Fuzzy Data Standardization

Abstract

Data standardization is a basic task in data analysis when several incommensurable criteria are involved. This paper discusses a data-standardization method for a set of fuzzy numbers that subtracts their minimum from the number to be standardized and divides the result by the difference between their maximum and minimum. Two approaches, i.e., membership grade and α-cut, are proposed, and associated models are developed based on the extension principle. Both models are nonlinear mathematical programs and, thus, to solve them directly, does not guarantee global optimal solutions. Since the feasible region of the program associated with the α-cut approach is an n-dimensional rectangular parallelepiped, a corner-point method is designed to find the solution. Because of the properties possessed by the standardization formula, the solution obtained from the corner-point method is guaranteed to be optimal. Two examples with different types of fuzzy number show the difficulties encountered to solve the nonlinear programs directly and demonstrate how to standardize fuzzy numbers by applying the corner-point method.