多目标随即加权模糊线性规划

表1　不同权重的计算结果

ω1,ω2

0.5,0.5

x

33

0.6,0.4(0.12896,0.04257)

0.8,0.2(0.14848,0.02694)(1.61950,0.63402)

(0.10652,0.07343)(1.43235,0.83357)

G

1.50475,0.69106)

31

ω2的　　从表1可以看出,随着ω1增大,x取值向单目标g(x)的最优解(0.16325,0)逼近,说明ω1、

大小确实代表了不同目标的不同重视程度。

3　结论

本文针对实际决策问题中经常碰到的资源量bi为随机变量且各个目标具有不同重要程度的情况,提出了多目标随机线性加权模糊规划模型,并用模糊集合理论把该模型转化为普通单目标线性规划问题。应用中可根据实际情况调整、确定权重,以适应不同的要求。

本模型有如下特点:

1)模型是单目标规划模型的推广;

2)如果约束条件有模糊性,可将约束条件模糊化;

3)对于利润系数cj或技术系数aij,但要复杂一些。

[参考文献]

[1]contrainedprogramming[J].ManagementScience,1959(6):73-79.

[2]Stancn-IM,WetsMJ.AResearchbibliographyinstochasticprogramming[J].OperationsResearch,1976

(24):1078-1119.

[3]BellmanRE,ZadehLA.Decisionmakinginafuzzyenvironment[J].ManagementScience,1970(17):141-146.[4]TongShaocheng.Intervalnumberandfuzzynumberlinearprogramming[J].FuzzySetsSystems,1994(66):301-306.[5]CarlessCh,FullerR.Fuzzymultiplecriteriadecisionmaking[J].FuzzySetsSystems,1996(78):139-153.

[6]CadenasJM,ingrankingfunctionsinmultiobjectivefuzzylinearprogramming[J].FuzzySetsSys2

tems,2000(111):47-53.

[7]MalekiHR,TataM,MashinchiM.Linearprogrammingwithfuzzyvariable[J].FuzzyandSystems,2000(109):21-33.

[8]刘德峰.多目标随机线性规划问题的模糊求解方法[J].应用数学与计算数学学报,1998,12(1):64-70.

Multi-objectiveWeightedFuzzyStochasticLinearProgramming

LIUTao,MENGXiao-yu

(DepartmentofMathematicsandPhysics,YunyangMedicalCollege,Shiyan,Hubei,442000,China)Abstract:Thispaperhasinvestigatedthemulti-objectivestochasticlinearprogrammingproblemswheretheresourcevalues,i.e.,onlyarerandomvariables,pointedthateveryobjectiveimportantdegreecommonlyisdifferent,builttheequivalentdeterministicweightedprogrammingmodelbasedonfuzzysettheoryformulti-objectivefuzzystochasticlinearprogramming.Casestudyshowsthatthemodelareefficientandhavesignifi2cantpracticalvalue.

Keywords:multi-objective;fuzzyset;stochasticlinearprogramming;weighted

71