# Managing Resources Based on Influential Indicators for Sustainable Economic Development: A Case Study in Serbia

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## Abstract

**:**

## 1. Introduction and Literature Review

## 2. Conceptual Framework

## 3. Materials and Methods

**Definition**

**1.**

- (1)
- Establishing a hierarchy by decomposing the problem of decision-making.
- (2)
- Creating comparison matrices by performing pairwise comparisons.
- (3)
- Calculation of weights and consistency of comparisons.
- (4)
- Aggregation of weights to obtain results and ranking of alternatives.

#### 3.1. Triangular Fuzzy Numbers and Fuzzy AHP Method

**Definition**

**2.**

- Addition:${\tilde{T}}_{1}\oplus {\tilde{T}}_{2}=\left({a}_{1}+{a}_{2},{m}_{1}+{m}_{2},{b}_{1}+{b}_{2}\right),$
- Subtraction:${\tilde{T}}_{1}\ominus {\tilde{T}}_{2}=\left({a}_{1}-{b}_{2},{m}_{1}-{m}_{2},{b}_{1}-{a}_{2}\right)$,
- Multiplication:${\tilde{T}}_{1}\odot {\tilde{T}}_{2}=\left({a}_{1}\xb7{a}_{2},{m}_{1}\xb7{m}_{2},{b}_{1}\xb7{b}_{2}\right),$
- Inverse:${T}_{1}^{-1}={\left({a}_{1},{m}_{1},{b}_{1}\right)}^{-1}=\left(1/{b}_{1},1/{m}_{1},1/{a}_{1}\right),$
- Division:${\tilde{T}}_{1}\oslash {\tilde{T}}_{2}={\tilde{T}}_{1}\odot {T}_{2}^{-1}=\left({a}_{1}/{b}_{2},{m}_{1}/{m}_{2},{b}_{1}/{a}_{2}\right),$
- Scalar multiplication:$\lambda {\tilde{T}}_{1}=\left(\lambda {a}_{1},\lambda {m}_{1},\lambda {b}_{1}\right)$.

- (1)
- Establishing the main goal and the criteria and sub-criteria contributing to the overall goal; developing the problem hierarchy.
- (2)
- Obtaining the fuzzy comparison matrices. A pairwise comparison has been made using a fuzzified evaluation scale. Using triangular fuzzy numbers, we form a comparison matrix $\tilde{C}={\left({\tilde{c}}_{ij}\right)}_{n\times n}$ for a fuzzy comparison of criteria by pairs, where ${\tilde{c}}_{ij}$ is a fuzzy value that expresses the relative importance of one criterion to another. At the diagonal, the fuzzy values ${\tilde{c}}_{ii}$ express the relative importance of the criterion to itself. Because of that, we put that ${\tilde{c}}_{ii}=\left(1,1,1\right).$ The aggregation of different experts’ opinions is calculated by the averaging method. Based on the corresponding linguistic assessments of k experts $\left({a}_{i},{m}_{i},{b}_{i}\right)$, aggregated crisp value has been obtained by $\frac{1}{k}\sum _{i=1}^{k}{m}_{i}$ rounding to the nearest integer. The corresponding fuzzy number value of the aggregate opinion is then obtained.
- (3)
- Examination of the comparison matrix $\tilde{C}$ consistency. We calculate the consistency index $CI$ and consistency ratio $CR$ for matrix $\tilde{C}={\left({\tilde{c}}_{ij}\right)}_{n\times n}$ by $CI=\frac{{\mathsf{\lambda}}_{max}-n}{n-1}$, $CR=\frac{CI}{RI}$, where ${\mathsf{\lambda}}_{max}$ represents the maximal eigenvalues, and RI is an accepted random index of a matrix $\tilde{C}$. The value $CR\le 0.10$ implies that we accept evaluated fuzzy elements of the matrix, while otherwise, we must remove the reasons for undesirably high estimations and repeat comparison in pairs until the degree of consistency belongs to desirable limits.
- (4)
- The fuzzy synthetic extents determination. The synthetic triangular fuzzy numbers have been calculated, according to Chang’s extent analysis method, by using triangular fuzzy numbers from the matrix $\tilde{C}={\left({\tilde{c}}_{ij}\right)}_{n\times n}$:$${\tilde{\mathcal{S}}}_{i}={\sum}_{j=1}^{n}{\tilde{c}}_{ij}\odot {\left({\sum}_{i=1}^{n}{\sum}_{j=1}^{n}{\tilde{c}}_{ij}\right)}^{-1},i=\overline{1,n}.$$

#### 3.2. Considering Indicators for the Sustainable Economic Development

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Triangular fuzzy comparison j matrix of the criteria S and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP $\left(CI=0.014,CR=0.012\right)$.

