Fuzzy Cluster Analysis Assignment Sample

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INTRODUCTION- FUZZY CLUSTER ANALYSIS

As per the analysis we see that the well # 30 has high membership in good and no membership in poor as the formulation quality is below in terms of thickness(feet) than the well #30 thickness measured (feet) for same porosity of 13%.

In fuzzy clustering we see that Any point x has a set of coefficients giving the degree of being in the kth cluster wk(x). With fuzzy c-means, the centroid of a cluster is the mean of all points, weighted by their degree of belonging to the cluster, or, mathematically,

Deviation is 109-105 = 4 feet thickness variation, and average membership is good So we measure the well thickness 109 of well# 30 with poor at 90ft and good at 115 ft

So points are A( 8,90) = POOR

B(16,115) = GOOD

Point ( 13, 109) is well# 30 point of ( porosity%, thickness(ft))

Distance is measured between point and A and point and B

Distance measured between poor and average =

= 5

Distance is measured between average and good

BC =

= 29.5

We see that the distance is more between the good and average well # 27 so this means they poses a lower membership between the porosity and thickness measurements for the wells

Well name

Porosity(%)

Thickness (ft)

Well#23

7

95

Well#24

12

90

Well#25

10

120

Well#26

18

110

Well#27

8

100

Well#28

15

85

Well#29

9

114

Well#30

13

109

Well#31

17

98

Well#32

14

104

Formation Quality

Formation Quality

Poor

8

90

 

Average

13

105

 

Good

16

115

 
       

Total number of clusters

3

Plots shows the deviation of the porosity along x axis and thickness in feet along y axis deviated from poor, average and good formulation resonating quality measured and variation is measured by finding distances and seeing lower ones has higher membership than higher distance measured values

Below are the conclusions made as follows as per the fuzzy cluster analysis made using the porosity and thickness measurements for 10 different well #’s

Well # 23 has membership only in formulation quality of Poor

Well# 27 has membership in poor and average and also in good formulation quality

Well #32 is partially good, partially average and partially good as formulation quality has no exact well found

 
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