Introduction
Regular maximal product in Pythagorean fuzzy graphs
Regular residue product in Pythagorean fuzzy graphs
Applications to decision-making
Evaluation of best company for investment
R
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\(x_{1}\)
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\(x_{2}\)
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\(x_{3}\)
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\(x_{4}\)
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\(x_{5}\)
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\(x_{6}\)
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---|---|---|---|---|---|---|
\(x_{1}\)
| (0.5, 0.5) | (0.4, 0.8) | (0.3, 0.6) | (0.7, 0.2) | (0.8, 0.6) | (0.1, 0.8) |
\(x_{2}\)
| (0.8, 0.4) | (0.5, 0.5) | (0.9, 0.4) | (0.5, 0.8) | (0.6, 0.8) | (0.5, 0.7) |
\(x_{3}\)
| (0.6, 0.3) | (0.4, 0.9) | (0.5, 0.5) | (0.7, 0.6) | (0.5, 0.8) | (0.9, 0.3) |
\(x_{4}\)
| (0.2, 0.7) | (0.8, 0.5) | (0.6, 0.7) | (0.5, 0.5) | (0.9, 0.3) | (0.5, 0.6) |
\(x_{5}\)
| (0.6, 0.8) | (0.8, 0.6) | (0.8, 0.5) | (0.3, 0.9) | (0.5, 0.5) | (0.8, 0.5) |
\(x_{6}\)
| (0.8, 0.1) | (0.7, 0.5) | (0.3, 0.9) | (0.6, 0.5) | (0.5, 0.8) | (0.5, 0.5) |
Alliance partner selection of a software company
\(R_{1}\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
---|---|---|---|---|---|
\(x_{1}\)
| (0.5, 0.5) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.3, 0.6) |
\(x_{2}\)
| (0.7, 0.5) | (0.5, 0.5) | (0.2, 0.9) | (0.7, 0.5) | (0.8, 0.3) |
\(x_{3}\)
| (0.4, 0.8) | (0.9, 0.2) | (0.5, 0.5) | (0.2, 0.6) | (0.9, 0.2) |
\(x_{4}\)
| (0.6, 0.7) | (0.5, 0.7) | (0.6, 0.2) | (0.5, 0.5) | (0.3, 0.7) |
\(x_{5}\)
| (0.6, 0.3) | (0.3, 0.8) | (0.2, 0.9) | (0.7, 0.3) | (0.5, 0.5) |
\(R_{2}\)
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\(x_{1}\)
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\(x_{2}\)
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\(x_{3}\)
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\(x_{4}\)
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\(x_{5}\)
|
---|---|---|---|---|---|
\(x_{1}\)
| (0.5, 0.5) | (0.9, 0.3) | (0.7, 0.2) | (0.3, 0.8) | (0.5, 0.8) |
\(x_{2}\)
| (0.3, 0.9) | (0.5, 0.5) | (0.6, 0.7) | (0.1, 0.5) | (0.8, 0.6) |
\(x_{3}\)
| (0.2, 0.7) | (0.7, 0.6) | (0.5, 0.5) | (0.7, 0.5) | (0.3, 0.7) |
\(x_{4}\)
| (0.8, 0.3) | (0.5, 0.1) | (0.5, 0.7) | (0.5, 0.5) | (0.8, 0.3) |
\(x_{5}\)
| (0.8, 0.5) | (0.6, 0.8) | (0.7, 0.3) | (0.3, 0.8) | (0.5, 0.5) |
\(R_{3}\)
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\(x_{1}\)
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\(x_{2}\)
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\(x_{3}\)
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\(x_{4}\)
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\(x_{5}\)
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---|---|---|---|---|---|
\(x_{1}\)
| (0.5, 0.5) | (0.7, 0.6) | (0.5, 0.8) | (0.3, 0.9) | (0.7, 0.6) |
\(x_{2}\)
| (0.6, 0.7) | (0.5, 0.5) | (0.8, 0.6) | (0.1, 0.7) | (0.3, 0.8) |
\(x_{3}\)
| (0.8, 0.5) | (0.6, 0.8) | (0.5, 0.5) | (0.4, 0.8) | (0.5, 0.7) |
\(x_{4}\)
| (0.9, 0.3) | (0.7, 0.1) | (0.8, 0.4) | (0.5, 0.5) | (0.8, 0.4) |
\(x_{5}\)
| (0.6, 0.7) | (0.8, 0.3) | (0.7, 0.5) | (0.4, 0.8) | (0.5, 0.5) |
Methods | Score of alternatives | Ranking of alternatives |
---|---|---|
Zhao et al. [40] | − 0.6800 −2.1800 − 0.9400 3.8200 − 0.0200 |
\({A_{4} \succ A_{5} \succ A_{1} \succ A_{3} \succ A_{2}}\)
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Our proposed method | 0.3367 0.2276 0.3276 0.6067 0.3595 |
\({A_{4} \succ A_{5} \succ A_{1} \succ A_{3} \succ A_{2}}\)
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