# Ranking Startups Using DEMATEL-ANP-Based Fuzzy PROMETHEE II

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}has the highest comprehensive potential, followed by startup project A

_{3}.

## 1. Introduction

## 2. Literature Review

#### 2.1. Accelerators and the Startup Selection Approach

#### 2.2. DEMATEL

#### 2.3. AHP

#### 2.4. Fuzzy PROMETHEE II

#### 2.5. Ranking Fuzzy Numbers

## 3. Model Establishment

#### 3.1. Fuzzy Set Theory

- Fuzzy Sets

- Fuzzy Numbers

- α-Cuts

- Arithmetic Operations on Fuzzy Numbers

- Linguistic Values

#### 3.2. Relative Maximizing and Minimizing Sets

_{i}is denoted as in Equation (8).

#### 3.3. Spread Area-Based RMMS

#### 3.4. The Hybrid DEMATEL-ANP Based Fuzzy PROMETHEE II Model

#### 3.4.1. DEMATEL

_{i}has on factor (criterion) C

_{j}in a system with m factors (criteria) $C=\left\{{C}_{1},{C}_{2},\dots ,{C}_{m}\right\}$ using an integer scale of No Effect (0), Low Effect (1), Medium Low Effect (2), Medium Effect (3), Medium High Effect (4), High Effect (5) and Extremely Strong Effect (6). Next, the individual direct-influence matrix ${Z}_{e}={\left[{z}_{ij}^{e}\right]}_{m\times m}$ provided by the eth expert can be constructed, where all main diagonal components are equal to zero and ${z}_{ij}^{e}$ represent the respondent’s evaluation of DM on the degree to which criterion C

_{i}affects C

_{j}.

_{j}influences other criteria and can be grouped into a causal group; if (D + R) is negative, the criterion C

_{j}is being influenced by the other criteria and can be grouped into an effect group. A causal diagram can be produced by mapping the (D + R, D − R) dataset, yielding valuable assessment perception. A threshold value can be defined to screen out the negligible factors [68,69]. In this work, factors that have a value higher than the average value of the “Prominence” (D + R) and/or (D − R) is positive are selected to use in the next step.

#### 3.4.2. ANP

_{i}is obtained through Equation (25), which is computed by each row’s average.

_{j}is the corresponding row of the comparison matrix, E is Eigenvector and E

_{j}represents the corresponding component in E.

_{max}is obtained by the average of the CM vector. The CI is calculated as shown in Equation (27).

#### 3.4.3. Fuzzy PROMETHEE-Based Ranking Method

_{ij}can be as

_{i}over A

_{i’}is obtained by Equations (32) and (33), based on Equation (3)

_{j}is the fuzzy preference function for the jth criterion and C

_{j}(A

_{i}) is the evaluation of alternative A

_{i}corresponding to criterion C

_{j}.

_{i}is determined as

_{i}is determined as

## 4. Numerical Comparison and Consistency Test

## 5. Numerical Example

_{6}) demand validation” has the greatest (D + R) value and is the most critical factor, followed by “(C

_{7}) customer affordability” and “(C

_{8}) market demographic”. All these factors need to be evaluated in the initial steps when building a product or service. Additionally, the (D − R) values of “(C

_{3}) prior startup experience”, “(C

_{1}) sales”, and “(C

_{2}) product development cost” demonstrate that these criteria have net influences on other factors. Other medium value factors that are selected when proceeding to the next steps are “(C

_{9}) concept maturity”, “(C

_{10}) product maturity”, “(C

_{11}) value proposition”, “(C

_{13}) technology experience”, “(C

_{15}) growth strategy”, “(C

_{18}) creativity”, and “(C

_{19}) negotiation”.

_{8}) market demographics” has the highest value with 0.1253, followed by “(C

_{6}) demand validation” with 0.1196 and “(C

_{3}) prior startup experience” with 0.0940. The lowest weight value is “(C

_{11}) value proposition” with 0.0215.

_{1}(−0.0519), A

_{2}(0.0905), A

_{3}(0.0594) and A

_{4}(−0.0980) as presented in Table 16. The final ranking of four startup projects ${A}_{4}<{A}_{1}<{A}_{3}<{A}_{2}$ indicates that startup project A

_{2}has the highest comprehensive potential, followed by startup project A

_{3}.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | C_{16} | C_{17} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0 | 2 | 1.5 | 4 | 5 | 1 | 1 | 1 | 1.5 | 1 | 2.75 | 4 | 4 | 3 | 2 | 5 | 3 | 3 | 3 |

C_{2} | 5.5 | 0 | 1.25 | 5 | 4 | 1.25 | 1 | 1.75 | 1.25 | 2 | 1 | 4 | 2 | 3 | 1 | 4 | 2 | 2 | 2 |

C_{3} | 6 | 6 | 0 | 6 | 6 | 4 | 5 | 4 | 3 | 3 | 4 | 6 | 5 | 6 | 6 | 5 | 6 | 5 | 5 |

C_{4} | 4 | 3 | 1 | 0 | 4 | 1 | 1.75 | 1 | 2 | 1 | 2 | 3 | 1 | 5 | 2 | 3 | 3 | 4 | 2 |

C_{5} | 3 | 4 | 1 | 4 | 0 | 1.75 | 2 | 2 | 1 | 2 | 1 | 4 | 4 | 6 | 1 | 2 | 3 | 5 | 4 |

C_{6} | 6 | 6 | 4 | 5.75 | 6 | 0 | 4.25 | 4.5 | 6 | 6 | 6 | 6 | 4 | 5.75 | 6 | 6 | 5.75 | 5.25 | 3.75 |

C_{7} | 6 | 6 | 3 | 6 | 6 | 3.75 | 0 | 3.25 | 6 | 5.75 | 5.75 | 6 | 6 | 6 | 5.25 | 5.5 | 6 | 4.75 | 3.75 |

C_{8} | 5.75 | 6 | 4 | 5.75 | 5.25 | 3.5 | 4.75 | 0 | 5.5 | 5.25 | 6 | 5.5 | 4 | 6 | 5.75 | 6 | 5.75 | 5 | 3.75 |

C_{9} | 6 | 6 | 5 | 6 | 6 | 1.5 | 1 | 2.5 | 0 | 6 | 5 | 6 | 3.25 | 6 | 6 | 6 | 5 | 4 | 4 |

C_{10} | 6 | 6 | 5 | 6 | 5.75 | 1 | 1 | 2.25 | 2 | 0 | 5 | 6 | 3 | 6 | 5 | 5 | 6 | 3 | 4 |

C_{11} | 5.25 | 6 | 4 | 6 | 6 | 2 | 2 | 1.75 | 2.75 | 3 | 0 | 6 | 5 | 5 | 3 | 6 | 4 | 3 | 3 |

C_{12} | 4 | 4 | 1 | 4.75 | 4 | 1 | 1 | 1 | 1 | 2 | 2 | 0 | 2 | 3 | 2 | 4 | 4 | 2 | 3 |

C_{13} | 4 | 6 | 3 | 6 | 4 | 4 | 2 | 4 | 4.75 | 5 | 3 | 6 | 0 | 6 | 6 | 5 | 5 | 6 | 6 |

C_{14} | 5 | 5 | 2 | 3 | 2 | 2.25 | 2 | 1.5 | 1.75 | 1.75 | 3 | 5 | 1 | 0 | 1 | 2 | 2 | 1 | 3 |

C_{15} | 6 | 6 | 2 | 6 | 6 | 1 | 2.75 | 2 | 1.75 | 3 | 5 | 6 | 2 | 6 | 0 | 6 | 6 | 2 | 3 |

C_{16} | 3 | 4 | 3 | 5 | 6 | 2 | 1.75 | 1 | 2 | 3 | 2 | 4 | 3 | 6 | 1 | 0 | 3 | 2 | 2 |

C_{17} | 5 | 6 | 2 | 5 | 5 | 1.75 | 2 | 2 | 3 | 2 | 4 | 4 | 3 | 6 | 2 | 5 | 0 | 3 | 2 |

C_{18} | 4.75 | 5.75 | 3 | 4 | 3 | 2.75 | 3 | 3 | 4 | 5 | 5 | 6 | 2 | 6 | 6 | 6 | 5 | 0 | 5 |

C_{19} | 5 | 6 | 3 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 2 | 5 | 5 | 6 | 6 | 3 | 0 |

## Appendix D

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | C_{16} | C_{17} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0 | 0.0206 | 0.0155 | 0.0412 | 0.0515 | 0.0103 | 0.0103 | 0.0103 | 0.0155 | 0.0103 | 0.0284 | 0.0412 | 0.0412 | 0.0309 | 0.0206 | 0.0515 | 0.0309 | 0.0309 | 0.0309 |

C_{2} | 0.0567 | 0 | 0.0129 | 0.0515 | 0.0412 | 0.0129 | 0.0103 | 0.0180 | 0.0129 | 0.0206 | 0.0103 | 0.0412 | 0.0206 | 0.0309 | 0.0103 | 0.0412 | 0.0206 | 0.0206 | 0.0206 |

C_{3} | 0.0619 | 0.0619 | 0 | 0.0619 | 0.0619 | 0.0412 | 0.0515 | 0.0412 | 0.0309 | 0.0309 | 0.0412 | 0.0619 | 0.0515 | 0.0619 | 0.0619 | 0.0515 | 0.0619 | 0.0515 | 0.0515 |

C_{4} | 0.0412 | 0.0309 | 0.0103 | 0 | 0.0412 | 0.0103 | 0.0180 | 0.0103 | 0.0206 | 0.0103 | 0.0206 | 0.0309 | 0.0103 | 0.0515 | 0.0206 | 0.0309 | 0.0309 | 0.0412 | 0.0206 |

