Introduction

The fcmTFN function extends the fuzzy c-means algorithm to handle ordinal data through a triangular fuzzy number (TFN) representation.

Example Dataset

data(sim_likert7)

head(sim_likert7)
#>   Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12
#> 1  2  2  3  2  2  3  2  1  2   2   2   2
#> 2  2  2  2  3  2  1  2  2  2   2   2   2
#> 3  2  1  2  2  2  3  2  2  2   2   2   2
#> 4  2  2  2  2  2  2  1  3  2   2   2   2
#> 5  2  2  2  2  2  3  2  3  1   2   2   2
#> 6  2  2  2  2  2  2  2  2  2   3   2   1

Running the Clustering Algorithm

result <- fcmTFN(
  data = sim_likert7,
  option = "B",
  k_values = 2:6
)
#> Running k = 2 
#> Running k = 3 
#> Running k = 4 
#> Running k = 5 
#> Running k = 6

summary(result)
#> 
#> Fuzzy C-Means Clustering for TFN
#> ---------------------------------
#> 
#> Optimal number of clusters (k):  3 
#> 
#> Weights:
#> wc = 0.61997 
#> ws = 0.38003 
#> 
#> Iterations: 11 
#> 
#> Scale configuration:
#> Type   : symmetric 
#> Option : B 
#> 
#> Xie-Beni values:
#> k = 2 : 0.067732 
#> k = 3 : 0.044298 
#> k = 4 : 4.477249e+14 
#> k = 5 : 4.077275e+15 
#> k = 6 : 3.137093e+15

Cluster Assignment

clusters <- cluster_assignment(result)

table(clusters)
#> clusters
#>   1   2   3 
#> 100 100 100

Cluster Quality

Prototype Interpretation

prototype_results(result, format = "table")
#> $Cluster_1
#>           l     c     r
#> Var1  3.007 4.007 5.007
#> Var2  3.061 4.061 5.060
#> Var3  2.970 3.970 4.969
#> Var4  3.008 4.008 5.007
#> Var5  3.062 4.061 5.061
#> Var6  3.006 4.006 5.006
#> Var7  2.972 3.972 4.971
#> Var8  3.028 4.027 5.027
#> Var9  2.993 3.993 4.992
#> Var10 3.006 4.006 5.005
#> Var11 3.005 4.005 5.005
#> Var12 2.971 3.970 4.970
#> 
#> $Cluster_2
#>           l     c     r
#> Var1  1.081 2.022 3.022
#> Var2  1.133 2.038 3.038
#> Var3  1.140 2.023 3.023
#> Var4  1.081 1.952 2.952
#> Var5  1.102 1.976 2.976
#> Var6  1.113 1.997 2.997
#> Var7  1.110 2.041 3.041
#> Var8  1.102 1.933 2.933
#> Var9  1.093 2.034 3.034
#> Var10 1.071 1.995 2.995
#> Var11 1.113 2.046 3.045
#> Var12 1.152 2.044 3.044
#> 
#> $Cluster_3
#>           l     c     r
#> Var1  4.969 5.969 6.851
#> Var2  5.060 6.060 6.930
#> Var3  5.060 6.060 6.912
#> Var4  5.030 6.030 6.909
#> Var5  4.957 5.957 6.918
#> Var6  4.945 5.945 6.859
#> Var7  5.018 6.018 6.881
#> Var8  5.029 6.029 6.930
#> Var9  4.989 5.989 6.881
#> Var10 4.989 5.989 6.891
#> Var11 4.994 5.994 6.898
#> Var12 4.985 5.985 6.888

plot_prototypes(result, view = "global")

Xie-Beni Index Visualization

plot_xb(result)

Conclusion

This vignette demonstrated the basic workflow for fuzzy clustering of ordinal data using the fcmTFN function from the fcmfd package.

Introduction to fcmTFN