Rules formation method using fuzzy c means clustering method.

I want to know about tool that automatically genreate the rules on the basis of dataset with fuzzy c means clustering method .Please explain with any dataset to generate rules automatically .It is very urgent for my study .

Answer 1

[Sam Chak]

Hi @Mamta

Here is a simple example of automatically generating fuzzy rules from data using the FCM clustering method. The data is randomly generated. For more information, you can look up the 'genfis()' command. Please note that this method requires the Fuzzy Logic Toolbox.

Let me know if the proposed approach in the Answer is helpful.

%% Data with 2 inputs and 1 output
inputData       = [2*rand(100,1) 3*rand(100,1)-1.5];    % input data
outputData      =  5*rand(100,1);                       % output data

%% Generate fuzzy rules from data using FCM clustering
opt             = genfisOptions('FCMClustering', 'FISType', 'mamdani'); % set method & FIS type
opt.NumClusters = 'auto';   % set auto or specify a fixed number of FCM clusters
opt.Verbose     = 0;
fis             = genfis(inputData, outputData, opt);   % generate FIS from the data
showrule(fis)

ans = 9×83 char array
    '1. If (in1 is in1cluster1) and (in2 is in2cluster1) then (out1 is out1cluster1) (1)'
    '2. If (in1 is in1cluster2) and (in2 is in2cluster2) then (out1 is out1cluster2) (1)'
    '3. If (in1 is in1cluster3) and (in2 is in2cluster3) then (out1 is out1cluster3) (1)'
    '4. If (in1 is in1cluster4) and (in2 is in2cluster4) then (out1 is out1cluster4) (1)'
    '5. If (in1 is in1cluster5) and (in2 is in2cluster5) then (out1 is out1cluster5) (1)'
    '6. If (in1 is in1cluster6) and (in2 is in2cluster6) then (out1 is out1cluster6) (1)'
    '7. If (in1 is in1cluster7) and (in2 is in2cluster7) then (out1 is out1cluster7) (1)'
    '8. If (in1 is in1cluster8) and (in2 is in2cluster8) then (out1 is out1cluster8) (1)'
    '9. If (in1 is in1cluster9) and (in2 is in2cluster9) then (out1 is out1cluster9) (1)'

%% Plot data
figure
scatter3(inputData(:,1), inputData(:,2), outputData), grid on
xlabel("Input 1"), ylabel("Input 2"), zlabel("Output")

%% Plot membership functions
figure
[in1, mf1] = plotmf(fis, 'input', 1);
subplot(3,1,1), plot(in1, mf1), grid on 
xlabel('Membership Functions for Input 1'), ylabel('\mu')

[in2, mf2] = plotmf(fis, 'input', 2);
subplot(3,1,2), plot(in2, mf2), grid on 
xlabel('Membership Functions for Input 2'), ylabel('\mu')

[out, mf3] = plotmf(fis, 'output', 1);
subplot(3,1,3), plot(out, mf3), grid on 
xlabel('Membership Functions for Output'), ylabel('\mu')

[Mamta]

Thanks .

Could you make fuzzy inference system of this generated rules .Please also give detailed explaination like previous question.

[Mamta]

hello sir.I have 9 inputs and 1 output after using your method i got four cluster and 4 rules now my next step is making fuzzy inference system of these genreated rules . Please explain in detail .It will be greate help for my study.

[Sam Chak]

Hi @Mamta,

The 'fuzzy inference system' object is generated when the genfis() command is used, and the object is stored with the name 'fis' (not the file extension name) in my Answer above. To avoid confusion, I renamed the 'fuzzy inference system' object as 'MamtaFIS' in the code below.

To access the FIS file, you can open the app and load the fuzzy inference system using the syntax 'fuzzyLogicDesigner(MamtaFIS)' (but this feature is unavailable on this forum platform).

%% Data with 2 inputs and 1 output
inputData       = [2*rand(100,1) 3*rand(100,1)-1.5];    % input data
outputData      =  5*rand(100,1);                       % output data

%% Generate fuzzy rules from data using FCM clustering
opt             = genfisOptions('FCMClustering', 'FISType', 'mamdani'); % set method & FIS type
opt.NumClusters = 'auto';   % set auto or specify a fixed number of FCM clusters
opt.Verbose     = 0;
MamtaFIS        = genfis(inputData, outputData, opt)   % generate FIS from the data

MamtaFIS = 
  mamfis with properties:

                       Name: "mamdani21"
                  AndMethod: "min"
                   OrMethod: "max"
          ImplicationMethod: "min"
          AggregationMethod: "max"
      DefuzzificationMethod: "centroid"
    DisableStructuralChecks: 0
                     Inputs: [1×2 fisvar]
                    Outputs: [1×1 fisvar]
                      Rules: [1×12 fisrule]

	See 'getTunableSettings' method for parameter optimization.