C_{5} | 0.0309 | 0.0412 | 0.0103 | 0.0412 | 0 | 0.0180 | 0.0206 | 0.0206 | 0.0103 | 0.0206 | 0.0103 | 0.0412 | 0.0412 | 0.0619 | 0.0103 | 0.0206 | 0.0309 | 0.0515 | 0.0412 |

C_{6} | 0.0619 | 0.0619 | 0.0412 | 0.0593 | 0.0619 | 0 | 0.0438 | 0.0464 | 0.0619 | 0.0619 | 0.0619 | 0.0619 | 0.0412 | 0.0593 | 0.0619 | 0.0619 | 0.0593 | 0.0541 | 0.0387 |

C_{7} | 0.0619 | 0.0619 | 0.0309 | 0.0619 | 0.0619 | 0.0387 | 0 | 0.0335 | 0.0619 | 0.0593 | 0.0593 | 0.0619 | 0.0619 | 0.0619 | 0.0541 | 0.0567 | 0.0619 | 0.0490 | 0.0387 |

C_{8} | 0.0593 | 0.0619 | 0.0412 | 0.0593 | 0.0541 | 0.0361 | 0.0490 | 0 | 0.0567 | 0.0541 | 0.0619 | 0.0567 | 0.0412 | 0.0619 | 0.0593 | 0.0619 | 0.0593 | 0.0515 | 0.0387 |

C_{9} | 0.0619 | 0.0619 | 0.0515 | 0.0619 | 0.0619 | 0.0155 | 0.0103 | 0.0258 | 0 | 0.0619 | 0.0515 | 0.0619 | 0.0335 | 0.0619 | 0.0619 | 0.0619 | 0.0515 | 0.0412 | 0.0412 |

C_{10} | 0.0619 | 0.0619 | 0.0515 | 0.0619 | 0.0593 | 0.0103 | 0.0103 | 0.0232 | 0.0206 | 0 | 0.0515 | 0.0619 | 0.0309 | 0.0619 | 0.0515 | 0.0515 | 0.0619 | 0.0309 | 0.0412 |

C_{11} | 0.0541 | 0.0619 | 0.0412 | 0.0619 | 0.0619 | 0.0206 | 0.0206 | 0.0180 | 0.0284 | 0.0309 | 0 | 0.0619 | 0.0515 | 0.0515 | 0.0309 | 0.0619 | 0.0412 | 0.0309 | 0.0309 |

C_{12} | 0.0412 | 0.0412 | 0.0103 | 0.0490 | 0.0412 | 0.0103 | 0.0103 | 0.0103 | 0.0103 | 0.0206 | 0.0206 | 0 | 0.0206 | 0.0309 | 0.0206 | 0.0412 | 0.0412 | 0.0206 | 0.0309 |

C_{13} | 0.0412 | 0.0619 | 0.0309 | 0.0619 | 0.0412 | 0.0412 | 0.0206 | 0.0412 | 0.0490 | 0.0515 | 0.0309 | 0.0619 | 0 | 0.0619 | 0.0619 | 0.0515 | 0.0515 | 0.0619 | 0.0619 |

C_{14} | 0.0515 | 0.0515 | 0.0206 | 0.0309 | 0.0206 | 0.0232 | 0.0206 | 0.0155 | 0.0180 | 0.0180 | 0.0309 | 0.0515 | 0.0103 | 0 | 0.0103 | 0.0206 | 0.0206 | 0.0103 | 0.0309 |

C_{15} | 0.0619 | 0.0619 | 0.0206 | 0.0619 | 0.0619 | 0.0103 | 0.0284 | 0.0206 | 0.0180 | 0.0309 | 0.0515 | 0.0619 | 0.0206 | 0.0619 | 0 | 0.0619 | 0.0619 | 0.0206 | 0.0309 |

C_{16} | 0.0309 | 0.0412 | 0.0309 | 0.0515 | 0.0619 | 0.0206 | 0.0180 | 0.0103 | 0.0206 | 0.0309 | 0.0206 | 0.0412 | 0.0309 | 0.0619 | 0.0103 | 0 | 0.0309 | 0.0206 | 0.0206 |

C_{17} | 0.0515 | 0.0619 | 0.0206 | 0.0515 | 0.0515 | 0.0180 | 0.0206 | 0.0206 | 0.0309 | 0.0206 | 0.0412 | 0.0412 | 0.0309 | 0.0619 | 0.0206 | 0.0515 | 0 | 0.0309 | 0.0206 |

C_{18} | 0.0490 | 0.0593 | 0.0309 | 0.0412 | 0.0309 | 0.0284 | 0.0309 | 0.0309 | 0.0412 | 0.0515 | 0.0515 | 0.0619 | 0.0206 | 0.0619 | 0.0619 | 0.0619 | 0.0515 | 0 | 0.0515 |

C_{19} | 0.0515 | 0.0619 | 0.0309 | 0.0619 | 0.0412 | 0.0412 | 0.0412 | 0.0412 | 0.0412 | 0.0412 | 0.0515 | 0.0515 | 0.0206 | 0.0515 | 0.0515 | 0.0619 | 0.0619 | 0.0309 | 0 |

## Appendix E

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | C_{16} | C_{17} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0.0681 | 0.0911 | 0.0507 | 0.1117 | 0.1165 | 0.0406 | 0.0418 | 0.0417 | 0.0532 | 0.0539 | 0.0754 | 0.1097 | 0.0820 | 0.1040 | 0.0655 | 0.1147 | 0.0891 | 0.0780 | 0.0781 |

C_{2} | 0.1152 | 0.0620 | 0.0442 | 0.1134 | 0.1000 | 0.0391 | 0.0381 | 0.0450 | 0.0462 | 0.0580 | 0.0532 | 0.1018 | 0.0581 | 0.0954 | 0.0504 | 0.0979 | 0.0727 | 0.0631 | 0.0629 |

C_{3} | 0.1930 | 0.1963 | 0.0692 | 0.1986 | 0.1895 | 0.0979 | 0.1110 | 0.1010 | 0.1050 | 0.1151 | 0.1353 | 0.1951 | 0.1320 | 0.2009 | 0.1486 | 0.1774 | 0.1747 | 0.1419 | 0.1419 |

C_{4} | 0.1022 | 0.0939 | 0.0424 | 0.0646 | 0.1001 | 0.0372 | 0.0459 | 0.0383 | 0.0542 | 0.0495 | 0.0642 | 0.0936 | 0.0488 | 0.1156 | 0.0607 | 0.0893 | 0.0830 | 0.0821 | 0.0635 |

C_{5} | 0.1045 | 0.1161 | 0.0487 | 0.1166 | 0.0708 | 0.0507 | 0.0543 | 0.0545 | 0.0524 | 0.0675 | 0.0635 | 0.1154 | 0.0841 | 0.1374 | 0.0606 | 0.0910 | 0.0938 | 0.1004 | 0.0917 |

C_{6} | 0.2028 | 0.2062 | 0.1154 | 0.2064 | 0.1997 | 0.0614 | 0.1072 | 0.1095 | 0.1383 | 0.1502 | 0.1615 | 0.2051 | 0.1286 | 0.2088 | 0.1554 | 0.1962 | 0.1806 | 0.1503 | 0.1363 |

C_{7} | 0.1983 | 0.2019 | 0.1034 | 0.2044 | 0.1952 | 0.0969 | 0.0626 | 0.0957 | 0.1360 | 0.1451 | 0.1556 | 0.2009 | 0.1449 | 0.2067 | 0.1453 | 0.1873 | 0.1790 | 0.1430 | 0.1338 |

C_{8} | 0.1952 | 0.2009 | 0.1124 | 0.2009 | 0.1873 | 0.0941 | 0.1096 | 0.0627 | 0.1307 | 0.1396 | 0.1577 | 0.1950 | 0.1254 | 0.2056 | 0.1493 | 0.1912 | 0.1759 | 0.1442 | 0.1326 |

C_{9} | 0.1810 | 0.1836 | 0.1125 | 0.1862 | 0.1783 | 0.0671 | 0.0657 | 0.0797 | 0.0652 | 0.1341 | 0.1349 | 0.1828 | 0.1071 | 0.1881 | 0.1389 | 0.1748 | 0.1541 | 0.1226 | 0.1237 |

C_{10} | 0.1690 | 0.1713 | 0.1054 | 0.1737 | 0.1641 | 0.0575 | 0.0606 | 0.0718 | 0.0791 | 0.0670 | 0.1258 | 0.1703 | 0.0975 | 0.1753 | 0.1205 | 0.1537 | 0.1528 | 0.1050 | 0.1152 |

C_{11} | 0.1562 | 0.1659 | 0.0934 | 0.1685 | 0.1614 | 0.0655 | 0.0677 | 0.0652 | 0.0846 | 0.0953 | 0.0727 | 0.1653 | 0.1140 | 0.1607 | 0.0988 | 0.1582 | 0.1293 | 0.1028 | 0.1029 |

C_{12} | 0.1037 | 0.1051 | 0.0431 | 0.1140 | 0.1026 | 0.0378 | 0.0393 | 0.0391 | 0.0452 | 0.0596 | 0.0648 | 0.0649 | 0.0595 | 0.0985 | 0.0614 | 0.1006 | 0.0942 | 0.0645 | 0.0739 |

C_{13} | 0.1672 | 0.1894 | 0.0965 | 0.1911 | 0.1631 | 0.0941 | 0.0785 | 0.0975 | 0.1172 | 0.1301 | 0.1213 | 0.1880 | 0.0765 | 0.1933 | 0.1446 | 0.1709 | 0.1593 | 0.1453 | 0.1463 |

