# Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methods

#### 3.1. R’DEMATEL Method

_{ij}

^{e}, where i = 1, 2, …, n; j = 1, 2, …, n. The value of each x

_{ij}

^{e}set takes one integer value of the following point scale: 0—no influence, 1—low influence, 2—moderate influence, 3—high influence, 4—very high influence. The response of the e-expert is expressed by the nonnegative matrix of the nxn range, whereas each element of the e-matrix in the expression X

^{e}= [x

^{e}

_{ij}]

_{n×n}presents integer nonnegative number x

_{ij}

^{e}, where 1 ≤ e ≤ m.

_{ij}

^{e}presents linguistic expressions from the previously defined linguistic scale used by the expert to present his comparison in the set of the criteria.

^{1}, X

^{2},…, X

^{m}are response matrices of the each of m experts. The diagonal elements of the response matrices of all experts take value zero because the same factors have no influence.

^{e}= [x

^{e}

_{ij}]

_{n×n}(1 ≤ e ≤ m) of all m experts, we obtain aggregate sequence matrix of experts X*.

^{1}, X

^{2},…, X

^{m}(where m is the number of the experts). In this way, for the group of rough matrices X

^{1}, X

^{2},…, X

^{m}on the position (ij) we obtain rough sequence $RN\left({x}_{ij}\right)=\left\{\left[\underset{\xaf}{Lim}({x}_{ij}^{1}),\text{}\overline{Lim}({x}_{ij}^{1})\right],\text{}\left[\underset{\xaf}{Lim}({x}_{ij}^{2}),\text{}\overline{Lim}({x}_{ij}^{2})\right],\cdots ,\left[\underset{\xaf}{Lim}({x}_{ij}^{m}),\text{}\overline{Lim}({x}_{ij}^{m})\right]\right\}$.

_{i}to the sum of columns C

_{i}in the total relation matrix T need to be converted into the crisp forms ${R}_{i}^{crisp}$ and ${C}_{i}^{crisp}$ by applying Equations (14)–(16).

_{ij}with values higher than a threshold value α, are chosen to present cause-and-effect relations.

#### 3.2. Rough EDAS Method

_{1}, k

_{2}, …, k

_{n}then the group rough matrix is obtained according to Zhai et al. [109]:

_{j}

^{L}and w

_{j}

^{U}are lower and upper limit of the criteria weight expressed as rough number.

## 4. Case Study

#### 4.1. Estimation of the Criteria Weight by Applying R’DEMATEL Method

#### 4.2. Supplier Selection Using Rough EDAS Method

## 5. Sensitivity Analysis and Discussion

_{k}). The comparison of the ranges was performed through mutual comparison of all 10 hybrid models (Table 15).

_{k}is 0.893. The least values of the correlation are obtained by comparison of the ranges R’A-R-MAIRCA model with R’D-R-MAIRCA, R’D-R-MULTIMOORA, R’D-R-COPRAS, and R’D-R-MABAC models, where the obtained values of r

_{k}are 0.657, 0.600, 0.600, and 0.657, respectively. The similar values are also obtained by comparison of R’A-R-COPRAS and R’A-R-MABAC with R’A-R-MAIRCA, R’D-R-MULTIMOORA, R’D-R-COPRAS, and R’D-R-MABAC models. These variations in r

_{k}values arise from application of different approaches for estimation of the weight coefficients. So, the obtained values of the weight coefficients have further influenced the changes in the ranges of the observed models. Therefore, in further analysis, we grouped the models using the same approaches for evaluation of the weight coefficients (R’AHP and R’DEMATEL) and analyzed their mutual correlation. So, for R’AHP model we obtain average r

_{k}= 0.951, while for R’DEMATEL model, we obtain r

_{k}> = 0.962. Taking into account that all values of r

_{k}in the frame of approaches (R’AHP and R’DEMATEL) are considerably higher than 0.8, as well as the average value of r

_{k}is 0.893, we can conclude that there is a very high correlation of the ranges, and that the proposed model has been confirmed.

