Data of system parameters of real systems have some uncertainty and they should be given by sets (or intervals) rather than fixed values. To analyze and design systems contaning such uncertain parameters, it is required to represent and treat uncertainty in data of parameters, and to compute value sets of characteristic polynomials and transfer functions. Interval arithmetic is one of the most powerful tools to perform such subjects. In this paper, Polygon Interval Arithmetic (PIA) on the set of polygons in the complex plane is considered, and the data structure and algorithms to execute PIA efficiently is proposed. Moreover, practical examples are shown to demonstrate how PIA is useful to compute the evaluation of value sets.