S_{1} | S_{2} | S_{3} | S_{4} | S_{5} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|---|

S_{1} | E | $\mathrm{W}$ | $\mathrm{W}$ | $\mathrm{WS}$ | $\mathrm{S}$ | 0.372998 | 0.407067 | 0.412316 | 0.426412 | 0.458904 |

S_{2} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | E | E | $\mathrm{EW}$ | $\mathrm{W}$ | 0.24581 | 0.217634 | 0.211868 | 0.196386 | 0.184391 |

S_{3} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | E | $\mathrm{EW}$ | $\mathrm{W}$ | 0.225686 | 0.192363 | 0.191169 | 0.187963 | 0.184391 |

S_{4} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | E | $\mathrm{EW}$ | 0.114065 | 0.110957 | 0.113216 | 0.119281 | 0.106287 |

S_{5} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | E | 0.041441 | 0.071978 | 0.071430 | 0.069958 | 0.0660273 |

**Table A2.**Triangular fuzzy comparison matrix of the sub-criteria S

_{1}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP $\left(CI=0.004,CR=0.007\right)$.

S_{11} | S_{12} | S_{13} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

S_{11} | E | $\mathrm{EW}$ | $\mathrm{W}$ | 0.469703 | 0.529412 | 0.521753 | 0.502793 | 0.539615 |

S_{12} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | E | $\mathrm{EW}$ | 0.335539 | 0.298349 | 0.303927 | 0.317737 | 0.296961 |

S_{13} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | E | 0.194758 | 0.172240 | 0.174320 | 0.179469 | 0.163424 |

**Table A3.**Triangular fuzzy comparison matrix of the sub-criteria S

_{2}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP $\left(CI=0.008,CR=0.006\right)$.

S_{21} | S_{22} | S_{23} | S_{24} | S_{25} | S_{26} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|

S_{21} | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{W}$ | $\mathrm{EW}$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.185275 | 0.176969 | 0.172707 | 0.161515 | 0.153574 |

S_{22} | $\mathrm{EW}$ | $\mathrm{E}$ | $\mathrm{WS}$ | $\mathrm{W}$ | $\mathrm{EW}$ | $\mathrm{E}$ | 0.235335 | 0.261599 | 0.262923 | 0.266398 | 0.273782 |

S_{23} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | 0.049273 | 0.058989 | 0.059074 | 0.059296 | 0.056289 |

S_{24} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{EW}$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | 0.117913 | 0.101658 | 0.100503 | 0.097470 | 0.088998 |

S_{25} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.176870 | 0.158077 | 0.157289 | 0.155218 | 0.153574 |

S_{26} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\mathrm{WS}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{W}$ | $\mathrm{E}$ | 0.235335 | 0.242707 | 0.247505 | 0.260101 | 0.273782 |

**Table A4.**Triangular fuzzy comparison matrix of the sub-criteria S

_{3}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.006,CR=0.007$ ).

S_{31} | S_{32} | S_{33} | S_{34} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|

S_{31} | $\mathrm{E}$ | $\mathrm{W}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.263272 | 0.236521 | 0.225833 | 0.203452 | 0.199916 |

S_{32} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | 0 | 0.081199 | 0.083232 | 0.087490 | 0.081531 |

S_{33} | $\mathrm{EW}$ | $\mathrm{WS}$ | $\mathrm{E}$ | $\mathrm{E}$ | 0.368364 | 0.361858 | 0.361721 | 0.361435 | 0.359276 |

S_{34} | $\mathrm{EW}$ | $\mathrm{WS}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\mathrm{E}$ | 0.368364 | 0.320422 | 0.329213 | 0.347623 | 0.359276 |

**Table A5.**Triangular fuzzy comparison matrix of sub-criteria S

_{4}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.003,CR=0.003$ ).

S_{41} | S_{42} | S_{43} | S_{44} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|

S_{41} | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{EW}$ | 0.225915 | 0.190410 | 0.194622 | 0.206108 | 0.18906 |

S_{42} | $\mathrm{EW}$ | $\mathrm{E}$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.312898 | 0.367517 | 0.361595 | 0.345444 | 0.350913 |

S_{43} | $\mathrm{EW}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.312898 | 0.321785 | 0.324043 | 0.330201 | 0.350913 |

S_{44} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | 0.148289 | 0.120288 | 0.119741 | 0.118247 | 0.109114 |

**Table A6.**Triangular fuzzy comparison matrix of the sub-criteria S

_{5}and its weighs for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.020,CR=0.016$ ).

