模糊统计试验

1、模糊统计试验模糊数学是近十几年来发展很迅速的一个数学分支， 模糊集合是隶属函数描述的，以隶属函数建立了模糊集合论。因此隶属函数的确定在模糊数学的应用中占有极为重要的地位。怎样确定隶属函数 u u是一个关键的问题，本实验通过模糊统计实验来确定隶属函数，而且只能建立近似的隶属函数是否符合实际直接影响效果的好坏。在本实验中，我们还对模糊统计加以改进，提出了更切实际的模糊统计算法。1.实验目的(1)(1)掌握模糊统计方法。设在模糊统计试验中，样本空间为 n,n,计算u 对 A 的隶属频率=u-A的次数(1)(1)n随着 n n 的增大，隶属频率会呈现出稳定，称之为隶属频率的稳定性。(2)(2)学习利用

2、模糊统计方法确定“青年人”这一模糊集的隶属函数。这个稳定的数称为 u u 的隶属度。由此来我们来确定隶属函数。(3)(3)学习利用 MATLABMATLAB 软件实现确定“青年人”隶属函数的模型。(4)(4)学习改进的模糊统计，得到更切实际的隶属函数。2.实验内容以人的年龄作为论域U=0,100】。随机抽取 129129 个大学生，在独立认真考虑“青年人”的含义之后，给出各自的答案，形成 129129 个“青年人”的年龄段关于青年人调查表18-2517-3017-2818-2516-3514-2518-3018-3518-3516-25153018-3517-3518-2518-3518-25

3、20-3018-3016-3020-35183018-3015-2528-3015-2816-2828-3018-3016-3018-3518-2518-2516-2818-3016-3016-2818-3518-3517-2716-2815-2816-3019-2815-3015-2617-2515-3618-3017-3018-3516-3515-2515-2518-2816-3015-2818-3518-3017-2818-3515-2818-3015-2515-2518-3016-2415-2516-3215-2718-3516-2518-2816-2818-3018-3518-301

4、8-3017-3018-3018-3516-3018-3517-2515-3018-2517-3014-2518-2618-2918-3518-2818-3018-2516-3517-2918-2517-3016-2818-3016-2815-3015-3515-3020-3020-3016-2517-3015-301-83016-3018-2818-3516-3015-3018-3518-3518-3017-3016-3517-3015-2518-3515-3015-2515-3018-3017-2518-2918-28根据上述统计的数据，建立“青年人”这一模糊集合的隶属函数,并绘制模糊统计

5、频率图3实验方法3.13.1 问题的分析本实验为利用模糊统计的方法来确定“青年人”的隶属函数。在确定“青年人”的隶属函数的实验中，年龄的论域取为U=b,i00，需要确定 U U 的每一个年龄 u u 隶属于 M M 的程度。实验时，每次明确 M M 的一个区间，一些区间可能不包含 u,u,最后可用实验中得到的包含 u u 的区间数除总实验次数作为 u u的隶属于 M M 的程度。这样就得到各个年龄的隶属度，根据隶属度画出这个隶属函数的图像。通过上述模糊统计方法描出“青年人”这一模糊集隶属函数的大致曲线，将它与常见的模糊分布曲线比较，选择最接近的一个，再根据实际确定符合实际的参数。这样，就很容易

6、的写出隶属函数的表达式。3.23.2 模型求解3.2.13.2.1 MATLABMATLAB 程序functionvarargout=FuzzyMath(varargin)%FUZZYMATHMATLABcodeforFuzzyMath.fig%FUZZYMATH,byitself,createsanewFUZZYMATHorraisestheexisting%singleton*.%H=FUZZYMATHreturnsthehandletoanewFUZZYMATHorthehandleto%theexistingsingleton*.%FUZZYMATH(CALLBACK,hObject,

7、eventData,handles,.)callsthelocal%functionnamedCALLBACKinFUZZYMATH.Mwiththegiveninputarguments.%FUZZYMATH(Property,Value,.)createsanewFUZZYMATHorraisesthe%existingsingleton*.Startingfromtheleft,propertyvaluepairsare%appliedtotheGUIbeforeFuzzyMath_OpeningFcngetscalled.An%unrecognizedpropertynameorinv

8、alidvaluemakespropertyapplication%stop.AllinputsarepassedtoFuzzyMath_OpeningFcnviavarargin.%*SeeGUIOptionsonGUIDEsToolsmenu.ChooseGUIallowsonlyone%instancetorun(singleton).%Seealso:GUIDE,GUIDATA,GUIHANDLES%EdittheabovetexttomodifytheresponsetohelpFuzzyMath%LastModifiedbyGUIDEv2.525-Nov-201322:31:02%

