1991 Volume 2 Issue 3 Pages 265-274
Linear regression analysis based on the theory of probability is used for modeling the relations between multi-variable data. On the other hand, fuzzy linear regression analysis with fuzzy numbers as coefficients of the linear system is proposed to analyze ambiguous relations between various factors affecting the question. By using the fuzzy linear regression analysis, degree of ambiguity of relation between input and output variables can be estimated from the fuzzy regression coefficients. Estimated fuzzy output is expressed as a mean value, and the probable range of the output depends on the value of input data.
In this paper, we propose two applications of the fuzzy regression analysis, i. e., fuzzy multivariateregression model and fuzzy contouring, to examine the potential of fuzzy theory in analysis of subsurface structure. Fuzzy multivariate regression model was applied to the analysis of the relation between variations of ground-water level and precipitation at four observation wells in the Kumamoto plain. For each well, the relative vagueness of correlation between variants was quantified, and the fluctuation model of the ground-water level was constructed. Fuzzy contouring, which fundamentally consists of a polynomial expression, is proposed in order to interpolate values between irregularly distributed data with different populations. As an example, this method is applied to interpolate the supposed N values of data at the same depth in subsurface ground occupied by gravels or by clay. It is clearly shown on the contour maps of N values for the mean values and probable ranges that the probable ranges of N values in the area near to the lithologic boundary are larger than those in other areas of the same soil.
