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Table 7 the comparisons of different forms of \(Z\left( t \right)\)

From: Probabilistic linguistic fuzzy cognitive maps: applications to the critical factors affecting the health of rural older adults

Factors

\(Z(t) = 1 - t\)

\(Z(t) = \frac{1 - t}{{1 + t}}\)

\(Z(t) = 1 - te^{t - 1}\)

\(Z(t) = 1 - t^{2}\)

Similarity

Ranks

Similarity

Ranks

Similarity

Ranks

Similarity

Ranks

\(C_{1}\)

0.9234

9

0.8577

9

0.9696

9

0.9941

9

\(C_{2}\)

0.9212

10

0.8538

10

0.9686

10

0.9938

10

\(C_{3}\)

0.9551

4

0.9141

4

0.9827

4

0.9980

4

\(C_{4}\)

0.9318

6

0.8723

6

0.9731

6

0.9953

6

\(C_{5}\)

0.9557

3

0.9151

3

0.9829

3

0.9980

3

\(C_{6}\)

0.9067

11

0.8293

11

0.9623

11

0.9913

11

\(C_{7}\)

0.9246

8

0.8598

8

0.9701

8

0.9943

8

\(C_{8}\)

0.8915

12

0.8043

12

0.9555

12

0.9882

12

\(C_{9}\)

0.9560

2

0.9157

2

0.9831

2

0.9981

2

\(C_{10}\)

0.9823

1

0.9652

1

0.9934

1

0.9997

1

\(C_{11}\)

0.9308

7

0.8705

7

0.9727

7

0.9952

7

\(C_{12}\)

0.9419

5

0.8901

5

0.9773

5

0.9966

5