9、Begininitializationcode-DONOTEDITgui_Singleton=1;gui_State=struct(gui_Singletongui_OpeningFcngui_OutputFcngui_LayoutFcngui_Callbackgui_Namemfilename,gui_Singleton,.,FuzzyMath_OpeningFcn,FuzzyMath_OutputFcn,，口，.,);ifnargin&ischar(varargin1)gui_State.gui_Callback=str2func(varargin1);endifnargoutva

10、rargout1:nargout=gui_mainfcn(gui_State,varargin:);elsegui_mainfcn(gui_State,varargin:);end%Endinitializationcode-DONOTEDIT%-ExecutesjustbeforeFuzzyMathismadevisible.functionFuzzyMath_OpeningFcn(hObject,eventdata,handles,varargin)%Thisfunctionhasnooutputargs,seeOutputFcn.%hObjecthandletofigure%eventd

11、atareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%varargincommandlineargumentstoFuzzyMath(seeVARARGIN)%ChoosedefaultcommandlineoutputforFuzzyMathhandles.output=hObject;%Updatehandlesstructureguidata(hObject,handles);%UIWAITmakesFuzzyMathwaitforuserres

12、ponse(seeUIRESUME)%uiwait(handles.figure1);%-Outputsfromthisfunctionarereturnedtothecommandline.functionvarargout=FuzzyMath_OutputFcn(hObject,eventdata,handles)%varargoutcellarrayforreturningoutputargs(seeVARARGOUT);%hObjecthandletofigure%eventdatareserved-tobedefinedinafutureversionofMATLAB%handles

13、structurewithhandlesanduserdata(seeGUIDATA)%Getdefaultcommandlineoutputfromhandlesstructurevarargout1=handles.output;functionedit1_Callback(hObject,eventdata,handles)%hObjecthandletoedit1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA

14、)%Hints:get(hObject,String)returnscontentsofedit1astext%str2double(get(hObject,String)returnscontentsofedit1asadoubleinput=str2num(get(hObject,String);if(isempty(input)set(hObject,String,0)endguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.functionedit1_CreateFcn(hO

15、bject,eventdata,handles)%hObjecthandletoedit1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,def

16、aultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit2_Callback(hObject,eventdata,handles)%hObjecthandletoedit2(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit2a

17、stext%str2double(get(hObject,String)returnscontentsofedit2asadoubleinput=str2num(get(hObject,String);if(isempty(input)set(hObject,String,0)endguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.functionedit2_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit2(seeG

18、CBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcns%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)calledset(hObject,Backgroun

19、dColor,white);end%-Executesonbuttonpressinpushbutton1.functionpushbutton1_Callback(hObject,eventdata,handles)%hObjecthandletopushbutton1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)ax=get(handles.edit1,String);bx=get(handles.edit2,

20、String);a=str2num(ax);b=str2num(bx);data=get(handles.uitable1,data);globalflg;globalda;data(flg+1,:)=a,b;set(handles.uitable1,data,data);flg=flg+1;da=data;guidata(hObject,handles);%-Executesonbuttonpressinpushbutton2.functionpushbutton2_Callback(hObject,eventdata,handles)%hObjecthandletopushbutton2(

21、seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)globalflg;globalda;flg=0;functionedit3_Callback(hObject,eventdata,handles)%hObjecthandletoedit3(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesa

22、nduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit3astext%str2double(get(hObject,String)returnscontentsofedit3asadoubleinput=str2num(get(hObject,String);if(isempty(input)set(hObject,String,0)endguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.funct

23、ionedit3_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit3(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcns%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundC

24、olor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);end%-Executesonbuttonpressinpushbutton3.functionpushbutton3_Callback(hObject,eventdata,handles)%hObjecthandletopushbuttons(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserd

25、ata(seeGUIDATA)globalda;da1=cell2mat(da);da1=da1;y1y2=size(da1);w=get(handles.edit3,String);ww=str2num(w);Ax=0;forj=1:y2if(ww=da1(1,j)&ww=da1(2,j)Ax=Ax+1;endendAx=Ax/y2;ax=num2str(Ax);set(handles.text8,String,ax);guidata(hObject,handles);functionpushbutton6_Callback(hObject,eventdata,handles)%hO

26、bjecthandletopushbutton6(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)globalda;da1=cell2mat(da);da1=da1;y1y2=size(da1);A1=da1(1,1);A2=da1(1,1);fori=1:1:y2if(da1(1,i)A2)A2=da1(2,i);endendx=1:(A2-A1)/100:100;Ax=;fori=1:1:length(x)calledAx(i)=0;forj=1:y2if(x(i)=da1(1,j)&x(i)=da1(2,j)Ax(i)=Ax(i)+1;endendAx(i)=Ax(i)/y2;endplot(x,Ax)axe