C_{14} | 0.1139 | 0.1143 | 0.0532 | 0.0973 | 0.0834 | 0.0500 | 0.0491 | 0.0441 | 0.0528 | 0.0576 | 0.0749 | 0.1143 | 0.0505 | 0.0667 | 0.0526 | 0.0819 | 0.0752 | 0.0545 | 0.0738 |

C_{15} | 0.1589 | 0.1607 | 0.0711 | 0.1633 | 0.1571 | 0.0529 | 0.0721 | 0.0642 | 0.0714 | 0.0909 | 0.1184 | 0.1600 | 0.0822 | 0.1648 | 0.0632 | 0.1535 | 0.1435 | 0.0885 | 0.0981 |

C_{16} | 0.1067 | 0.1181 | 0.0692 | 0.1289 | 0.1331 | 0.0533 | 0.0525 | 0.0452 | 0.0619 | 0.0774 | 0.0734 | 0.1175 | 0.0770 | 0.1404 | 0.0606 | 0.0716 | 0.0952 | 0.0737 | 0.0738 |

C_{17} | 0.1379 | 0.1492 | 0.0659 | 0.1415 | 0.1357 | 0.0558 | 0.0599 | 0.0598 | 0.0781 | 0.0755 | 0.1011 | 0.1297 | 0.0846 | 0.1527 | 0.0777 | 0.1331 | 0.0749 | 0.0909 | 0.0815 |

C_{18} | 0.1638 | 0.1759 | 0.0910 | 0.1614 | 0.1443 | 0.0770 | 0.0827 | 0.0822 | 0.1032 | 0.1224 | 0.1324 | 0.1772 | 0.0915 | 0.1816 | 0.1359 | 0.1703 | 0.1496 | 0.0782 | 0.1285 |

C_{19} | 0.1689 | 0.1808 | 0.0923 | 0.1833 | 0.1570 | 0.0904 | 0.0939 | 0.0932 | 0.1056 | 0.1148 | 0.1343 | 0.1701 | 0.0941 | 0.1755 | 0.1281 | 0.1727 | 0.1613 | 0.1115 | 0.0810 |

## Appendix F

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 2 | 3 | 3 | 1/4 | 1/5 | 1/4 | 1/5 | 3 | 1/7 | 1/4 | 1/3 | 1/2 |

C_{2} | 1/2 | 1 | 1/3 | 3 | 1/5 | 1/8 | 1/4 | 1/5 | 1/4 | 1/8 | 1/3 | 1/8 | 1/5 |

C_{3} | 1/3 | 3 | 1 | 3 | 1/5 | 1/4 | 2 | 1/2 | 3 | 1/6 | 1/3 | 1/3 | 1/6 |

C_{6} | 1/3 | 1/3 | 1/3 | 1 | 1/5 | 1/8 | 1/2 | 1/5 | 1/3 | 1/8 | 1/6 | 1/8 | 1/3 |

C_{7} | 4 | 5 | 5 | 5 | 1 | 3 | 6 | 3 | 6 | 1/2 | 4 | 2 | 3 |

C_{8} | 5 | 8 | 4 | 8 | 1/3 | 1 | 5 | 2 | 5 | 1/3 | 2 | 2 | 3 |

C_{9} | 4 | 4 | 1/2 | 2 | 1/6 | 1/5 | 1 | 1/2 | 2 | 1/8 | 1/2 | 1/7 | 1/5 |

C_{10} | 5 | 5 | 2 | 5 | 1/3 | 1/2 | 2 | 1 | 3 | 1/6 | 1/2 | 1/2 | 2 |

C_{11} | 1/3 | 4 | 1/3 | 3 | 1/6 | 1/5 | 1/2 | 1/3 | 1 | 1/8 | 1/2 | 1/5 | 1/4 |

C_{13} | 7 | 8 | 6 | 8 | 2 | 3 | 8 | 6 | 8 | 1 | 4 | 2 | 4 |

C_{15} | 4 | 3 | 3 | 6 | 1/4 | 1/2 | 2 | 2 | 2 | 1/4 | 1 | 1/2 | 1/2 |

C_{18} | 3 | 8 | 3 | 8 | 1/2 | 1/2 | 7 | 5 | 5 | 1/2 | 2 | 1 | 2 |

C_{19} | 2 | 5 | 6 | 3 | 1/3 | 1/3 | 5 | 4 | 4 | 1/4 | 2 | 1/2 | 1 |

Inconsistency: 0.08328 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 1/6 | 1/5 | 1/7 | 1/8 | 1/8 | 1/6 | 1/8 | 3 | 1/2 | 3 | 1/4 | 3 |

C_{2} | 6 | 1 | 1/3 | 1/5 | 1/2 | 1/4 | 1/3 | 1/2 | 3 | 1/2 | 4 | 1/2 | 4 |

C_{3} | 5 | 3 | 1 | 3 | 3 | 1/2 | 2 | 4 | 7 | 2 | 5 | 2 | 6 |

C_{6} | 7 | 5 | 1/3 | 1 | 5 | 3 | 2 | 3 | 9 | 5 | 7 | 3 | 7 |

C_{7} | 8 | 2 | 1/3 | 1/5 | 1 | 1/6 | 3 | 1/2 | 5 | 2 | 4 | 1/2 | 4 |

C_{8} | 8 | 4 | 2 | 1/3 | 6 | 1 | 3 | 2 | 8 | 6 | 4 | 2 | 6 |

C_{9} | 6 | 3 | 1/2 | 1/2 | 1/3 | 1/3 | 1 | 1/2 | 4 | 2 | 4 | 1/3 | 5 |

C_{10} | 8 | 2 | 1/4 | 1/3 | 2 | 1/2 | 2 | 1 | 6 | 1/3 | 4 | 1/2 | 4 |

C_{11} | 1/3 | 1/3 | 1/7 | 1/9 | 1/5 | 1/8 | 1/4 | 1/6 | 1 | 1/3 | 1/2 | 1/7 | 1/3 |

C_{13} | 2 | 2 | 1/2 | 1/5 | 1/2 | 1/6 | 1/2 | 3 | 3 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/3 | 1/4 | 1/5 | 1/7 | 1/4 | 1/4 | 1/4 | 1/4 | 2 | 1/3 | 1 | 1/6 | 2 |

C_{18} | 4 | 2 | 1/2 | 1/3 | 2 | 1/2 | 3 | 2 | 7 | 2 | 6 | 1 | 4 |

C_{19} | 1/3 | 1/4 | 1/6 | 1/7 | 1/4 | 1/6 | 1/5 | 1/4 | 3 | 1/2 | 1/2 | 1/4 | 1 |

Inconsistency: 0.09659 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 3 | 3 | 1/2 | 3 | 2 | 8 | 5 | 6 | 3 | 2 | 4 | 3 |

C_{2} | 1/3 | 1 | 3 | 1/2 | 2 | 2 | 4 | 3 | 3 | 2 | 4 | 2 | 1/2 |

C_{3} | 1/3 | 1/3 | 1 | 1/3 | 3 | 1/2 | 2 | 1/3 | 2 | 1/3 | 1/2 | 3 | 1/4 |

C_{6} | 2 | 2 | 3 | 1 | 1/2 | 2 | 4 | 2 | 4 | 3 | 2 | 5 | 2 |

C_{7} | 1/3 | 1/2 | 1/3 | 2 | 1 | 1/2 | 2 | 1/3 | 2 | 1/2 | 3 | 2 | 1/3 |

C_{8} | 1/2 | 1/2 | 2 | 1/2 | 2 | 1 | 3 | 1/2 | 3 | 1/2 | 2 | 3 | 1/2 |

C_{9} | 1/8 | 1/4 | 1/2 | 1/4 | 1/2 | 1/3 | 1 | 1/4 | 1/2 | 1/3 | 1/2 | 1/2 | 1/4 |

C_{10} | 1/5 | 1/3 | 3 | 1/2 | 3 | 2 | 4 | 1 | 2 | 3 | 1/2 | 4 | 1/3 |

C_{11} | 1/6 | 1/3 | 1/2 | 1/4 | 1/2 | 1/3 | 2 | 1/2 | 1 | 1/2 | 1/3 | 1/2 | 1/5 |

C_{13} | 1/3 | 1/2 | 3 | 1/3 | 2 | 2 | 3 | 1/3 | 2 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/2 | 1/4 | 2 | 1/2 | 1/3 | 1/2 | 2 | 2 | 3 | 1/3 | 1 | 3 | 1/3 |

C_{18} | 1/4 | 1/2 | 1/3 | 1/5 | 1/2 | 1/3 | 2 | 1/4 | 2 | 2 | 1/3 | 1 | 1/2 |

C_{19} | 1/3 | 2 | 4 | 2 | 3 | 2 | 4 | 3 | 5 | 1/2 | 3 | 2 | 1 |

Inconsistency: 0.09391 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 1/6 | 1/5 | 1/7 | 1/6 | 1/7 | 1/4 | 1/5 | 3 | 2 | 3 | 3 | 4 |