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

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Criteria | References |
---|---|

Quality of material | [6,21,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] |

Price of material | [6,21,26,27,28,29,30,31,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] |

Certification of products | [26,31,40,42,44,50,52,57] |

Delivery time | [21,26,27,28,29,30,31,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,51,53,54,55,56,58] |

Reputation | [6,21,26,28,29,34,36,43,46,48,49,54,55,58,59,60] |

Volume discounts | [37,40,42] |

Warranty period | [21,26,31,35,37,40] |

Reliability | [6,26,30,33,34,36,42,48,50,51,54,56,57,60] |

Method of payment | [26,38,39,40,44,45,47,57] |

E_{1} | E_{2} | |||||||||||||||||

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

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

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

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

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

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

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

C_{7} | 4 | 4 | 3 | 4 | 2 | 4 | 0 | 5 | 5 | 4 | 2 | 4 | 5 | 2 | 5 | 0 | 5 | 5 |

C_{8} | 3 | 3 | 4 | 2 | 1 | 2 | 2 | 0 | 3 | 4 | 2 | 5 | 4 | 1 | 4 | 2 | 0 | 3 |

C_{9} | 3 | 3 | 4 | 2 | 2 | 2 | 3 | 3 | 0 | 3 | 1 | 4 | 3 | 2 | 4 | 3 | 3 | 0 |

… | ||||||||||||||||||

E_{6} | E_{7} | |||||||||||||||||

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

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

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

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

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

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

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

C_{7} | 5 | 3 | 3 | 4 | 2 | 3 | 0 | 3 | 5 | 4 | 3 | 3 | 5 | 2 | 4 | 0 | 5 | 4 |

C_{8} | 4 | 3 | 4 | 2 | 1 | 3 | 1 | 0 | 4 | 3 | 3 | 4 | 4 | 1 | 5 | 2 | 0 | 3 |

C_{9} | 3 | 3 | 4 | 2 | 1 | 3 | 3 | 5 | 0 | 2 | 3 | 5 | 3 | 1 | 5 | 3 | 4 | 0 |

Criterion | ${\mathit{R}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$ | ${\mathit{C}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$ | ${\mathit{R}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$+${\mathit{C}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$ | ${\mathit{R}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$−${\mathit{C}}_{\mathit{i}}^{\mathit{c}\mathit{r}\mathit{i}\mathit{s}\mathit{p}}$ |
---|---|---|---|---|

C_{1} | 14.201 | 12.939 | 27.141 | 1.262 |

C_{2} | 10.678 | 11.270 | 21.948 | −0.592 |

C_{3} | 11.663 | 14.171 | 25.835 | −2.508 |

C_{4} | 11.708 | 14.628 | 26.336 | −2.920 |

C_{5} | 15.157 | 5.545 | 20.702 | 9.612 |

C_{6} | 10.105 | 14.642 | 24.747 | −4.538 |

C_{7} | 12.624 | 9.870 | 22.495 | 2.754 |

C_{8} | 9.290 | 13.360 | 22.650 | −4.070 |

C_{9} | 9.919 | 12.082 | 22.000 | −2.163 |

Criterion | $\mathit{R}\mathit{N}({\mathit{R}}_{\mathit{i}})$ | $\mathit{R}\mathit{N}({\mathit{C}}_{\mathit{i}})$ | $\mathit{R}\mathit{N}({\mathit{R}}_{\mathit{i}})$+$\mathit{R}\mathit{N}({\mathit{C}}_{\mathit{i}})$ | $\mathit{R}\mathit{N}({\mathit{R}}_{\mathit{i}})$−$\mathit{R}\mathit{N}({\mathit{C}}_{\mathit{i}})$ |
---|---|---|---|---|

