Fuzzy Approximations with Non-symmetric Fuzzy Parameters in Fuzzy Regression Analysis

This paper proposes fuzzy regression analysis with non-symmetric fuzzy coefficients. By assuming non-symmetric triangular fuzzy coefficients and applying the quadratic programming formulation, the center of the obtained fuzzy regression model attains more central tendency compared to the one with symmetric triangular fuzzy coefficients. For a data set composed of crisp inputs-fuzzy outputs, two approximation models called an upper approximation model and a lower approximation model are considered as regression models. Thus, we also propose an integrated quadratic programming problem by which the upper approximation model always includes the lower approximation model at any threshold level under the assumption of the same centers in the two approximation models. Since non-symmetric fuzzy coefficients are assumed, we can obtain models with more reduced spreads as well as with more central tendency, compared to the ones with symmetric triangular fuzzy coefficients. Sensitivities of weight coefficients in the proposed quadratic programming approaches are investigated through real data.