C_{2} | 6 | 1 | 1/3 | 1/4 | 1/2 | 1/4 | 1/3 | 1/3 | 3 | 1/2 | 4 | 1/2 | 3 |

C_{3} | 5 | 3 | 1 | 4 | 3 | 1/2 | 2 | 4 | 6 | 3 | 4 | 6 | 7 |

C_{6} | 7 | 4 | 1/4 | 1 | 4 | 1/2 | 2 | 2 | 7 | 8 | 6 | 6 | 7 |

C_{7} | 6 | 2 | 1/3 | 1/4 | 1 | 1/2 | 1/3 | 2 | 5 | 3 | 4 | 3 | 2 |

C_{8} | 7 | 4 | 2 | 2 | 2 | 1 | 3 | 2 | 8 | 5 | 8 | 6 | 7 |

C_{9} | 4 | 3 | 1/2 | 1/2 | 3 | 1/3 | 1 | 2 | 7 | 3 | 7 | 3 | 5 |

C_{10} | 5 | 3 | 1/4 | 1/2 | 1/2 | 1/2 | 1/2 | 1 | 5 | 3 | 4 | 3 | 5 |

C_{11} | 1/3 | 1/3 | 1/6 | 1/7 | 1/5 | 1/8 | 1/7 | 1/5 | 1 | 1/3 | 1/2 | 1/4 | 1/2 |

C_{13} | 1/2 | 2 | 1/3 | 1/8 | 1/3 | 1/5 | 1/3 | 3 | 3 | 1 | 4 | 1/2 | 1/2 |

C_{15} | 1/3 | 1/4 | 1/4 | 1/6 | 1/4 | 1/8 | 1/7 | 1/4 | 2 | 1/4 | 1 | 1/3 | 1/2 |

C_{18} | 1/3 | 2 | 1/6 | 1/6 | 1/3 | 1/6 | 1/3 | 1/3 | 4 | 2 | 3 | 1 | 3 |

C_{19} | 1/4 | 1/3 | 1/7 | 1/7 | 1/2 | 1/7 | 1/5 | 1/5 | 2 | 2 | 2 | 1/3 | 1 |

Inconsistency: 0.09784 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 1/5 | 1/5 | 1/4 | 1/6 | 1/7 | 1/4 | 1/5 | 3 | 2 | 3 | 3 | 4 |

C_{2} | 5 | 1 | 1/4 | 1/4 | 1/2 | 1/4 | 1/3 | 1/4 | 3 | 1/2 | 4 | 1/2 | 3 |

C_{3} | 5 | 4 | 1 | 4 | 2 | 1/2 | 2 | 4 | 6 | 3 | 4 | 6 | 7 |

C_{6} | 4 | 4 | 1/4 | 1 | 4 | 1/2 | 2 | 2 | 7 | 8 | 6 | 6 | 7 |

C_{7} | 6 | 2 | 1/2 | 1/4 | 1 | 1/2 | 1/3 | 2 | 5 | 3 | 4 | 3 | 2 |

C_{8} | 7 | 4 | 2 | 2 | 2 | 1 | 3 | 2 | 8 | 5 | 8 | 6 | 7 |

C_{9} | 4 | 3 | 1/2 | 1/2 | 3 | 1/3 | 1 | 2 | 7 | 3 | 7 | 3 | 5 |

C_{10} | 5 | 4 | 1/4 | 1/2 | 1/2 | 1/2 | 1/2 | 1 | 5 | 3 | 4 | 3 | 5 |

C_{11} | 1/3 | 1/3 | 1/6 | 1/7 | 1/5 | 1/8 | 1/7 | 1/5 | 1 | 1/3 | 1/2 | 1/4 | 1/2 |

C_{13} | 1/2 | 2 | 1/3 | 1/8 | 1/3 | 1/5 | 1/3 | 3 | 3 | 1 | 4 | 1/2 | 1/2 |

C_{15} | 1/3 | 1/4 | 1/4 | 1/6 | 1/4 | 1/8 | 1/7 | 1/4 | 2 | 1/4 | 1 | 1/3 | 1/2 |

C_{18} | 1/3 | 2 | 1/6 | 1/6 | 1/3 | 1/6 | 1/3 | 1/3 | 4 | 2 | 3 | 1 | 3 |

C_{19} | 1/4 | 1/3 | 1/7 | 1/7 | 1/2 | 1/7 | 1/5 | 1/5 | 2 | 2 | 2 | 1/3 | 1 |

Inconsistency: 0.09426 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 1/5 | 1/5 | 1/4 | 1/6 | 1/7 | 1/4 | 1/5 | 3 | 2 | 3 | 3 | 4 |

C_{2} | 5 | 1 | 1/4 | 1/4 | 1/2 | 1/4 | 1/3 | 1/4 | 3 | 1/2 | 4 | 1/2 | 3 |

C_{3} | 5 | 4 | 1 | 4 | 2 | 1/2 | 2 | 4 | 6 | 3 | 4 | 6 | 7 |

C_{6} | 4 | 4 | 1/4 | 1 | 4 | 1/2 | 2 | 2 | 7 | 5 | 5 | 4 | 5 |

C_{7} | 6 | 2 | 1/2 | 1/4 | 1 | 1/2 | 1/3 | 2 | 5 | 3 | 4 | 3 | 2 |

C_{8} | 7 | 4 | 2 | 2 | 2 | 1 | 3 | 2 | 8 | 5 | 8 | 6 | 7 |

C_{9} | 4 | 3 | 1/2 | 1/2 | 3 | 1/3 | 1 | 2 | 7 | 3 | 7 | 3 | 5 |

C_{10} | 5 | 4 | 1/4 | 1/2 | 1/2 | 1/2 | 1/2 | 1 | 5 | 3 | 4 | 3 | 5 |

C_{11} | 1/3 | 1/3 | 1/6 | 1/7 | 1/5 | 1/8 | 1/7 | 1/5 | 1 | 1/3 | 1/2 | 1/4 | 1/2 |

C_{13} | 1/2 | 2 | 1/3 | 1/5 | 1/3 | 1/5 | 1/3 | 3 | 3 | 1 | 4 | 1/2 | 1/2 |

C_{15} | 1/3 | 1/4 | 1/4 | 1/5 | 1/4 | 1/8 | 1/7 | 1/4 | 2 | 1/4 | 1 | 1/2 | 1/3 |

C_{18} | 1/3 | 2 | 1/6 | 1/4 | 1/3 | 1/6 | 1/3 | 1/3 | 4 | 2 | 2 | 1 | 2 |

C_{19} | 1/4 | 1/3 | 1/7 | 1/5 | 1/2 | 1/7 | 1/5 | 1/5 | 2 | 2 | 3 | 1/2 | 1 |

Inconsistency: 0.09230 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 3 | 3 | 1/2 | 3 | 2 | 6 | 3 | 4 | 2 | 2 | 4 | 2 |

C_{2} | 1/3 | 1 | 3 | 1/2 | 2 | 2 | 5 | 3 | 3 | 2 | 4 | 2 | 1/2 |

C_{3} | 1/3 | 1/3 | 1 | 1/3 | 1/2 | 1/2 | 2 | 1/3 | 2 | 1/3 | 1/2 | 3 | 1/4 |

C_{6} | 2 | 2 | 3 | 1 | 1/2 | 2 | 4 | 2 | 4 | 3 | 2 | 5 | 2 |

C_{7} | 1/3 | 1/2 | 2 | 2 | 1 | 1/2 | 2 | 1/3 | 2 | 1/2 | 3 | 2 | 1/3 |

C_{8} | 1/2 | 1/2 | 2 | 1/2 | 2 | 1 | 3 | 1/2 | 3 | 1/2 | 2 | 3 | 1/2 |

C_{9} | 1/6 | 1/5 | 1/2 | 1/4 | 1/2 | 1/3 | 1 | 1/4 | 1/2 | 1/3 | 1/2 | 1/2 | 1/4 |

C_{10} | 1/3 | 1/3 | 3 | 1/2 | 3 | 2 | 4 | 1 | 2 | 3 | 1/2 | 4 | 1/3 |

C_{11} | 1/4 | 1/3 | 1/2 | 1/4 | 1/2 | 1/3 | 2 | 1/2 | 1 | 1/2 | 1/3 | 1/2 | 1/5 |

C_{13} | 1/2 | 1/2 | 3 | 1/3 | 2 | 2 | 3 | 1/3 | 2 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/2 | 1/4 | 2 | 1/2 | 1/3 | 1/2 | 2 | 2 | 3 | 1/3 | 1 | 3 | 1/3 |

C_{18} | 1/4 | 1/2 | 1/3 | 1/5 | 1/2 | 1/3 | 2 | 1/4 | 2 | 2 | 1/3 | 1 | 1/2 |

C_{19} | 1/2 | 2 | 4 | 2 | 3 | 2 | 4 | 3 | 5 | 1/2 | 3 | 2 | 1 |

Inconsistency: 0.09890 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 3 | 3 | 1/2 | 3 | 2 | 7 | 3 | 4 | 3 | 2 | 4 | 2 |

C_{2} | 1/3 | 1 | 3 | 1/2 | 2 | 2 | 5 | 3 | 3 | 2 | 4 | 2 | 1/2 |

C_{3} | 1/3 | 1/3 | 1 | 1/3 | 1/2 | 1/2 | 2 | 1/3 | 2 | 1/3 | 1/2 | 3 | 1/4 |

C_{6} | 2 | 2 | 3 | 1 | 1/2 | 2 | 4 | 2 | 4 | 3 | 2 | 4 | 2 |

C_{7} | 1/3 | 1/2 | 2 | 2 | 1 | 1/2 | 2 | 1/3 | 2 | 1/2 | 3 | 2 | 1/3 |

C_{8} | 1/2 | 1/2 | 2 | 1/2 | 2 | 1 | 3 | 1/2 | 3 | 1/2 | 2 | 3 | 1/2 |

C_{9} | 1/7 | 1/5 | 1/2 | 1/4 | 1/2 | 1/3 | 1 | 1/4 | 1/2 | 1/3 | 1/2 | 1/2 | 1/4 |

C_{10} | 1/3 | 1/3 | 3 | 1/2 | 3 | 2 | 4 | 1 | 2 | 3 | 1/2 | 4 | 1/3 |

C_{11} | 1/4 | 1/3 | 1/2 | 1/4 | 1/2 | 1/3 | 2 | 1/2 | 1 | 1/3 | 1/3 | 1/2 | 1/5 |

C_{13} | 1/3 | 1/2 | 3 | 1/3 | 2 | 2 | 3 | 1/3 | 3 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/2 | 1/4 | 2 | 1/2 | 1/3 | 1/2 | 2 | 2 | 3 | 1/3 | 1 | 3 | 1/3 |