C1 | [2.740, 25.844] | [2.551, 23.891] | [5.292, 49.734] | [−21.150, 23.292] |

C2 | [2.190, 21.469] | [2.067, 22.051] | [4.257, 43.521] | [−19.861, 19.402] |

C3 | [2.278, 22.797] | [2.779, 25.344] | [5.057, 48.141] | [−23.067, 20.018] |

C4 | [2.424, 22.705] | [2.541, 26.193] | [4.964, 48.898] | [−23.770, 20.164] |

C5 | [2.841, 27.027] | [1.387, 13.850] | [4.228, 40.876] | [−11.008, 25.640] |

C6 | [2.122, 20.699] | [2.477, 26.275] | [4.599, 46.975] | [−24.153, 18.223] |

C7 | [2.522, 23.897] | [2.171, 19.896] | [4.693, 43.793] | [−17.374, 21.725] |

C8 | [1.935, 19.686] | [2.554, 24.467] | [4.488, 44.153] | [−22.532, 17.133] |

C9 | [1.939, 20.628] | [2.464, 22.784] | [4.403, 43.412] | [−20.845, 18.164] |

E_{1} | E_{2} | |||||||||||||||||

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

A_{1} | 7 | 1 | 3 | 9 | 1 | 3 | 5 | 3 | 3 | 9 | 1 | 3 | 7 | 9 | 7 | 5 | 9 | 7 |

A_{2} | 7 | 3 | 7 | 9 | 3 | 5 | 5 | 5 | 3 | 7 | 3 | 9 | 5 | 7 | 7 | 5 | 7 | 5 |

A_{3} | 5 | 7 | 7 | 5 | 7 | 7 | 7 | 5 | 7 | 3 | 9 | 7 | 1 | 5 | 5 | 7 | 5 | 5 |

A_{4} | 5 | 3 | 3 | 5 | 7 | 3 | 9 | 5 | 5 | 3 | 7 | 3 | 1 | 5 | 3 | 7 | 5 | 5 |

A_{5} | 5 | 9 | 9 | 3 | 7 | 5 | 9 | 5 | 7 | 3 | 9 | 9 | 1 | 5 | 5 | 9 | 5 | 5 |

A_{6} | 3 | 7 | 7 | 3 | 5 | 3 | 3 | 3 | 3 | 5 | 7 | 7 | 3 | 5 | 5 | 3 | 5 | 3 |

E_{3} | E_{4} | |||||||||||||||||

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

A_{1} | 3 | 1 | 1 | 9 | 1 | 3 | 3 | 1 | 3 | 5 | 3 | 3 | 9 | 3 | 1 | 3 | 1 | 1 |

A_{2} | 3 | 3 | 5 | 9 | 3 | 5 | 5 | 3 | 1 | 5 | 1 | 5 | 7 | 5 | 3 | 1 | 1 | 3 |

A_{3} | 5 | 3 | 3 | 7 | 7 | 3 | 5 | 3 | 3 | 7 | 5 | 5 | 7 | 5 | 5 | 3 | 3 | 5 |

A_{4} | 5 | 5 | 1 | 7 | 5 | 5 | 3 | 3 | 5 | 7 | 3 | 3 | 5 | 5 | 3 | 3 | 3 | 3 |

A_{5} | 5 | 5 | 5 | 5 | 9 | 7 | 5 | 5 | 5 | 3 | 5 | 7 | 5 | 7 | 7 | 3 | 5 | 5 |

A_{6} | 3 | 7 | 3 | 5 | 3 | 3 | 3 | 3 | 7 | 5 | 5 | 5 | 5 | 3 | 5 | 3 | 5 | 7 |

E_{5} | E_{6} | |||||||||||||||||

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

A_{1} | 7 | 1 | 1 | 9 | 3 | 7 | 5 | 7 | 7 | 5 | 3 | 3 | 9 | 1 | 5 | 3 | 5 | 5 |

A_{2} | 7 | 3 | 7 | 9 | 5 | 7 | 5 | 9 | 5 | 5 | 3 | 7 | 9 | 1 | 3 | 5 | 5 | 5 |

A_{3} | 5 | 7 | 5 | 5 | 9 | 9 | 7 | 9 | 7 | 5 | 5 | 7 | 7 | 9 | 7 | 5 | 7 | 3 |