%% Open the Fuzzy Logic Designer app and load the FIS object
fuzzyLogicDesigner(MamtaFIS)

[Mamta]

Thank you sir .

[Mamta]

Number of cluster centers of data set will decide the number of rules of fis ?

I have a paper in that dataset =424 ,input=3,output=1, after using fcm on 424 data set they got 27 cluster centers and according to cluster centers they are saying that they have 27 rules.

Please answer this.

[Mamta]

https://in.mathworks.com/help/fuzzy/mamfis.html

AddRules — Option for automatically adding rules

"allcombinations" (default) | "none"

Option for automatically adding rules, specified as one of the following:

• "allcombinations" — If both NumInputs and NumOutputs are greater than zero, create rules with antecedents that contain all input membership function combinations. Each rule consequent contains all the output variables and uses the first membership function of each output.

could you explain above underlined text i copied from above link.

i want to genreate all combination of rules .

i have 9 inputs (low , moderate, high) , one output (very low,low,moderate,high,very high)

how can i genreate all combinations of rules.

please answer also this question .

Answer 2

[Sam Chak]

Hi @Mamta

Your observation is correct. When employing the data clustering method, the fuzzy system (FIS) will have one fuzzy rule for each cluster, and each input and output variable will have one membership function per cluster. In the following example, I have set a fixed number of clusters.

%% Data with 2 inputs and 1 output
inputData       = [2*rand(100,1) 3*rand(100,1)-1.5];    % input data
outputData      =  5*rand(100,1);                       % output data

%% Generate fuzzy rules from data using FCM clustering
opt             = genfisOptions('FCMClustering', 'FISType', 'mamdani'); % set method & FIS type
opt.NumClusters = 3;   % set a fixed number of FCM clusters
opt.Verbose     = 0;
myFIS           = genfis(inputData, outputData, opt);   % generate FIS from the data
showrule(myFIS)

ans = 3×83 char array
    '1. If (in1 is in1cluster1) and (in2 is in2cluster1) then (out1 is out1cluster1) (1)'
    '2. If (in1 is in1cluster2) and (in2 is in2cluster2) then (out1 is out1cluster2) (1)'
    '3. If (in1 is in1cluster3) and (in2 is in2cluster3) then (out1 is out1cluster3) (1)'

%% Plot membership functions
figure
[in1, mf1] = plotmf(myFIS, 'input', 1);
subplot(3,1,1), plot(in1, mf1), grid on 
xlabel('Membership Functions for Input 1'), ylabel('\mu')

[in2, mf2] = plotmf(myFIS, 'input', 2);
subplot(3,1,2), plot(in2, mf2), grid on 
xlabel('Membership Functions for Input 2'), ylabel('\mu')

[out, mf3] = plotmf(myFIS, 'output', 1);
subplot(3,1,3), plot(out, mf3), grid on 
xlabel('Membership Functions for Output'), ylabel('\mu')

[Mamta]

In this input/output contains numeric data.

can we use string like low, medium, high in input/output dataset.

Please answer this.If yes please explain with example.

Answer 3

[Sam Chak]

Hi @Mamta,

Here is the 3rd answer at your request. If you want to generate rules with antecedents that contain all possible combinations of the input membership function, then you must use the Grid Partition method. However, this "non-clustering" method will produce only the Sugeno FIS, which, in my opinion, is more powerful than the classic Mamdani FIS.

Don't forget to vote for other answers as tokens of appreciation for providing explanations and guidance.

%% Data with 2 inputs and 1 output
inputData       = [2*rand(100,1) 3*rand(100,1)-1.5];    % input data
outputData      =  5*rand(100,1);                       % output data

%% Generate fuzzy rules from data using FCM clustering
opt             = genfisOptions('GridPartition');       % will create Sugeno FIS
opt.NumMembershipFunctions      = [3 3];                % specify number of MFs for each input
opt.InputMembershipFunctionType = "gaussmf";
myFIS           = genfis(inputData, outputData, opt);   % generate Sugeno FIS from the data
showrule(myFIS)