C_{18} | 1/4 | 1/2 | 1/3 | 1/4 | 1/2 | 1/3 | 2 | 1/4 | 2 | 2 | 1/3 | 1 | 1/4 |

C_{19} | 1/2 | 2 | 4 | 2 | 3 | 2 | 4 | 3 | 5 | 1/2 | 3 | 4 | 1 |

Inconsistency: 0.09964 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 2 | 3 | 3 | 1/4 | 1/2 | 1/2 | 1/4 | 1/3 | 1/3 | 1/2 | 1/3 | 1/2 |

C_{2} | 1/2 | 1 | 1/2 | 2 | 1/4 | 1/3 | 1/2 | 1/4 | 1/2 | 1/7 | 1/4 | 1/5 | 1/3 |

C_{3} | 1/3 | 2 | 1 | 3 | 1/5 | 1/4 | 2 | 1/2 | 3 | 1/6 | 1/3 | 1/3 | 1/6 |

C_{6} | 1/3 | 1/2 | 1/3 | 1 | 1/5 | 1/8 | 1/2 | 1/5 | 1/3 | 1/8 | 1/6 | 1/4 | 1/3 |

C_{7} | 4 | 4 | 5 | 5 | 1 | 2 | 5 | 3 | 3 | 1/2 | 3 | 2 | 2 |

C_{8} | 2 | 3 | 4 | 8 | 1/2 | 1 | 5 | 2 | 1/2 | 1/3 | 2 | 2 | 3 |

C_{9} | 2 | 2 | 1/2 | 2 | 1/5 | 1/5 | 1 | 1/2 | 2 | 1/8 | 1/2 | 1/7 | 1/5 |

C_{10} | 4 | 4 | 2 | 5 | 1/3 | 1/2 | 2 | 1 | 1/3 | 1/6 | 1/2 | 1/2 | 2 |

C_{11} | 3 | 2 | 1/3 | 3 | 1/3 | 2 | 1/2 | 3 | 1 | 1/5 | 1/2 | 1/3 | 1/2 |

C_{13} | 3 | 7 | 6 | 8 | 2 | 3 | 8 | 6 | 5 | 1 | 4 | 2 | 4 |

C_{15} | 2 | 4 | 3 | 6 | 1/3 | 1/2 | 2 | 2 | 2 | 1/4 | 1 | 1/2 | 1/2 |

C_{18} | 3 | 5 | 3 | 4 | 1/2 | 1/2 | 7 | 5 | 3 | 1/2 | 2 | 1 | 2 |

C_{19} | 2 | 3 | 6 | 3 | 1/2 | 1/3 | 5 | 4 | 2 | 1/4 | 2 | 1/2 | 1 |

Inconsistency: 0.09801 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 4 | 4 | 1/2 | 3 | 2 | 7 | 4 | 6 | 3 | 2 | 4 | 3 |

C_{2} | 1/4 | 1 | 3 | 1/2 | 2 | 2 | 4 | 3 | 3 | 2 | 4 | 2 | 1/2 |

C_{3} | 1/4 | 1/3 | 1 | 1/3 | 3 | 1/2 | 2 | 1/3 | 2 | 1/2 | 1/2 | 2 | 1/2 |

C_{6} | 2 | 2 | 3 | 1 | 3 | 2 | 4 | 2 | 4 | 3 | 2 | 5 | 2 |

C_{7} | 1/3 | 1/2 | 1/3 | 1/3 | 1 | 1/2 | 2 | 1/3 | 2 | 1/2 | 3 | 2 | 1/3 |

C_{8} | 1/2 | 1/2 | 2 | 1/2 | 2 | 1 | 3 | 1/2 | 3 | 1/2 | 2 | 3 | 1/2 |

C_{9} | 1/7 | 1/4 | 1/2 | 1/4 | 1/2 | 1/3 | 1 | 1/4 | 1/2 | 1/3 | 1/2 | 1/2 | 1/4 |

C_{10} | 1/4 | 1/3 | 3 | 1/2 | 3 | 2 | 4 | 1 | 2 | 3 | 1/2 | 4 | 1/3 |

C_{11} | 1/6 | 1/3 | 1/2 | 1/4 | 1/2 | 1/3 | 2 | 1/2 | 1 | 1/2 | 1/3 | 1/2 | 1/5 |

C_{13} | 1/3 | 1/2 | 2 | 1/3 | 2 | 2 | 3 | 1/3 | 2 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/2 | 1/4 | 2 | 1/2 | 1/3 | 1/2 | 2 | 2 | 3 | 1/3 | 1 | 3 | 1/3 |

C_{18} | 1/4 | 1/2 | 1/2 | 1/5 | 1/2 | 1/3 | 2 | 1/4 | 2 | 2 | 1/3 | 1 | 1/2 |

C_{19} | 1/3 | 2 | 2 | 2 | 3 | 2 | 4 | 3 | 5 | 1/2 | 3 | 2 | 1 |

Inconsistency: 0.09084 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 5 | 4 | 3 | 1/4 | 1/4 | 1/3 | 1/4 | 4 | 1/5 | 1/4 | 1/3 | 1/2 |

C_{2} | 1/5 | 1 | 1/3 | 3 | 1/5 | 1/7 | 1/3 | 1/5 | 1/4 | 1/8 | 1/4 | 1/6 | 1/4 |

C_{3} | 1/4 | 3 | 1 | 3 | 1/5 | 1/4 | 2 | 1/2 | 3 | 1/6 | 1/3 | 1/3 | 1/6 |

C_{6} | 1/3 | 1/3 | 1/3 | 1 | 1/5 | 1/8 | 1/2 | 1/5 | 1/3 | 1/8 | 1/6 | 1/8 | 1/3 |

C_{7} | 4 | 5 | 5 | 5 | 1 | 3 | 6 | 3 | 6 | 1/2 | 4 | 2 | 3 |

C_{8} | 4 | 7 | 4 | 8 | 1/3 | 1 | 5 | 2 | 5 | 1/3 | 2 | 2 | 3 |

C_{9} | 3 | 3 | 1/2 | 2 | 1/6 | 1/5 | 1 | 1/2 | 2 | 1/8 | 1/2 | 1/7 | 1/5 |

C_{10} | 4 | 5 | 2 | 5 | 1/3 | 1/2 | 2 | 1 | 3 | 1/6 | 1/2 | 1/2 | 2 |

C_{11} | 1/4 | 4 | 1/3 | 3 | 1/6 | 1/5 | 1/2 | 1/3 | 1 | 1/8 | 1/2 | 1/5 | 1/4 |

C_{13} | 5 | 8 | 6 | 8 | 2 | 3 | 8 | 6 | 8 | 1 | 4 | 2 | 4 |

C_{15} | 4 | 4 | 3 | 6 | 1/4 | 1/2 | 2 | 2 | 2 | 1/4 | 1 | 1/2 | 1/2 |

C_{18} | 3 | 6 | 3 | 8 | 1/2 | 1/2 | 7 | 5 | 5 | 1/2 | 2 | 1 | 2 |

C_{19} | 2 | 4 | 6 | 3 | 1/3 | 1/3 | 5 | 4 | 4 | 1/4 | 2 | 1/2 | 1 |

Inconsistency: 0.08784 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 2 | 3 | 3 | 1/4 | 1/5 | 1/5 | 1/4 | 4 | 1/5 | 1/4 | 1/3 | 1/2 |

C_{2} | 1/2 | 1 | 1/3 | 3 | 1/5 | 1/7 | 1/3 | 1/5 | 1/4 | 1/8 | 1/4 | 1/6 | 1/4 |

C_{3} | 1/3 | 3 | 1 | 3 | 1/5 | 1/4 | 2 | 1/2 | 3 | 1/6 | 1/3 | 1/3 | 1/6 |

C_{6} | 1/3 | 1/3 | 1/3 | 1 | 1/4 | 1/7 | 1/2 | 1/5 | 1/3 | 1/7 | 1/5 | 1/6 | 1/4 |

C_{7} | 4 | 5 | 5 | 4 | 1 | 3 | 6 | 3 | 6 | 1/2 | 4 | 2 | 3 |

C_{8} | 5 | 7 | 4 | 7 | 1/3 | 1 | 5 | 2 | 5 | 1/3 | 2 | 2 | 3 |

C_{9} | 5 | 3 | 1/2 | 2 | 1/6 | 1/5 | 1 | 1/2 | 2 | 1/8 | 1/2 | 1/7 | 1/5 |

C_{10} | 5 | 5 | 2 | 5 | 1/3 | 1/2 | 2 | 1 | 3 | 1/6 | 1/2 | 1/2 | 2 |

C_{11} | 1/4 | 4 | 1/3 | 3 | 1/6 | 1/5 | 1/2 | 1/3 | 1 | 1/8 | 1/2 | 1/5 | 1/4 |

C_{13} | 5 | 8 | 6 | 7 | 2 | 3 | 8 | 6 | 8 | 1 | 4 | 2 | 4 |

C_{15} | 4 | 4 | 3 | 5 | 1/4 | 1/2 | 2 | 2 | 2 | 1/4 | 1 | 1/2 | 1/2 |

C_{18} | 3 | 6 | 3 | 6 | 1/2 | 1/2 | 7 | 5 | 5 | 1/2 | 2 | 1 | 2 |

C_{19} | 2 | 4 | 6 | 4 | 1/3 | 1/3 | 5 | 4 | 4 | 1/4 | 2 | 1/2 | 1 |

Inconsistency: 0.08708 |

C_{1} | C_{2} | C_{3} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{13} | C_{15} | C_{18} | C_{19} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 4 | 4 | 2 | 3 | 2 | 5 | 4 | 6 | 3 | 2 | 4 | 3 |