A_{4} | 5 | 5 | 1 | 5 | 9 | 9 | 9 | 9 | 9 | 3 | 3 | 3 | 7 | 7 | 5 | 3 | 5 | 5 |

A_{5} | 5 | 9 | 9 | 1 | 9 | 5 | 9 | 9 | 9 | 7 | 5 | 9 | 7 | 9 | 7 | 5 | 7 | 3 |

A_{6} | 3 | 7 | 7 | 3 | 7 | 7 | 3 | 7 | 3 | 5 | 5 | 7 | 7 | 1 | 5 | 3 | 5 | 5 |

E_{7} | ||||||||||||||||||

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

A_{1} | 5 | 3 | 3 | 9 | 1 | 5 | 3 | 5 | 7 | |||||||||

A_{2} | 5 | 3 | 7 | 9 | 1 | 7 | 5 | 5 | 5 | |||||||||

A_{3} | 5 | 5 | 7 | 7 | 9 | 7 | 5 | 7 | 5 | |||||||||

A_{4} | 5 | 3 | 3 | 7 | 7 | 5 | 3 | 5 | 7 | |||||||||

A_{5} | 5 | 5 | 9 | 7 | 9 | 3 | 5 | 7 | 7 | |||||||||

A_{6} | 5 | 5 | 7 | 7 | 1 | 5 | 3 | 5 | 7 |

A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | |
---|---|---|---|---|---|---|

C_{1} | [4.72, 7.03] | [4.74, 6.37] | [4.48, 5.52] | [4.00, 5.43] | [4.00, 5.43] | [3.65, 4.63] |

C_{2} | [1.37, 2.35] | [2.47, 2.96] | [4.72, 7.03] | [3.35, 4.99] | [5.73, 7.69] | [5.65, 6.63] |

C_{3} | [2.02, 2.84] | [6.00, 7.43] | [5.01, 6.65] | [2.02, 2.84] | [7.39, 8.83] | [5.39, 6.83] |

C_{4} | [8.47, 8.96] | [7.39, 8.83] | [4.37, 6.60] | [4.12, 6.33] | [2.56, 5.67] | [3.72, 5.73] |

C_{5} | [1.44, 4.26] | [2.22, 4.95] | [6.27, 8.28] | [5.63, 7.26] | [7.01, 8.65] | [3.05, 5.78] |

C_{6} | [3.05, 5.78] | [4.09, 5.91] | [4.97, 7.28] | [3.67, 5.88] | [4.74, 6.37] | [4.00, 5.43] |

C_{7} | [3.37, 4.35] | [3.94, 4.92] | [4.74, 6.37] | [3.77, 6.78] | [5.11, 7.78] | [3.00, 3.00] |

C_{8} | [2.54, 6.38] | [3.39, 6.61] | [4.22, 6.95] | [4.05, 6.03] | [5.35, 6.99] | [4.00, 5.43] |

C_{9} | [3.26, 6.12] | [3.01, 4.65] | [4.09, 5.91] | [4.57, 6.65] | [4.72, 7.03] | [3.93, 6.07] |

PDA | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0.18 | 0.92 | 0.17 | 0.74 | 0.22 | 0.51 | 0.30 | 0.49 | 0.30 | 0.49 | 0.00 | 0.00 |

C_{2} | 0.19 | 1.17 | 0.07 | 0.84 | 0.00 | 0.00 | 0.32 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{3} | 0.00 | 0.00 | 0.02 | 0.87 | 0.15 | 0.67 | 0.00 | 0.00 | 0.25 | 1.22 | 0.09 | 0.72 |

C_{4} | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.61 | 0.28 | 0.66 | 0.18 | 1.02 | 0.19 | 0.75 |

C_{5} | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 1.26 | 0.14 | 0.98 | 0.07 | 1.36 | 0.00 | 0.00 |

