Word Count : 126

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Apply FCM with $m=2$. For two clusters the membership $u_{i1}=\dfrac{1}{1+(d_{i1}/d_{i2})^{2}}$ and $u_{i2}=1-u_{i1}$, where $d_{ik}=\|x_i-v_k\|$. Distances to $v_1=(5,5)$ and $v_2=(10,10)$: $x_1=(3,11):\ d_{1,1}=\sqrt{40}\approx6.3249,\ d_{1,2}=\sqrt{50}\approx7.0711\Rightarrow (d_{1,1}/d_{1,2})^2=0.8$ $\Rightarrow u_{1,1}=1/(1+0.8)=5/9\approx0.555556,\ u_{1,2}\approx0.444444.$ $x_2=(3,10):\ d_{2,1}=\sqrt{29}\approx5.3852,\ d_{2,2}=7\Rightarrow (d_{2,1}/d_{2,2})^2=29/49$ $\Rightarrow ___ _______ _______ _____ _____ __________ ______ ____.
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