C_{2} | 1/4 | 1 | 3 | 1/2 | 2 | 2 | 5 | 3 | 3 | 2 | 4 | 2 | 1/2 |

C_{3} | 1/4 | 1/3 | 1 | 1/3 | 3 | 1/2 | 2 | 1/3 | 2 | 1/3 | 1/2 | 2 | 1/2 |

C_{6} | 1/2 | 2 | 3 | 1 | 3 | 2 | 4 | 2 | 4 | 3 | 2 | 5 | 2 |

C_{7} | 1/3 | 1/2 | 1/3 | 1/3 | 1 | 1/2 | 2 | 1/3 | 2 | 1/2 | 3 | 2 | 1/3 |

C_{8} | 1/2 | 1/2 | 2 | 1/2 | 2 | 1 | 3 | 1/2 | 3 | 1/2 | 2 | 3 | 1/2 |

C_{9} | 1/5 | 1/5 | 1/2 | 1/4 | 1/2 | 1/3 | 1 | 1/4 | 1/2 | 1/3 | 1/2 | 1/2 | 1/4 |

C_{10} | 1/4 | 1/3 | 3 | 1/2 | 3 | 2 | 4 | 1 | 2 | 3 | 1/2 | 4 | 1/3 |

C_{11} | 1/6 | 1/3 | 1/2 | 1/4 | 1/2 | 1/3 | 2 | 1/2 | 1 | 1/2 | 1/3 | 1/2 | 1/5 |

C_{13} | 1/3 | 1/2 | 3 | 1/3 | 2 | 2 | 3 | 1/3 | 2 | 1 | 3 | 1/2 | 2 |

C_{15} | 1/2 | 1/4 | 2 | 1/2 | 1/3 | 1/2 | 2 | 2 | 3 | 1/3 | 1 | 3 | 1/3 |

C_{18} | 1/4 | 1/2 | 1/2 | 1/5 | 1/2 | 1/3 | 2 | 1/4 | 2 | 2 | 1/3 | 1 | 1/2 |

C_{19} | 1/3 | 2 | 2 | 2 | 3 | 2 | 4 | 3 | 5 | 1/2 | 3 | 2 | 1 |

Inconsistency: 0.09114 |

## Appendix G

DMs | Alternatives | Qualitative Criteria | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | C_{12} | C_{13} | C_{14} | C_{15} | ||

D_{1} | A_{1} | H | EH | H | M | H | H | VP | VH | H | H |

A_{2} | VH | H | H | VH | H | H | VH | H | VH | M | |

A_{3} | H | H | VH | VH | H | VH | VH | H | VH | H | |

A_{4} | M | H | M | M | H | M | M | VP | EP | M | |

D_{2} | A_{1} | H | EH | M | M | H | H | P | VH | M | H |

A_{2} | H | VH | M | VH | H | H | VH | H | VH | H | |

A_{3} | M | H | H | VH | H | M | VH | H | VH | M | |

A_{4} | H | M | M | M | M | M | M | VP | P | M | |

D_{3} | A_{1} | H | EH | M | H | VH | H | P | VH | M | H |

A_{2} | EH | H | H | VH | H | H | VH | H | M | M | |

A_{3} | VH | H | H | VH | H | P | VH | H | H | H | |

A_{4} | M | M | M | M | M | H | M | P | P | M | |

D_{4} | A_{1} | H | EH | H | H | M | M | P | VH | M | H |

A_{2} | H | H | M | H | EH | P | VH | H | M | M | |

A_{3} | H | VH | H | VH | H | P | VH | H | VH | M | |

A_{4} | M | M | M | P | M | H | M | P | P | M |

## Appendix H

Alternatives | Quantitative Criteria | ||||||||
---|---|---|---|---|---|---|---|---|---|