C_{6} | 0.00 | 0.00 | 0.33 | 0.69 | 0.19 | 1.08 | 0.00 | 0.00 | 0.22 | 0.82 | 0.00 | 0.00 |

C_{7} | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.86 | 0.32 | 0.98 | 0.08 | 1.28 | 0.00 | 0.00 |

C_{8} | 0.00 | 0.00 | 0.47 | 0.96 | 0.34 | 1.07 | 0.37 | 0.79 | 0.16 | 1.08 | 0.00 | 0.00 |

C_{9} | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.75 | 0.25 | 0.97 | 0.22 | 1.09 | 0.35 | 0.80 |

NDA | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.57 |

C_{2} | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 1.11 | 0.00 | 0.00 | 0.09 | 1.31 | 0.07 | 0.99 |

C_{3} | 0.19 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{4} | 0.21 | 1.05 | 0.05 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{5} | 0.09 | 1.39 | 0.20 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.95 |

C_{6} | 0.37 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.70 | 0.00 | 0.00 | 0.32 | 0.60 |

C_{7} | 0.17 | 0.63 | 0.27 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.74 |

C_{8} | 0.47 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.71 |

C_{9} | 0.45 | 0.83 | 0.21 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

VPI | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0.07 | 0.92 | 0.07 | 0.74 | 0.09 | 0.51 | 0.12 | 0.49 | 0.12 | 0.49 | 0.00 | 0.00 |

C_{2} | 0.07 | 1.02 | 0.03 | 0.73 | 0.00 | 0.00 | 0.12 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{3} | 0.00 | 0.00 | 0.01 | 0.82 | 0.07 | 0.64 | 0.00 | 0.00 | 0.11 | 1.16 | 0.04 | 0.68 |

C_{4} | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.58 | 0.12 | 0.64 | 0.08 | 0.98 | 0.09 | 0.73 |

C_{5} | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 1.11 | 0.03 | 0.86 | 0.02 | 1.20 | 0.00 | 0.00 |

C_{6} | 0.00 | 0.00 | 0.15 | 0.63 | 0.08 | 0.99 | 0.00 | 0.00 | 0.10 | 0.75 | 0.00 | 0.00 |

C_{7} | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.77 | 0.10 | 0.88 | 0.03 | 1.14 | 0.00 | 0.00 |

C_{8} | 0.00 | 0.00 | 0.20 | 0.83 | 0.14 | 0.92 | 0.15 | 0.68 | 0.07 | 0.93 | 0.00 | 0.00 |

C_{9} | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.65 | 0.10 | 0.83 | 0.09 | 0.93 | 0.14 | 0.69 |

VNI | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.57 |

C_{2} | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.97 | 0.00 | 0.00 | 0.03 | 1.14 | 0.03 | 0.86 |

C_{3} | 0.08 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{4} | 0.09 | 1.01 | 0.02 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

C_{5} | 0.02 | 1.22 | 0.04 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.84 |

C_{6} | 0.17 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.64 | 0.00 | 0.00 | 0.14 | 0.55 |

C_{7} | 0.06 | 0.56 | 0.09 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.66 |

C_{8} | 0.20 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.61 |

C_{9} | 0.18 | 0.72 | 0.08 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

SPi | SNi | NSPi | NSNi | ASi | Rank | |
---|---|---|---|---|---|---|

A_{1} | [0.14, 1.94] | [0.79, 6.23] | [0.02, 3.20] | [0.87, −6.89] | −1.40 | 5 |

A_{2} | [0.45, 3.76] | [0.24, 3.21] | [0.06, 6.21] | [0.96, −3.07] | 2.08 | 4 |

A_{3} | [0.70, 6.16] | [0.04, 0.97] | [0.09, 10.17] | [0.99, −0.22] | 5.52 | 2 |

A_{4} | [0.74, 4.88] | [0.26, 1.57] | [0.10, 8.06] | [0.96, −0.99] | 4.07 | 3 |

A_{5} | [0.61, 7.57] | [0.03, 1.14] | [0.08, 12.49] | [0.99, −0.44] | 6.56 | 1 |

A_{8} | [0.26, 2.10] | [0.46, 4.09] | [0.03, 0.28] | [0.93, −4.19] | −1.48 | 6 |

E_{1} | E_{2} | |||||||||||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |

