Evolutionary Computation of the Generalized Hesitant Fuzzy Envelopment Analysis and Its Application in the Contractor Selection of Green Building Project

The evaluation presentation and numerical weight are two key factors that can affect final results in a decision-making process. In this article, we introduce the hesitant fuzzy set and the envelopment rate calculation to address these two issues respectively. Unlike the previous decision-making approaches, the newly proposed methods in this article focus on mutual influence relationships of all alternatives and make decisions by achieving the Pareto optimality. To do this, we first define the mutual hesitant fuzzy envelopment rate (MHFER) and then propose the generalized hesitant fuzzy envelopment analysis method and its two desired properties. Based on this, we develop an evolutionary computation by introducing the ideas of cooperative equilibrium and achieving the Pareto optimality of the whole decision-making process from a global perspective. After that, we further improve the evolutionary computation by fusing some inequality constraints to make the calculated MHFERs distinguishable. Then, the modeling steps and the pseudocode algorithm of the evolutionary computation are provided for an understanding of the proposed methods. Also, the computational convergence is proven, which shows the feasibility and effectiveness of the above methods. Finally, we present an example to select a suitable contractor for a green building project and it fully demonstrates the application of the proposed models. Moreover, the comparison calculations and further analysis are also provided.