ans = 9×76 char array
    '1. If (input1 is in1mf1) and (input2 is in2mf1) then (output is out1mf1) (1)'
    '2. If (input1 is in1mf1) and (input2 is in2mf2) then (output is out1mf2) (1)'
    '3. If (input1 is in1mf1) and (input2 is in2mf3) then (output is out1mf3) (1)'
    '4. If (input1 is in1mf2) and (input2 is in2mf1) then (output is out1mf4) (1)'
    '5. If (input1 is in1mf2) and (input2 is in2mf2) then (output is out1mf5) (1)'
    '6. If (input1 is in1mf2) and (input2 is in2mf3) then (output is out1mf6) (1)'
    '7. If (input1 is in1mf3) and (input2 is in2mf1) then (output is out1mf7) (1)'
    '8. If (input1 is in1mf3) and (input2 is in2mf2) then (output is out1mf8) (1)'
    '9. If (input1 is in1mf3) and (input2 is in2mf3) then (output is out1mf9) (1)'

%% Plot membership functions
figure
[in1, mf1] = plotmf(myFIS, 'input', 1);
subplot(2,1,1), plot(in1, mf1), grid on 
xlabel('Membership Functions for Input 1'), ylabel('\mu')

[in2, mf2] = plotmf(myFIS, 'input', 2);
subplot(2,1,2), plot(in2, mf2), grid on 
xlabel('Membership Functions for Input 2'), ylabel('\mu')

Answer 4

[Sam Chak]

Hi @Mamta

Here is an example to demonstrate how to change the names of the membership functions to 'low,' 'med,' and 'high' for Input 1. Don't forget to vote on the Answer.

%% Data with 2 inputs and 1 output
inputData       = [2*rand(50,1) 3*rand(50,1)-1.5];      % input data
outputData      =  5*rand(50,1);                        % output data

%% Generate fuzzy rules from data using FCM clustering
opt             = genfisOptions('FCMClustering', 'FISType', 'mamdani'); % set method & FIS type
opt.NumClusters = 3;   % set auto or specify a fixed number of FCM clusters
opt.Verbose     = 0;
myFIS           = genfis(inputData, outputData, opt)    % generate FIS from the data

myFIS = 
  mamfis with properties:

                       Name: "mamdani21"
                  AndMethod: "min"
                   OrMethod: "max"
          ImplicationMethod: "min"
          AggregationMethod: "max"
      DefuzzificationMethod: "centroid"
    DisableStructuralChecks: 0
                     Inputs: [1×2 fisvar]
                    Outputs: [1×1 fisvar]
                      Rules: [1×3 fisrule]

	See 'getTunableSettings' method for parameter optimization.

%% genfis auto-assigned the names of the fuzzy sets as in1cluster1, in1cluster2, in1cluster3
plotmf(myFIS, 'input', 1)

%% Check the names of the fuzzy sets of Input 2
myFIS.Inputs(2).MembershipFunctions

ans = 
  1×3 fismf array with properties:

    Type
    Parameters
    Name

  Details:
             Name           Type           Parameters     
         _____________    _________    ___________________

    1    "in2cluster1"    "gaussmf"    0.52096    -0.18857
    2    "in2cluster2"    "gaussmf"    0.51323    0.090115
    3    "in2cluster3"    "gaussmf"    0.51528    -0.32533

%% The names of the fuzzy sets can be renamed using this syntax
myFIS.Inputs(1).MembershipFunctions(1).Name = "low";
myFIS.Inputs(1).MembershipFunctions(2).Name = "med";
myFIS.Inputs(1).MembershipFunctions(3).Name = "high";

plotmf(myFIS, 'input', 1)

[Mamta]

I just want to know what is the benefit to use fcm in mamdani fis.

second i have dataset of 430 after apply method it produce 4 cluster and 4 rules . i want to know that whole fis dependens only these 4 rules because i have 9 inputs three membership function if i manually write there can be more than 4 rules. very confusing please clear it .

[Mamta]

sir please explain about rules .after clustering got 4 rules and i am very confuse that whole system depends only these 4 rules .

should i enter manually all possible rules in rule base .

[Sam Chak]

Hi @Mamta

The benefit is that FCM allows for flexibility in the number of clusters to be formed, and therefore, rules can be generated for an arbitrary number of clusters. Regarding why it generated 4 rules, it is because the membership values obtained from FCM can be interpreted as the strength of association of a data point with different clusters. Something like "If the input is similar to cluster A, then the output is associated with class A."

The real question is, "Did the FCM produce a fairly accurate fuzzy system with only 4 rules to predict the input-output pair?" If it didn't, the data may exhibit a complex pattern that can be better captured by a varying number of clusters. Therefore, multiple runs with different initializations may be necessary.

If you want to manually enter all possible rules for 9 inputs of three membership functions for each input, then you will have to decide on the outputs of number of rules. How accurate it will be? That's another story.