Moreover , we proved that when the fuzzy decision is equal to 0 . 5 , the optimal solution to fuzzy linear programming can be obtained if the linear programming ( lo ) and ( la ) have identical optimal basic 从而导出,若线性规划( lo )和( l1 )有相同的最优基,模糊线性规划的最优解在模糊判决为= 0 . 5时达到。
Furthermore , the value of optimal solution are decided by the fuzzy decision a . at the same time : when the fuzzy linear programming is degenerate , results mentioned above still hold 而且最优解的值由所得的模糊判决决定。与此同时,本文还论证了:当模糊线性规划为退化情形时,上述模糊判决的结果依然成立。
This paper has four chapters . matrix form of the simplex method , the definition , properties and operation of fuzzy sets and the definition of fuzzy linear programming have been introduced in the first chapter 全篇共分为四章,第一章简单介绍了单纯形法的矩阵形式,模糊集的定义,性质和运算,给出了模糊线性规划的定义。
At last , a method to fuzzy linear programming with fuzzy constraints is presented , and it is illustrated that the conclusion of this paper are correct and this algorithm is more simplex algorithm by numerical example 最后给出了约束条件带有模糊性的模糊线性规划的相应解法,并用实例说明了本文结论的正确性与算法的简捷性。
In term of the difference in the form of fuzzinesss , fuzzy linear programming can be divided into two classes : one is that the objective function or constraints are uncertain , but their coefficients and constant belong to real numbers . the other is that at least one of the coefficients of the objective function and constraint are fuzzy numbers 根据模糊性出现形式的不同,把模糊线性规划分成两类:是目标函数或约束条件带有模糊关系,为非精确定义,但系数和常数为普通实数;是目标函数或约束条件的系数有一个或多个为模糊数。
Considering uncertainty of crude oils supplying , uncertainty of the capability and yield of equipments , uncertainty of the price of crude oils . the result is compared with the result found by pros vi . 5 , verifying the advantage and realizability of fuzzy linear programming . the model can be used to workout a short - term , middle - term , long - term production plan , also it can be modified to optimize stratagem programming with more uncertainties 建立了兰州炼油厂的生产计划模糊模型,该模型综合考虑了原油供给的不确定性、生产装置的生产负荷和收率分布的不确定性、原油价格的不确定性,并进行了求解,求解结果和申迪公司图形建模优化排产软件模型结果作了对比,证明模糊优化方法编制炼油厂生产计划的可实现性和优越性。
The paper also analysis the change of benefits and distribute of the water resources when we have different prices on yellow river water . in consideration of the short of yellow river , the paper presents the optimization decision variable , i . e . , the yellow river water volumes used for irrigation , by applying the tolerance approach of fuzzy linear programming 鉴于目前灌区已超计划用黄河水,将来无法实施充分灌溉的事实,本文对引黄可供水量进行了水资源模糊优化,并运用模糊线性规划容差法,给出了最大隶属度下的引黄水量最优决策方案。
In spite of different methods to a fuzzy optimal solution to the two classes of fuzzy linear programming , these methods have similar ideas : first is to fuzzify the objective function and constraints , i . e . , to display the definition of fuzzy membership function . second is to transfer the fuzzy linear programming into one general linear programming , based on the fuzzy decision , then we can obtain the fuzzy optimal solution by solving this linear programming 虽然求这两类模糊线性规划的模糊最优解的方法并不相同,但其思想具有相似性:首先是把目标函数或约束条件模糊化,给出他们的隶属函数的定义;然后给出模糊判决,在此基础上,规划最终都可化为求一个普通规划的解,这个解可看成模糊线性规划的模糊最优解。
Lastly , in the thesis the fuzzy linear programming with fuzzy variables is discussed . in practice , there are many problems in which all decision parameters are fuzzy numbers , and either possibilistic programming or multiobjective programming methods usually solves such problems . unfortunately , all these methods have shortcomings 实际上,在许多的数学规划问题中,所有决策变参量都为模糊数,对于此类问题通常采用可能性规划或多目标规划方法来解决,遗憾的是,所有这些方法均存在不足。
Traditional uncertain programming mainly contains stochastic programming and fuzzy programming , which have many applications in manufacture , economy and management etc . especially , the theory of stochastic or fuzzy linear programming is more complete , so it has more applications than stochastic or fuzzy nonlinear programming 传统的不确定规划主要分为两大类:随机规划和模糊规划,并且在生产、经济及管理等诸多方面已有广泛的应用,特别是随机线性规划和模糊线性规划理论较为完善,应用更加广泛。