一般梯形模糊逼近算子及其在模糊运输问题中的应用  

A generalized trapezoidal approximation operator and its application to fuzzy transportation problems

作　　者：谢海斌[1] 陈迪三[1] 梁燕燕[1] 

机构地区：[1]广西师范大学漓江学院理工系,广西桂林541006

出　　处：《运筹学学报》2017年第1期65-77,共13页Operations Research Transactions

基　　金：2016年度广西高校中青年教师基础能力提升项目(No.KY2016LX555);2014年广西师范大学漓江学院科研项目(No.201410B)

摘　　要：研究运输成本信息为一般模糊数的模糊运输问题.首先,在保持一般模糊数的核不变的条件下,建立一般模糊数与一般梯形模糊数的距离最小优化模型,通过求解模型得到一般模糊数的一般梯形模糊逼近算子,并给出该逼近算子具有的性质如数乘不变性、平移不变性、连续性等.然后利用该逼近算子将一般模糊运输信息表转换成一般梯形模糊运输信息表,再根据已有GFLCM和GFMDM算法得到模糊运输问题的近似最优解,最后给出具体算例分析说明方法的有效性和合理性.This paper studies fuzzy transportation problems with general fuzzy trans- portation costs. Firstly, by preserving the core of a generalized fuzzy number, the minimal optimization model is structured based on the distance between general fuzzy numbers and general trapezoidal fuzzy numbers. By solving the optimization model, a generalized trapezoidal approximation operator is obtained and some properties of the operator axe studied such as scale invaxiance, translation invaxiance, continuity. Secondly, the approx- imation operator is used to convert generalized fuzzy transportation table to generalized trapezoidal fuzzy transportation table. Moreover, the existing GFLCM and GFMDM algorithms are used to get the nearest optimal solution of fuzzy transportation problems. Finally, a numerical example is presented to illustrate the feasibility and validity of the proposed method.

关 键 词：一般模糊数 一般梯形模糊数 逼近算子 运输成本 

分 类 号：O221[理学—运筹学与控制论]