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

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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

written 3.9 years ago by

teamques10 ★ 69k

• modified 3.0 years ago

soft computing

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written 3.9 years ago by

teamques10 ★ 69k

• modified 3.0 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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