基于双论域粗糙集的快捷货物运输方案选择

针对多种不确定因素下的快捷货物运输方案决策问题，提出一种基于双论域直觉模糊粗糙集的快捷货物运输方案决策模型与决策规则。依据双论域直觉模糊粗糙集理论来确定快捷货物运输方案决策的双论域模糊近似空间。将固定成本、运输成本、转运成本、碳排放、转运时间等评价指标的消耗程度视为直觉模糊数，利用评价指标与运输方案之间的直觉模糊关系计算求得下近似集与上近似集，并引入最大直觉性指标及海明贴近度得出运输方案决策规则。以兰州至北京的一条快捷货物运输线路为例，依据决策规则从公路、普铁、航空组合出的9种运输方式中选择出最优运输方案。对运输成本、转运成本进行灵敏度分析以验证结果的准确性。最终选择出的两种最优运输方案表明了双论域直觉模糊粗糙集在此类问题上的适用性。

Selection of express freight transportation schemes based on rough set over two universes

Aiming at the problem of express freight scheme decision under multiple uncertain factors, the express freight scheme decision model and decision rule based on intuitionistic fuzzy rough set over two universes were proposed. Based on the intuitionistic fuzzy rough set theory over two universes, a fuzzy approximate space over two universes for express freight scheme decision was determined. The consumption degrees of fixed cost, transportation cost, transfer cost, carbon emission, transfer time and other transportation indices were regarded as intuitionistic fuzzy numbers, and the intuitionistic fuzzy relation between evaluation indices and transportation schemes were used to calculate the lower approximation set and upper approximation set, and the maximum intuitionistic index and Hamming closeness degree were introduced to determine the transportation scheme decision rules. Taking an express freight transportation line from Lanzhou to Beijing as the example, the optimal transportation scheme was selected from the 9 modes of transportation combined by road, ordinary speed railway and air according to the decision rules. Sensitivity analysis of transportation cost and transfer cost was performed to verify the accuracy of the results. The two optimal transportation schemes finally selected show the applicability of the intuitionistic fuzzy rough set over two universes on such problems.