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If a fuzzy set defined by: $[A=\frac{0.5}{x_{1}}+\frac{0.4}{x_{2}}+\frac{0.7}{x_{3}}+\frac{1}{x_{4}}]$ List all $\alpha$ cuts of set A
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written 3.5 years ago by
teamques10
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• modified 2.7 years ago |
Solution:
$\alpha$ - level sets:
$A_{\alpha =0.4}= \{x_1,x_2,x_3,x_4 \}\\ A_{\alpha =0.5}=\{ x_1,x_3,x_4 \}\\ A_{\alpha =0.7}=\{ x_3,x_4 \}\\ A_{\alpha =1}= \{x_4\} \\ $
strong $\alpha$ -level sets:
$A_{\alpha ^ {'} =0.4}= \{x_1,x_3,x_4 \}\\ A_{\alpha ^ {'} =0.5}=\{x_3,x_4 \}\\ A_{\alpha ^ {'} =0.7}=\{ x_4 \}\\ A_{\alpha ^ {'}=1}= \{ \}=\Phi $
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