An Extended TOPSIS Method Based on Gaussian Interval Type-2 Fuzzy Set

Abstract

Compared with trapezoidal interval type-2 fuzzy set (IT2 FS), Gaussian IT2 FS is more concise in representation and can meanwhile capture sufficient uncertainties. Therefore, in this paper the Gaussian IT2 FS is used to model words in multi-attribute decision-making (MADM) process and a comprehensive method is developed under the Gaussian IT2 FS environment. Firstly, a new type of Gaussian IT2 FS is proposed and the ranking rule is constructed to determine the ideal solutions. Secondly, the Euclidean distance is extended to Gaussian IT2 FS to measure the difference between alternatives and ideal solutions. Further, a complete MADM method is established under the framework of TOPSIS (technique for order preference by similarity to an ideal solution). In the end, the effectiveness of the proposed method is illustrated by an investment decision-making example.