C1 | 1 | 4 | 9 | 7 | 8 | 3 | 6 | 5 | 2 | 1 | 3 | 8 | 6 | 7 | 2 | 5 | 4 | 2 |

C2 | 0.25 | 1 | 5 | 3 | 4 | 0.50 | 3 | 2 | 0.33 | 0.33 | 1 | 5 | 3 | 4 | 0.500 | 3 | 2 | 0.33 |

C3 | 0.11 | 0.20 | 1 | 0.33 | 0.50 | 0.16 | 0.25 | 0.33 | 0.12 | 0.12 | 0.20 | 1 | 0.33 | 0.500 | 0.16 | 0.25 | 0.33 | 0.12 |

C4 | 0.14 | 0.33 | 3 | 1 | 2 | 0.25 | 0.50 | 0.33 | 0.16 | 0.16 | 0.33 | 3 | 1 | 2 | 0.25 | 0.500 | 0.33 | 0.16 |

C5 | 0.12 | 0.25 | 2 | 0.50 | 1 | 0.20 | 0.33 | 0.25 | 0.14 | 0.14 | 0.25 | 2 | 0.500 | 1 | 0.20 | 0.33 | 0.25 | 0.14 |

C6 | 0.33 | 2 | 6 | 4 | 5 | 1 | 3 | 3 | 0.50 | 0.500 | 2 | 6 | 4 | 5 | 1 | 3 | 3 | 0.500 |

C7 | 0.16 | 0.33 | 4 | 2 | 3 | 0.33 | 1 | 0.50 | 0.25 | 0.20 | 0.33 | 4 | 2 | 3 | 0.33 | 1 | 0.500 | 0.25 |

C8 | 0.20 | 0.50 | 3 | 3 | 4 | 0.33 | 2 | 1 | 0.33 | 0.25 | 0.500 | 3 | 3 | 4 | 0.33 | 2 | 1 | 0.33 |

C9 | 0.50 | 3 | 8 | 6 | 7 | 2 | 4 | 3 | 1 | 0.50 | 3 | 8 | 6 | 7 | 2 | 4 | 3 | 1 |

… | ||||||||||||||||||

E_{6} | E_{7} | |||||||||||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |

C1 | 1 | 4 | 9 | 5 | 8 | 3 | 6 | 5 | 2 | 1 | 3 | 8 | 5 | 7 | 2 | 5 | 4 | 3 |

C2 | 0.25 | 1 | 5 | 2 | 4 | 0.50 | 3 | 2 | 0.33 | 0.33 | 1 | 6 | 3 | 4 | 0.50 | 4 | 2 | 1 |

C3 | 0.11 | 0.20 | 1 | 0.25 | 0.50 | 0.16 | 0.25 | 0.33 | 0.12 | 0.12 | 0.16 | 1 | 0.25 | 0.50 | 0.16 | 0.33 | 0.25 | 0.20 |

C4 | 0.20 | 0.50 | 4 | 1 | 4 | 0.33 | 2 | 1 | 0.25 | 0.20 | 0.33 | 4 | 1 | 3 | 0.33 | 1 | 0.50 | 0.33 |

C5 | 0.12 | 0.25 | 2 | 0.25 | 1 | 0.20 | 0.33 | 0.25 | 0.14 | 0.14 | 0.25 | 2 | 0.33 | 1 | 0.20 | 0.33 | 0.25 | 0.25 |

C6 | 0.33 | 2 | 6 | 3 | 5 | 1 | 3 | 3 | 0.50 | 0.50 | 2 | 6 | 3 | 5 | 1 | 3 | 2 | 2 |

C7 | 0.16 | 0.33 | 4 | 0.50 | 3 | 0.33 | 1 | 0.50 | 0.25 | 0.20 | 0.25 | 3 | 1 | 3 | 0.33 | 1 | 0.50 | 0.33 |

C8 | 0.20 | 0.50 | 3 | 1 | 4 | 0.33 | 2 | 1 | 0.33 | 0.25 | 0.50 | 0.25 | 2 | 4 | 0.50 | 2 | 1 | 0.50 |

C9 | 0.50 | 3 | 8 | 4 | 7 | 2 | 4 | 3 | 1 | 0.33 | 1 | 5 | 3 | 4 | 0.50 | 3 | 2 | 1 |

A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | |
---|---|---|---|---|---|---|

