Interpolative model for fuzzy arithmetic

Standard model of fuzzy computations is based on extension principle. It is known to work well, in practice, only for continuous fuzzy numbers, while producing unintuitive results when one or more arguments are discrete. It is also computationally cumbersome for all but linear operations. Another model was proposed for trapezoidal numbers only. Its operations amount to computing on the four vertices of the trapezoids, and then spanning a new trapezoid on the four resulting vertices. It is efficient, but produces fairly crude approximations for curvilinear fuzzy numbers; moreover, it is not applicable when discrete arguments are present. A model based on approximating fuzzy numbers, whether continuous or discrete, by multitrapezoidal curves and then performing coordinate-wise computations was proposed first by Ramer. It was applied to economical decision problems by his doctoral student James Wang. In this paper we place this computational method in context of fuzzy interpolations. We show how interpolation can bring quite disparate argument into a standardized form, thus permitting for efficient computations and avoid unintuitive results. Here we use the model of multiple trapezoids, but other classes of curves can be considered