A Multi-Depot Green Vehicle Routing Problem (MDGVRP) is considered in this paper. In MDGVRP, Alternative Fuel-powered Vehicles (AFVs) start from different depots, serve customers, and, at the end, return to the original depots. The limited fuel tank capacity of AFVs forces them to visit Alternative Fuel Stations (AFS) for refueling. The objective is to minimize the total carbon emissions. A Two-stage Ant Colony System (TSACS) is proposed to find a feasible and acceptable solution for this NP-hard (Non-deterministic polynomial-time) optimization problem. The distinct characteristic of the proposed TSACS is the use of two distinct types of ants for two different purposes. The first type of ant is used to assign customers to depots, while the second type of ant is used to find the routes. The solution for the MDGVRP is useful and beneficial for companies that employ AFVs to deal with the various inconveniences brought by the limited number of AFSs. The numerical experiments confirm the effectiveness of the proposed algorithms in this research.

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.