C_{1} | [1, 1] | [2.78, 3.49] | [7.78, 8.49] | [5.51, 6.22] | [7.08, 7.49] | [2.08, 2.49] |

C_{2} | [0.3, 0.38] | [1, 1] | [5.18, 5.99] | [2.78, 3.83] | [4.18, 4.99] | [0.42, 0.63] |

C_{3} | [0.12, 0.13] | [0.17, 0.19] | [1, 1] | [0.29, 0.33] | [0.51, 0.63] | [0.16, 0.17] |

C_{4} | [0.16, 0.18] | [0.28, 0.38] | [3.08, 3.49] | [1, 1] | [2.18, 2.99] | [0.23, 0.29] |

C_{5} | [0.14, 0.14] | [0.2, 0.24] | [1.74, 1.98] | [0.36, 0.47] | [1, 1] | [0.18, 0.20] |

C_{6} | [0.42, 0.49] | [1.78, 2.49] | [6.04, 6.53] | [3.53, 4.51] | [5.06, 5.8] | [1, 1] |

C_{7} | [0.19, 0.22] | [0.26, 0.32] | [3.74, 3.98] | [1.35, 1.92] | [3.02, 3.26] | [0.31, 0.33] |

C_{8} | [0.23, 0.29] | [0.39, 0.49] | [2.27, 2.94] | [2.19, 2.91] | [3.74, 3.98] | [0.34, 0.38] |

C_{9} | [0.50, 1.08] | [2.19, 3.52] | [7.17, 8.22] | [4.66, 6.15] | [6.19, 7.45] | [1.34, 2.23] |

Alternative | R’D-R-MAIRCA | R’D-R-MULTIMOORA | R’D-R-COPRAS | R’D-R-MABAC | R’D-R-EDAS | ||||||||||

Value | Rank | Value | Rank | Value | Rank | Value | Rank | Value | Rank | ||||||

A1 | −0.243 | 1.540 | 6 | 0.778 | 4.055 | 6 | 63.32 | 83.67 | 6 | −9.508 | 8.469 | 6 | 0.892 | −3.690 | 5 |

A2 | −0.324 | 1.449 | 4 | 0.962 | 4.392 | 3 | 79.70 | 87.89 | 3 | −9.053 | 8.875 | 4 | 1.021 | 3.139 | 4 |

A3 | −0.543 | 1.394 | 2 | 1.059 | 5.080 | 2 | 88.60 | 93.74 | 2 | −8.779 | 9.968 | 2 | 1.086 | 9.949 | 2 |

A4 | −0.402 | 1.454 | 3 | 0.858 | 4.406 | 4 | 78.93 | 88.10 | 4 | −9.079 | 9.263 | 3 | 1.057 | 7.073 | 3 |

A5 | −0.696 | 1.332 | 1 | 1.150 | 5.402 | 1 | 100.00 | 100.00 | 1 | −8.470 | 10.73 | 1 | 1.075 | 12.053 | 1 |

A6 | −0.170 | 1.463 | 5 | 0.933 | 4.137 | 5 | 77.23 | 78.93 | 5 | −9.123 | 8.106 | 5 | 0.960 | −3.913 | 6 |

Alternative | R’A-R-MAIRCA | R’A-R-MULTIMOORA | R’A-R-COPRAS | R’A-R-MABAC | R’A-R-EDAS | ||||||||||

Value | Rank | Value | Rank | Value | Rank | Value | Rank | Value | Rank | ||||||

