Search code examples
artificial-intelligencecluster-analysisdata-miningfuzzy

fuzzy clustering membership value calculation

for the following simple portion from my data-set , 

                                attributes 
States                     X1        X2       X3 .......      XM 
A                          10        15        0               1
B                           1        0         0               5
C                           0        0         5               2
etc ..

i have applied hierarchical clustering algorithm , and i found clusters for these data ,

My question Is how i can using fuzzy clustering membership function to define each state belong-ship to k clusters witch is fall [0,1]

for example : State A --> F(A)= 0.8 from cluster 1 and F(A)= 0.2 from cluster 2 ..etc any suggestion please ?

Solution

  • Firstly, fuzzy membership function result can't be directly categorized as a final result for fuzzy system. We still need implication process, defuzzification process, etc.

    but for this case, i think you didn't need to count a fuzzy membership function. You just can use a value of attributes in your new data input (vector data).
    For example, we can use CBR Method (Cased Based Reasoning) with fuzzy k-NN (k nearest neighbors). This algorithm will measuring the fit cluster for your new data simply using a 'distance'.

    First step, we measuring the distance between your new data with the members of each clusters.
    after that, we determine same 'k' numbers, and choose k lowest distance for each cluster and accumulated the chosen distances.
    So, each cluster will have one measurement distance with your new data input.
    The smallest distance cluster will be chosen as data's cluster category.

    For measuring distance you can use common formula like Euclidian Distance or Manhattan Distance. Here some example for f k-NN, i used Euclidian distance for this example : https://docs.google.com/spreadsheets/d/1HDdvKcYBvtihClr-QstdOC9LAtedSvqHdmzB9K2M9_A/edit?usp=sharing