C_{1} | C_{2} | C_{3} | |||||||

A_{1} | 2001 | 2500 | 3000 | 101 | 150 | 200 | 3 | 4 | 5 |

A_{2} | 4001 | 4500 | 5000 | 401 | 450 | 500 | 9 | 10 | 11 |

A_{3} | 3001 | 3500 | 4000 | 201 | 250 | 300 | 6 | 7 | 8 |

A_{4} | 1001 | 1500 | 2000 | 101 | 150 | 200 | 6 | 7 | 8 |

## References

- Peterson, R.; Valliere, D. Entrepreneurship and National Economic Growth: The European Entrepreneurial Deficit. Eur. J. Int. Manag.
**2008**, 2, 471. [Google Scholar] [CrossRef] - Vandenberg, P.; Hampel-Milagrosa, A.; Helble, M. Financing of Tech Startups in Selected Asian Countries. Tokyo ADBI 2020. Available online: https://www.adb.org/publications/financing-tech-startups-selected-asian-countries (accessed on 24 May 2020).
- Stam, E. Entrepreneurial Ecosystems and Regional Policy: A Sympathetic Critique. Eur. Plan. Stud.
**2015**, 23, 1759–1769. [Google Scholar] [CrossRef] [Green Version] - Chang, C. Portfolio Company Selection Criteria: Accelerators vs. Venture Capitalists. CMC Senior Theses. 2013. Available online: http://scholarship.claremont.edu/cmc_theses/566 (accessed on 6 May 2013).
- Yin, B.; Luo, J. How Do Accelerators Select Startups? Shifting Decision Criteria Across Stages. IEEE Trans. Eng. Manag.
**2018**, 65, 574–589. [Google Scholar] [CrossRef] - Amezcua, A.S.; Grimes, M.G.; Bradley, S.W.; Wiklund, J. Organizational Sponsorship and Founding Environments: A Contingency View on the Survival of Business-Incubated Firms, 1994–2007. Acad. Manag. J.
**2013**, 56, 1628–1654. [Google Scholar] [CrossRef] - Lin, M.; Chen, Z.; Chen, R.; Fujita, H. Evaluation of Startup Companies Using Multicriteria Decision Making Based on Hesitant Fuzzy Linguistic Information Envelopment Analysis Models. Int. J. Intell. Syst.
**2021**, 36, 2292–2322. [Google Scholar] [CrossRef] - Kahraman, C.; Onar, S.C.; Oztaysi, B. Fuzzy Multicriteria Decision-Making: A Literature Review. Int. J. Comput. Intell. Syst.
**2015**, 8, 637. [Google Scholar] [CrossRef] [Green Version] - Liu, J.; Yin, Y. An Integrated Method for Sustainable Energy Storing Node Optimization Selection in China. Energy Convers. Manag.
**2019**, 199, 112049. [Google Scholar] [CrossRef] - Drori, I.; Wright, M. Accelerators: Characteristics, Trends and the New Entrepreneurial Ecosystem; Edward Elgar Publishing: Cheltenham, UK, 2018. [Google Scholar] [CrossRef] [Green Version]
- Seed-DB. Seed-DB Charts and Tables. Available online: https://www.seed-db.com/accelerators (accessed on 19 April 2023).
- 500startups. 2021. Available online: https://500.co/accelerators/500-global-flagship-accelerator-program (accessed on 22 December 2021).
- Butz, H.; Mrożewski, M.J. The Selection Process and Criteria of Impact Accelerators. An Exploratory Study. Sustainability
**2021**, 13, 6617. [Google Scholar] [CrossRef] - Garrido, T.M.; de Lema, D.G.P.; Duréndez, A. Assessment Criteria for Seed Accelerators in Entrepreneurial Project Selections. Int. J. Entrep. Innov.
**2020**, 24, 53. [Google Scholar] [CrossRef] - Majumdar, R.; Mittal, A. Startup Financing: Some Evidence from the Indian Venture Capital Industry. FIIB Bus. Rev.
**2023**, 23197145221142109. [Google Scholar] [CrossRef] - Sreenivasan, A.; Suresh, M. Agility Adaptability and Alignment in Start-Ups. J. Sci. Technol. Policy Manag. 2023. [CrossRef]
- Honoré, F.; Ganco, M. Entrepreneurial Teams’ Acquisition of Talent: Evidence from Technology Manufacturing Industries Using a Two-sided Approach. Strateg. Manag. J.
**2020**, 44, 141–170. [Google Scholar] [CrossRef] - Zavadskas, E.K.; Turskis, Z.; Kildienė, S. State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Econ.
**2014**, 20, 165–179. [Google Scholar] [CrossRef] [Green Version] - Kumar, A.; Sah, B.; Singh, A.R.; Deng, Y.; He, X.; Kumar, P.; Bansal, R.C. A Review of Multi Criteria Decision Making (MCDM) towards Sustainable Renewable Energy Development. Renew. Sust. Energ. Rev.
**2017**, 69, 596–609. [Google Scholar] [CrossRef] - Stojčić, M.; Zavadskas, E.; Pamučar, D.; Stević, Ž.; Mardani, A. Application of MCDM Methods in Sustainability Engineering: A Literature Review 2008–2018. Symmetry
**2019**, 11, 350. [Google Scholar] [CrossRef] [Green Version] - Jamwal, A.; Agrawal, R.; Sharma, M.; Kumar, V. Review on Multi-Criteria Decision Analysis in Sustainable Manufacturing Decision Making. Int. J. Sustain. Eng.
**2020**, 14, 202–225. [Google Scholar] [CrossRef] - Gabus, A.; Fontela, E. World Problems, an Invitation to Further Thought within the Framework of DEMATEL; Battelle Geneva Research Center: Geneva, Switzerland, 1972; pp. 1–8. [Google Scholar]
- Fontela, E.; Gabus, A. The DEMATEL Observer; DEMATEL 1976 report; Battelle Geneva Research Center: Geneva, Switzerland, 1976. [Google Scholar]
- Moraga, J.A.; Quezada, L.E.; Palominos, P.I.; Oddershede, A.M.; Silva, H.A. A Quantitative Methodology to Enhance a Strategy Map. Int. J. Prod. Econ.
**2020**, 219, 43–53. [Google Scholar] [CrossRef] - Altuntas, F.; Gok, M.S. The Effect of COVID-19 Pandemic on Domestic Tourism: A DEMATEL Method Analysis on Quarantine Decisions. Int. J. Hosp. Manag.
**2021**, 92, 102719. [Google Scholar] [CrossRef] [PubMed] - Wang, Y.; Qi, L.; Dou, R.; Shen, S.; Hou, L.; Liu, Y.; Yang, Y.; Kong, L. An Accuracy-Enhanced Group Recommendation Approach Based on DEMATEL. Pattern Recognit. Lett.
**2023**, 167, 171–180. [Google Scholar] [CrossRef] - Si, S.-L.; You, X.-Y.; Liu, H.-C.; Zhang, P. DEMATEL Technique: A Systematic Review of the State-of-the-Art Literature on Methodologies and Applications. Math. Probl. Eng.
**2018**, 2018, 1–33. [Google Scholar] [CrossRef] [Green Version] - Saaty, T.L.; Vargas, L.G. The Analytic Network Process, Decision Making with the Analytic Network Process; Springer: Berlin, Germany, 2013; pp. 1–40. [Google Scholar]
- Saaty, T.L. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation; McGraw-Hill International Book Company: New York, NY, USA, 1980. [Google Scholar]
- Saaty, T.L. The Analytic Network Process: Decision Making with Dependence and Feedback, 2nd ed.; RWS Publications: Pittsburgh, PA, USA, 2001. [Google Scholar]
- Saaty, T.L. Theory and Applications of the Analytic Network Process: Decision Making with Benefits, Opportunities, Costs, and Risks; RWS Publications: Pittsburgh, PA, USA, 2005. [Google Scholar]
- Yu, D.; Kou, G.; Xu, Z.; Shi, S. Analysis of Collaboration Evolution in AHP Research: 1982–2018. Int. J. Inf. Technol. Decis. Mak.
**2021**, 20, 7–36. [Google Scholar] [CrossRef] - Rahiminezhad Galankashi, M.; Mokhatab Rafiei, F.; Ghezelbash, M. Portfolio Selection: A Fuzzy-ANP Approach. Financ. Innov
**2020**, 6, 17. [Google Scholar] [CrossRef] [Green Version] - Saputro, K.E.A.; Hasim; Karlinasari, L.; Beik, I.S. Evaluation of Sustainable Rural Tourism Development with an Integrated Approach Using MDS and ANP Methods: Case Study in Ciamis, West Java, Indonesia. Sustainability
**2023**, 15, 1835. [Google Scholar] [CrossRef] - Kadoić, N. Characteristics of the Analytic Network Process, a Multi-Criteria Decision-Making Method. Croat. Oper. Res. Rev.
**2018**, 9, 235–244. [Google Scholar] [CrossRef] [Green Version] - Zheng, Y.; He, Y.; Xu, Z.; Pedrycz, W. Assessment for Hierarchical Medical Policy Proposals Using Hesitant Fuzzy Linguistic Analytic Network Process. Knowl. Based Syst.
**2018**, 161, 254–267. [Google Scholar] [CrossRef] - Brans, J.P. Lingenierie de La Decision. Elaboration Dinstruments Daide a La Decision. Methode PROMETHEE. In Laide a la Decision: Nature, Instruments et Perspectives Davenir; Nadeau, R., Landry, M., Eds.; Presses de Universite Laval: Québec, QC, Canada, 1982; pp. 183–214. [Google Scholar]
- Brans, J.P.; Vincke, P. Note—A Preference Ranking Organisation Method. Manage Sci.
**1985**, 31, 647–656. [Google Scholar] [CrossRef] [Green Version] - Brans, J.-P. The Space of Freedom of the Decision Maker Modelling the Human Brain. Eur. J. Oper. Res.
**1996**, 92, 593–602. [Google Scholar] [CrossRef] - Seikh, M.R.; Mandal, U. Interval-Valued Fermatean Fuzzy Dombi Aggregation Operators and SWARA Based PROMETHEE II Method to Bio-Medical Waste Management. Expert Syst. Appl.
**2023**, 226, 120082. [Google Scholar] [CrossRef] - Khorasaninejad, E.; Fetanat, A.; Hajabdollahi, H. Prime Mover Selection in Thermal Power Plant Integrated with Organic Rankine Cycle for Waste Heat Recovery Using a Novel Multi Criteria Decision Making Approach. Appl. Therm. Eng.
**2016**, 102, 1262–1279. [Google Scholar] [CrossRef] - Govindan, K.; Kannan, D.; Shankar, M. Evaluation of Green Manufacturing Practices Using a Hybrid MCDM Model Combining DANP with PROMETHEE. Int. J. Prod. Res.
**2014**, 53, 6344–6371. [Google Scholar] [CrossRef] - Hua, Z.; Jing, X. A Generalized Shapley Index-Based Interval-Valued Pythagorean Fuzzy PROMETHEE Method for Group Decision-Making. Soft Comput.
**2023**, 27, 6629–6652. [Google Scholar] [CrossRef] - Zadeh, L.A. Fuzzy Sets. Inf. Control.
**1965**, 8, 338–353. [Google Scholar] [CrossRef] [Green Version] - Al-Tahan, M.; Hoskova-Mayerova, S.; Al-Kaseasbeh, S.; Tahhan, S.A. Linear Diophantine Fuzzy Subspaces of a Vector Space. Mathematics
**2023**, 11, 503. [Google Scholar] [CrossRef] - Ardil, C. Aircraft Supplier Selection Using Multiple Criteria Group Decision Making Process with Proximity Measure Method for Determinate Fuzzy Set Ranking Analysis. Int. J. Ind. Syst. Eng.
**2023**, 17, 127–135. [Google Scholar] - Karmaker, C.L.; Aziz, R.A.; Palit, T.; Bari, A.B.M.M. Analyzing Supply Chain Risk Factors in the Small and Medium Enterprises under Fuzzy Environment: Implications towards Sustainability for Emerging Economies. Sustain. Technol. Entrep.
**2023**, 2, 100032. [Google Scholar] [CrossRef] - Kahraman, C.; Öztaysi, B.; Onar, S.C. A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory. Int. J. Comput. Intell. Syst.
**2016**, 9 (Suppl. S1), 3. [Google Scholar] [CrossRef] [Green Version] - Jain, R. Decision-making in the Presence of Fuzzy Variables. IEEE Trans. Syst. Man Cybern. Syst.
**1976**, SMC-6, 698–703. [Google Scholar] [CrossRef] - Dubois, D.; Prade, H. Ranking Fuzzy Numbers in the Setting of Possibility Theory. Inf. Sci.
**1983**, 30, 183–224. [Google Scholar] [CrossRef] - Chen, S.-H. Ranking Fuzzy Numbers with Maximizing Set and Minimizing Set. Fuzzy Sets Syst.
**1985**, 17, 113–129. [Google Scholar] [CrossRef] - Fortemps, P.; Roubens, M. Ranking and Defuzzification Methods Based on Area Compensation. Fuzzy Sets Syst.
**1996**, 82, 319–330. [Google Scholar] [CrossRef] - Deng, Y.; Zhenfu, Z.; Qi, L. Ranking Fuzzy Numbers with an Area Method Using Radius of Gyration. Comput. Math. Appl.
**2006**, 51, 1127–1136. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.-X.; Liu, Y.-J.; Fan, Z.-P.; Feng, B. Ranking L–R Fuzzy Number Based on Deviation Degree. Inf. Sci.
**2009**, 179, 2070–2077. [Google Scholar] [CrossRef] - Chen, S.-M.; Chen, J.-H. Fuzzy Risk Analysis Based on Ranking Generalized Fuzzy Numbers with Different Heights and Different Spreads. Expert Syst. Appl.
**2009**, 36, 6833–6842. [Google Scholar] [CrossRef] - Nguyen, H.T.; Chu, T.-C. Using a Fuzzy Multiple Criteria Decision-Making Method to Evaluate Personal Diversity Perception to Work in a Diverse Workgroup. J. Intell. Fuzzy Syst.
**2021**, 41, 1407–1428. [Google Scholar] [CrossRef] - Wang, Y.-M.; Luo, Y. Area Ranking of Fuzzy Numbers Based on Positive and Negative Ideal Points. Comput. Math. Appl.
**2009**, 58, 1769–1779. [Google Scholar] [CrossRef] [Green Version] - Asady, B. The Revised Method of Ranking LR Fuzzy Number Based on Deviation Degree. Expert Syst. Appl.
**2010**, 37, 5056–5060. [Google Scholar] [CrossRef] - Nejad, A.M.; Mashinchi, M. Ranking Fuzzy Numbers Based on the Areas on the Left and the Right Sides of Fuzzy Number. Comput. Math. Appl.
**2011**, 61, 431–442. [Google Scholar] [CrossRef] - Yu, V.F.; Chi, H.T.X.; Shen, C. Ranking Fuzzy Numbers Based on Epsilon-Deviation Degree. Appl. Soft Comput.
**2013**, 13, 3621–3627. [Google Scholar] [CrossRef] [Green Version] - Chutia, R. Ranking of Fuzzy Numbers by Using Value and Angle in the Epsilon-Deviation Degree Method. Appl. Soft Comput.
**2017**, 60, 706–721. [Google Scholar] [CrossRef] - Ghasemi, R.; Nikfar, M.; Roghanian, E. A Revision on Area Ranking and Deviation Degree Methods of Ranking Fuzzy Numbers. Sci. Iran.
**2015**, 22, 1142–1154. [Google Scholar] - Chu, T.-C.; Nguyen, H.T. Ranking Alternatives with Relative Maximizing and Minimizing Sets in a Fuzzy MCDM Model. Int. J. Fuzzy Syst.
**2019**, 21, 1170–1186. [Google Scholar] [CrossRef] - Kaufman, A.; Gupta, M.M. Introduction to Fuzzy Arithmetic; Van Nostrand Reinhold Company: New York, NY, USA, 1991. [Google Scholar]
- Zadeh, L.A. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Trans. Syst. Man Cybern. Syst.
**1973**, SMC-3, 28–44. [Google Scholar] [CrossRef] [Green Version] - Yeh, C.-H.; Kuo, Y.-L. Evaluating Passenger Services of Asia-Pacific International Airports. Transp. Res. Part E Logist. Transp. Rev.
**2003**, 39, 35–48. [Google Scholar] [CrossRef] - Huang, C.-Y.; Shyu, J.Z.; Tzeng, G.-H. Reconfiguring the Innovation Policy Portfolios for Taiwan’s SIP Mall Industry. Technovation
**2007**, 27, 744–765. [Google Scholar] [CrossRef] - Tzeng, G.; Chiang, C.; Li, C. Evaluating Intertwined Effects in E-Learning Programs: A Novel Hybrid MCDM Model Based on Factor Analysis and DEMATEL. Expert Syst. Appl.
**2007**, 32, 1028–1044. [Google Scholar] [CrossRef] - Chien, K.-F.; Wu, Z.-H.; Huang, S.-C. Identifying and Assessing Critical Risk Factors for BIM Projects: Empirical Study. Autom. Constr.
**2014**, 45, 1–15. [Google Scholar] [CrossRef] - Lin, W.-R.; Wang, Y.-H.; Hung, Y.-M. Analyzing the Factors Influencing Adoption Intention of Internet Banking: Applying DEMATEL-ANP-SEM Approach. PLoS ONE
**2020**, 15, e0227852. [Google Scholar] [CrossRef] - Farman, H.; Javed, H.; Jan, B.; Ahmad, J.; Ali, S.; Khalil, F.N.; Khan, M. Analytical Network Process Based Optimum Cluster Head Selection in Wireless Sensor Network. PLoS ONE
**2017**, 12, e0180848. [Google Scholar] [CrossRef] - Geldermann, J.; Spengler, T.; Rentz, O. Fuzzy Outranking for Environmental Assessment. Case Study: Iron and Steel Making Industry. Fuzzy Sets Syst.
**2000**, 115, 45–65. [Google Scholar] [CrossRef] - Maity, S.R.; Chakraborty, S. Tool Steel Material Selection Using PROMETHEE II Method. Int. J. Adv. Manuf. Technol.
**2015**, 78, 1537–1547. [Google Scholar] [CrossRef]

Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

R.I | 0 | 0 | 0.52 | 0.89 | 1.11 | 1.25 | 1.35 | 1.40 | 1.45 | 1.49 |

**Table 2.**Modified comparison based on Examples 2, 3, and 4 from Nejad and Mashinchi [59].

Situations | Methods | Results | Results after Adding New FNs | |
---|---|---|---|---|

(1) | (1.1) ${A}_{4}=(-3,-2,-1)$ | (1.2) ${A}_{4}=(8.75,9.5,11)$ | ||

${A}_{1}=(2,3,5,6)$ ${A}_{2}=(1,4,7)$ ${A}_{3}=(4,5,7)$ | [54] | ${A}_{1}={A}_{2}\prec {A}_{3}$ | ${A}_{2}\prec {A}_{1}\prec {A}_{3}$ | ${A}_{1}={A}_{2}\prec {A}_{3}$ |

[59] | ${A}_{1}={A}_{2}\prec {A}_{3}$ | ${A}_{1}={A}_{2}\prec {A}_{3}$ | ${A}_{1}={A}_{2}\prec {A}_{3}$ | |

Proposed method | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | |

(2) | (2.1) ${A}_{4}=(-1.5,-0.8,-0.6)$ | (2.2) ${A}_{4}=(1.15,2.5,3.15)$ | ||

${A}_{1}=(0.2,0.5,0.8)$ ${A}_{2}=(0.4,0.5,0.6)$ | [54] | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}={A}_{2}$ |

[59] | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | |

Proposed method | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | |

(3) | ${A}_{1}\succ {A}_{2}$ | (3.1) ${A}_{4}=(-5,-4,-3,-1)$ | (3.2) ${A}_{4}=(6,6,7,8)$ | |

${A}_{1}=(1,2,5)$ ${A}_{2}=(1,2,2,4)$ | [54] | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}={A}_{2}$ |

[59] | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{2}$ | ||

Proposed method | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{2}$ |

Situations | Methods | Results | Results after Adding New FNs | |
---|---|---|---|---|

(1) | (1.1) ${A}_{5}=(-5,-4,-3)$ | (1.2) ${A}_{5}=(8,9,10)$ | ||

${A}_{1}=(3,3,3)$ ${A}_{2}=(3,3,6)$ ${A}_{3}=(3,3,8)$ ${A}_{4}=(3,3,6,8)$ | [54] | ${A}_{1}={A}_{2}={A}_{3}={A}_{4}$ | ${A}_{1}={A}_{2}={A}_{3}={A}_{4}$ | ${A}_{1}={A}_{2}={A}_{3}={A}_{4}$ |

[59] | ${A}_{1}={A}_{2}={A}_{3}={A}_{4}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}\prec {A}_{4}$ | ${A}_{1}={A}_{2}={A}_{3}={A}_{4}$ | |

Proposed method | ${A}_{1}\prec {A}_{2}\prec {A}_{3}\prec {A}_{4}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}\prec {A}_{4}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}\prec {A}_{4}$ | |

(2) | (2.1) ${A}_{4}=(-7,-5,-3,-2)$ | (2.2) ${A}_{4}=(7,9,11,12)$ | ||

${A}_{1}=(3,3,3)$ ${A}_{2}=(3,3,6)$ ${A}_{3}=(3,3,5,6)$ | [54] | ${A}_{1}={A}_{2}={A}_{3}$ | ${A}_{1}={A}_{2}={A}_{3}$ | ${A}_{1}={A}_{2}={A}_{3}$ |

[59] | ${A}_{1}={A}_{2}={A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}={A}_{2}={A}_{3}$ | |

Proposed method | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | |

(3) | (3.1) ${A}_{3}=(-4,-2.5,-1.5)$ | (3.2) ${A}_{3}=(6,7.8,8.5)$ | ||

${A}_{1}=(2,2,7)$ ${A}_{2}=(2,4,4)$ | [54] | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ |

[59] | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\succ {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | |

Proposed method | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ |

**Table 4.**Numerical comparison with Chu and Nguyen [63].

Situations | Methods | Results | Results after Adding New FNs | |
---|---|---|---|---|

(1) | (1.1) ${A}_{3}=(1,4,5)$ | (1.2) ${A}_{3}=(-3,-2,-1)$ | ||

${A}_{1}=(1,3,5)$ ${A}_{2}=(2,3,4)$ | [63] | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ |

Proposed method | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | |

(2) | (2.1) ${A}_{3}=(2,3,7)$ | (2.2) ${A}_{3}=(-4,-2,-2)$ | ||

${A}_{1}=(2,2,4)$ ${A}_{2}=(2,2,6)$ | [63] | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ | ${A}_{1}={A}_{2}$ |

Proposed method | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ | ${A}_{1}\prec {A}_{2}$ |

µ | Examples | ||
---|---|---|---|

(1) Three FNs ${\mathit{A}}_{1}=(2,3,5,6)$, ${\mathit{A}}_{2}=(1,4,7)$ ${\mathit{A}}_{3}=(4,5,7)$ | (2) Add an FN to the Right Side ${\mathit{A}}_{1}=(2,3,5,6)$, ${\mathit{A}}_{2}=(1,4,7)$ ${\mathit{A}}_{3}=(4,5,7)$, ${\mathit{A}}_{4}=(8,9,10)$ | (3) Add an FN to the Left Side ${\mathit{A}}_{1}=(2,3,5,6)$, ${\mathit{A}}_{2}=(1,4,7)$ ${\mathit{A}}_{3}=(4,5,7)$, ${\mathit{A}}_{4}=(-3,-2,-1)$ | |

0.1 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.2 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.3 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.4 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.5 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.6 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.7 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.8 | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ | ${A}_{1}\prec {A}_{2}\prec {A}_{3}$ |

0.9 | ${A}_{1}$ |