A1 | 0.024 | 0.628 | 3 | 0.711 | 2.103 | 4 | 90.72 | 100.00 | 3 | −2.638 | 2.919 | 3 | 0.759 | 0.255 | 5 |

A2 | 0.115 | 0.595 | 5 | 0.796 | 1.991 | 5 | 93.58 | 91.70 | 5 | −2.470 | 2.466 | 5 | 1.056 | 2.312 | 4 |

A3 | 0.064 | 0.568 | 2 | 0.928 | 2.320 | 2 | 98.60 | 92.26 | 2 | −2.334 | 2.721 | 2 | 1.205 | 4.461 | 2 |

A4 | 0.075 | 0.599 | 4 | 0.810 | 2.151 | 3 | 94.25 | 92.67 | 4 | −2.489 | 2.668 | 4 | 1.148 | 3.928 | 3 |

A5 | 0.034 | 0.560 | 1 | 0.966 | 2.420 | 1 | 100.00 | 95.39 | 1 | −2.295 | 2.872 | 1 | 1.195 | 4.844 | 1 |

A6 | 0.225 | 0.650 | 6 | 0.820 | 1.982 | 6 | 83.13 | 80.28 | 6 | −2.746 | 1.915 | 6 | 0.879 | −1.461 | 6 |

Methods | R’D-R-MAI RCA | R’D-R-MULTI MOORA | R’D-R-COP RAS | R’D-R-MA BAC | R’D-R- EDAS | R’A-R-MA IRCA | R’A-R-MULTI MOORA | R’A-R-COP RAS | R’A-R-MA BAC | R’A-R- EDAS | Average |
---|---|---|---|---|---|---|---|---|---|---|---|

R’D-R-MAIRCA | 1.000 | 0.943 | 0.943 | 1.000 | 0.943 | 0.657 | 0.829 | 0.657 | 0.657 | 0.943 | 0.857 |

R’D-R-MULTIMOORA | - | 1.000 | 1.000 | 0.943 | 0.886 | 0.600 | 0.714 | 0.600 | 0.600 | 0.886 | 0.803 |

R’D-R-COPRAS | - | - | 1.000 | 0.943 | 0.886 | 0.600 | 0.714 | 0.600 | 0.600 | 0.886 | 0.779 |

R’D-R-MABAC | - | - | - | 1.000 | 0.943 | 0.657 | 0.829 | 0.657 | 0.657 | 0.943 | 0.812 |

R'D-R-EDAS | - | - | - | - | 1.000 | 0.829 | 0.943 | 0.829 | 0.829 | 1.000 | 0.905 |

R’A-R-MAIRCA | - | - | - | - | - | 1.000 | 0.943 | 1.000 | 1.000 | 0.829 | 0.954 |

R’A-R-MULTIMOORA | - | - | - | - | - | - | 1.000 | 0.943 | 0.943 | 0.943 | 0.957 |

R’A-R-COPRAS | - | - | - | - | - | - | - | 1.000 | 1.000 | 0.829 | 0.943 |

R’A-R-MABAC | - | - | - | - | - | - | - | - | 1.000 | 0.829 | 0.915 |

R’A-R-EDAS | - | - | - | - | - | - | - | - | - | 1.000 | 1.000 |

Overall average | 0.893 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Stević, Ž.; Pamučar, D.; Vasiljević, M.; Stojić, G.; Korica, S.
Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company. *Symmetry* **2017**, *9*, 279.
https://doi.org/10.3390/sym9110279

**AMA Style**

Stević Ž, Pamučar D, Vasiljević M, Stojić G, Korica S.
Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company. *Symmetry*. 2017; 9(11):279.
https://doi.org/10.3390/sym9110279

**Chicago/Turabian Style**

Stević, Željko, Dragan Pamučar, Marko Vasiljević, Gordan Stojić, and Sanja Korica.
2017. "Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company" *Symmetry* 9, no. 11: 279.
https://doi.org/10.3390/sym9110279