基于效用值的模糊最短路问题的研究

模糊数学是研究和处理模糊现象的一种数学方法，而最短路径问题一直是运筹学、地理信息科学、计算机科学等学科的一个研究热点，被广泛地应用于交通运输、通讯工程、计算机网络和供应链管理等领域．模糊最短路问题的求解，实质就是比较模糊数的序关系，对模糊数进行排序，从而得出模糊最短路问题的结果．在基于对效用值的研究基础上，综合考虑了模糊数隶属函数的分布情况，得到一种新的三角模糊数和梯形模糊数的排序．并应用于求解模糊最短路问题，获得了求解模糊最短路问题的新算法．通过几个实例，验证了方法的有效性和实用性．

Research on the Fuzzy Shortest Path Problem Based on Utility Values

Fuzzy mathematics is a mathematical method to study and process the fuzzy phenomenon, but the shortest path problem, which is widely used in transport and communication trade, communicating engineering, computer network, and supply chain management, is always a hot topic for operational research, geographic information technology, computer science, etc. The substance of the shortest path problem is to compare the order relation. By arranging the order of the fuzzy number, the paper gives the result of the shortest path problem. In this paper, which based on the research of the utility value, a new ordering method of trigonometric fuzzy number and trapezium fuzzy number is presented under the condition of the arrangement of membership function of fuzzy number. This method would be applied to solve fuzzy shortest path problem, and a new algorithm is obtained for searching the fuzzy shortest path. The new algorithm is effective and feasible by means of calculating some examples.