promising means to tackle the problems arising from the existence of fuzzy data or fuzzy variables. Regression analysis on fuzzy data in dealing with fuzziness is called fuzzy regression analysis. A major difference between fuzzy regression and conventional regression is that the deviations between the observed values and the estimated values are assumed to depend on the vagueness of the parameters in fuzzy regression models rather on its measurement errors or randomness in ordinary regression techniques [2].

The fuzzy regression analysis was first introduced by Tanaka et al. [1], a number of developments and applications have been followed [3,4,5]. The fuzzy regression models can be classified in two classes: crisp inputs-fuzzy output and fuzzy inputs-fuzzy output. Most of fuzzy regression models are based on least-squares approaches such that regression coefficients are estimated by minimizing the error (or deviation) between the observed data and estimated values. The principle advantage of the least-squares approach is that the residual gives some idea of the accuracy of the estimated model.

This paper presented a least-squares approach to a crisp inputs-fuzzy output fuzzy linear regression model that can be used to analyze multiple variables. An illustrative example regarding the cost estimate for excavation construction was exemplified to demonstrate the capability of the model. The results show that this approach performs better than the conventional regression for the description fuzzy observed data or fuzzy independent variables.

1

Y.H. Chang, B.M. Ayyub, "Hybrid fuzzy regression analysis and its Applications: Uncertainty Modelling and Analysis in Civil Engineering", CRC Press Inc, 33-41, 1996.

2

Tanaka, H., Uejima, S., Asai, K., "Linear regression analysis with fuzzy models", IEEE Systems Trans. Systems Man Cybernet SMC-2(6), 903-907, 1982. doi:10.1109/TCS.1982.1085119

3

P. Diamond, "Fuzzy least squares", Inform. Sci., 46, 141-157, 1988. doi:10.1016/0020-0255(88)90047-3

4

X. Ruoning, C. Li, "Multidimensional least-squares fitting with a fuzzy model", Fuzzy Sets and Systems, 119, 215-223, 2001. doi:10.1016/S0165-0114(98)00350-9

5

M. Sakawa, H. Yano, "Multiobjective fuzzy linear regression analysis for fuzzy input-output data", Fuzzy Sets and Systems 47, 173-181, 1992. doi:10.1016/0165-0114(92)90175-4

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