Table 7 Comparison of relative similarity grades.

From: A strategic decision-making framework for evaluating barriers to green supply chain management using fractional fuzzy similarity measures

Similarity measures in different structures

Relative grades

Ranking order

\(\:{\varvec{\uprho\:}}_{1}\)

\(\:{\varvec{\uprho\:}}_{2}\)

\(\:{\varvec{\uprho\:}}_{3}\)

\(\:{\varvec{\uprho\:}}_{4}\)

\(\:{\varvec{\uprho\:}}_{5}\)

\(\:{\varvec{\uprho\:}}_{6}\)

Wei52

0.2153

0.1939

0.2004

0.2674

0.2842

0.2932

\(\:{{\uprho\:}}_{6}\:>\:{{\uprho\:}}_{5}\)>\(\:{{\uprho\:}}_{4}\)>\(\:{{\uprho\:}}_{1}\)>\(\:{{\uprho\:}}_{2}\)>\(\:{{\uprho\:}}_{3}\)

Ullah et al14.

0.2396

0.2140

0.2027

0.2419

0.2650

0.2751

\(\:{{\uprho\:}}_{6}\:>{{\uprho\:}}_{5}\)>\(\:{{\uprho\:}}_{4}\)>\(\:{{\uprho\:}}_{1}\)>\(\:{{\uprho\:}}_{2}\)>\(\:{{\uprho\:}}_{3}\)

Shishavan et al71.

0.2922

0.2759

0.2482

0.3146

0.3478

0.3553

\(\:{{\uprho\:}}_{6}\:>{{\uprho\:}}_{5}\)>\(\:{{\uprho\:}}_{4}\)>\(\:{{\uprho\:}}_{1}\)>\(\:{{\uprho\:}}_{2}\)>\(\:{{\uprho\:}}_{3}\)

Gupta and Kumar72

0.2158

0.2028

0.2110

0.2361

0.2547

0.2637

\(\:{{\uprho\:}}_{6}\:>{{\uprho\:}}_{5}\)>\(\:{{\uprho\:}}_{4}\)>\(\:{{\uprho\:}}_{1}\)>\(\:{{\uprho\:}}_{2}\)>\(\:{{\uprho\:}}_{3}\)

Wu et al50.

0.3590

0.3148

0.3036

0.3866

0.4214

0.4214

\(\:{{\uprho\:}}_{6}\:>{{\uprho\:}}_{5}\)>\(\:{{\uprho\:}}_{4}\)>\(\:{{\uprho\:}}_{1}\)>\(\:{{\uprho\:}}_{2}\)>\(\:{{\uprho\:}}_{3}\)

Proposed structure of SM for p, q,r − FFS

\(\:0.8614\)

\(\:0.8441\)

\(\:0.8343\)

\(\:0.8219\)

\(\:0.8626\)

\(\:0.8641\)

\(\:{{\uprho\:}}_{6}>{{\uprho\:}}_{5}>{{\uprho\:}}_{1}>{{\uprho\:}}_{2}>{{\uprho\:}}_{3}>{{\uprho\:}}_{4}\)