A new multiple attribute decision making method for selecting design schemes in sponge city construction with trapezoidal interval type-2 fuzzy information

Abstract

Selecting the most suitable design scheme in sponge city construction can be seen as a multiple attribute decision-making (MADM) problem. To express the uncertain and fuzzy decision-making information, interval type-2 fuzzy sets (IT2FSs) are useful tools. The paper focuses on decision making with trapezoidal interval type-2 fuzzy numbers (TIT2FNs) and discusses the evaluation of municipal road design schemes in sponge city construction. To do these, several operations on TIT2FNs based on Hamacher t-norm and t-conorm are first defined, where both the operations on the membership degree and on eight non-negative real values are considered. Then, two (2-additive) generalized Shapley trapezoidal interval type-2 fuzzy Hamacher Choquet integral operators are presented, which globally reflect interactions among elements. Considering the case where the decision-making weighting information is incomplete known, Manhattan distance measure-based models for obtaining the optimal fuzzy measure and 2-additive measure are constructed, respectively. Furthermore, an approach for trapezoidal interval type-2 fuzzy MADM is developed. Finally, a practical example is provided to illustrate the utilization of the new method, and comparison analysis is provided.