Question
Asked May 20, 2019

1.6 Compute the scalar cardinality and the fuzzy cardinality for each of the
following fuzzy set.

c)C-Σ
te(x)-(x/(x +1)),
Hc(x)/x where
xe {0,1,2,
10}
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c)C-Σ te(x)-(x/(x +1)), Hc(x)/x where xe {0,1,2, 10}

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Expert Answer

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Step 1

The scalar cardinality of a fuzzy set is calculated using the formula:

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Step 2

The fuzzy cardinality of a fuzzy set can be calculated using the formula:

Where |A| is the size of fuzzy set and Aα is α-cut set.

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Step 3

For set A = {(x, 0.4), (y, 0.5), (z, 0.9), (w, 1)}

The scalar cardinality:

|A| = 0.4 + 0.5 + 0.9 + 1 = 2.8

The fuzzy cardinality:

For &...

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