The development of prediction models for simultaneously using quantitative and qualitative data to forecast or explain the variance of a criterion variable is an intricate problem. The principles and applications of regression models exist in the literature [1]. However, the design and implementation of fuzzy regression models for coalescing continuous and discrete independent variables are not straightforward. In particular, it is difficult to meaningfully interpret the predicted results derived from fuzzy regression and fuzzy inferential models.

Alex presents a fuzzy regression model (FRM) for merging real-value and categorical variables as predictors of a real-interval criterion variable. The FRM differentiates the set of all fuzzy sets on a group of sampling points in the universe of discussion, and then uses membership functions to hazily categorize each sampling point to a fuzzy subset. The author introduces the principle of degree of maximal membership for fuzzy regression, and for untangling the predicted outcomes. The paper outlines a FRM that operates on groups of sample points, and a fuzzy inference model (FIM) containing the expert rules for combining quantitative and qualitative data in prediction equations.

The relationships between FRM and FIM are exhibited in a forecast of the costs of prefabricated Japanese houses, using rank of housing material, first floor space, second floor space, number of rooms, and the number of Japanese-style rooms as predictors. Three expert rules were used to classify the prices of the houses as low, medium, and high (depending on the housing material’s rank, floor spaces, and number of Japanese-style rooms). The membership functions derived for the three fuzzy categories of the prices and three fuzzy clusters of the house sizes were used to establish a fuzzy regression-inference equation. The experimental results showed significant improvement for the joint FRM and FIM over the simple FRM alone.

This paper indisputably reveals FRM and FIM as open research areas with several appealing computational and interpretative challenges. In particular, the generalized approval of the combined FRM and FIM is at stake. This is due to its heavy reliance on expert rules, and the incongruent procedures for combining the mixture of dissimilarly scaled continuous and discrete predictors in alternative regression applications.