Table 1 Decision-matrix of IVFPFN.
| Â | \({\mathcal{C}}_{1}\) | \({\mathcal{C}}_{2}\) | \({\mathcal{C}}_{3}\) | \({\mathcal{C}}_{4}\) |
|---|---|---|---|---|
\({\upepsilon }_{1}\) | ||||
 \({\acute{Y} }_{1}\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right],\left[\text{0.2,0.4}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) |
 \({\acute{Y} }_{2}\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.1,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) | \(\left(\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right],\left[\text{0.1,0.2}\right]\right)\) |
 \({\acute{Y} }_{3}\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right],\left[\text{0.1,0.3}\right]\right)\) |
 \({\acute{Y} }_{4}\) | \(\left(\left[\text{0.2,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right],\left[\text{0.2,0.4}\right]\right)\) | \(\left(\left[\text{0.1,0.4}\right],\left[\text{0.0,0.3}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.4,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) |
\({\upepsilon }_{2}\) | ||||
 \({\acute{Y} }_{1}\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.4,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right],\left[\text{0.2,0.4}\right]\right)\) |
 \({\acute{Y} }_{2}\) | \(\left(\left[\text{0.1,0.4}\right],\left[\text{0.0,0.3}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right]\right)\) |
 \({\acute{Y} }_{3}\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.1,0.2}\right],\left[\text{0.2,0.4}\right]\right)\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right]\right)\) |
 \({\acute{Y} }_{4}\) | \(\left(\left[\text{0.2,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) | \(\left(\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.1,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.0,0.3}\right]\right)\) | \(\left(\left[\text{0.2,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) |
\({\upepsilon }_{3}\) | ||||
 \({\acute{Y} }_{1}\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.3,0.5}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) |
 \({\acute{Y} }_{2}\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.2,0.4}\right],\left[\text{0.4,0.5}\right],\left[\text{0.0,0.1}\right]\right)\) |
 \({\acute{Y} }_{3}\) | \(\left(\left[\text{0.2,0.4}\right],\left[\text{0.0,0.1}\right],\left[\text{0.3,0.4}\right]\right)\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.3,0.4}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.1,0.2}\right],\left[\text{0.1,0.3}\right],\left[\text{0.2,0.4}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.1,0.4}\right],\left[\text{0.0,0.2}\right]\right)\) |
 \({\acute{Y} }_{4}\) | \(\left(\left[\text{0.3,0.5}\right],\left[\text{0.0,0.2}\right],\left[\text{0.1,0.2}\right]\right)\) | \(\left(\left[\text{0.3,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.2,0.3}\right]\right)\) | \(\left(\left[\text{0.1,0.4}\right],\left[\text{0.2,0.3}\right],\left[\text{0.1,0.3}\right]\right)\) | \(\left(\left[\text{0.1,0.3}\right],\left[\text{0.2,0.5}\right],\left[\text{0.1,0.2}\right]\right)\) |
