Fuzzy regression provides a means for fitting data when the relationship between the independent and dependent variables is vague, or data are imprecise, or the amount of data is insufficient. In this paper, we use it to determine the three parameters of the Archie equation from core resistivity measurements. First, we outline the methodology of fuzzy regression analysis. Next, we show the minimization of a fuzzy objective function by making use of the simplex method described in the previous paper. Last, we illustrate the approach with the same example used in the previous paper.
In the previous paper, we demonstrated that the Archie parameters may be obtained directly by the application of the simplex method. In the present paper, we go back to the least-squares regression approach but with a new twist. That is, in the classical regression model, deviations between the measured and estimated values are assumed to be solely due to measurement errors; however, in fuzzy regression, we regard these deviations as arising from the fuzziness of the parameters of the model.