S_{51} | S_{52} | S_{53} | S_{54} | S_{55} | S_{56} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|

S_{51} | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{EW}$ | $\mathrm{EW}$ | $\mathrm{W}$ | $\mathrm{S}$ | 0.250825 | 0.235493 | 0.231698 | 0.222953 | 0.232901 |

S_{52} | $\mathrm{EW}$ | $\mathrm{E}$ | $\mathrm{W}$ | $\mathrm{W}$ | $\mathrm{WS}$ | $\mathrm{SV}$ | 0.309864 | 0.313714 | 0.317928 | 0.327637 | 0.366723 |

S_{53} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{WS}$ | 0.178903 | 0.161625 | 0.161192 | 0.160196 | 0.138193 |

S_{54} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{WS}$ | 0.159103 | 0.145126 | 0.148022 | 0.154696 | 0.138193 |

S_{55} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.101304 | 0.106154 | 0.102018 | 0.092487 | 0.0838608 |

S_{56} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{SV}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | 0 | 0.037887 | 0.039141 | 0.042030 | 0.0401283 |

**Table A7.**Triangular fuzzy comparison matrix of the criteria E and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0,CR=0$ ).

E_{1} | E_{2} | E_{3} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

E_{1} | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{E}$ | 0.394737 | 0.445455 | 0.433884 | 0.409091 | 0.4 |

E_{2} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.210526 | 0.200000 | 0.203857 | 0.212121 | 0.2 |

E_{3} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | $\mathrm{EW}$ | $\mathrm{E}$ | 0.394737 | 0.354545 | 0.362259 | 0.378788 | 0.4 |

**Table A8.**Triangular fuzzy comparison matrix of the sub-criteria E

_{1}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP $\left(CI=0,CR=0\right)$.

E_{11} | E_{12} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|

E_{11} | $\mathrm{E}$ | $\mathrm{EW}$ | 0.692308 | 0.666667 | 0.658163 | 0.642857 | 0.666667 |

E_{12} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | 0.307692 | 0.333333 | 0.341837 | 0.357143 | 0.333333 |

**Table A9.**Triangular fuzzy comparison matrix of the sub-criteria E

_{2}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.0161203,CR=0.0179114$ ).

E_{21} | E_{22} | E_{23} | E_{24} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|

E_{21} | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{WS}$ | $\mathrm{S}$ | 0.504296 | 0.449824 | 0.453298 | 0.460482 | 0.491839 |

E_{22} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\mathrm{W}$ | $\mathrm{WS}$ | 0.391579 | 0.331107 | 0.327465 | 0.319933 | 0.305571 |

E_{23} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\mathrm{EW}$ | 0.104125 | 0.144724 | 0.142439 | 0.137713 | 0.124793 |

E_{24} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | 0 | 0.074344 | 0.076798 | 0.081871 | 0.0777981 |

**Table A10.**Triangular fuzzy comparison matrix of the sub-criteria E

_{3}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP $(CI=0.004,CR=0.007$ ).

E_{31} | E_{32} | E_{33} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

E_{31} | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{EW}$ | 0.335539 | 0.298349 | 0.298349 | 0.317737 | 0.296961 |

E_{32} | $\mathrm{EW}$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.469703 | 0.529412 | 0.529412 | 0.502793 | 0.539615 |

E_{33} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | 0.194758 | 0.172240 | 0.172240 | 0.179469 | 0.163424 |

**Table A11.**Triangular fuzzy comparison matrix of the criteria N and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.004,CR=0.007$ ).

N_{1} | N_{2} | N_{3} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

N_{1} | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | 0.194758 | 0.17224 | 0.17432 | 0.179469 | 0.163424 |

N_{2} | $\mathrm{EW}$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.335539 | 0.298349 | 0.303927 | 0.317737 | 0.296961 |

N_{3} | $\mathrm{W}$ | $\mathrm{EW}$ | $\mathrm{E}$ | 0.469703 | 0.529412 | 0.521753 | 0.502793 | 0.539615 |

**Table A12.**Triangular fuzzy comparison matrix of the sub-criteria N

_{1}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.006,CR=0.007$).

N_{11} | N_{12} | N_{13} | N_{14} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|

N_{11} | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{EW}$ | $\mathrm{WS}$ | 0.368364 | 0.361858 | 0.361721 | 0.361435 | 0.359276 |

N_{12} | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{EW}$ | $\mathrm{WS}$ | 0.368364 | 0.320422 | 0.329213 | 0.347623 | 0.359276 |

N_{13} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.263272 | 0.236521 | 0.225833 | 0.203452 | 0.199916 |

N_{14} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | 0 | 0.081199 | 0.083232 | 0.087490 | 0.081531 |

**Table A13.**Triangular fuzzy comparison matrix of the sub-criteria N

_{2}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.004,CR=0.007$ ).

N_{21} | N_{22} | N_{23} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

N_{21} | $\mathrm{E}$ | $\mathrm{EW}$ | $\mathrm{W}$ | 0.469703 | 0.529412 | 0.521753 | 0.502793 | 0.539615 |

N_{22} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | $\mathrm{EW}$ | 0.335539 | 0.298349 | 0.303927 | 0.317737 | 0.296961 |

N_{23} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{E}$ | 0.194758 | 0.17224 | 0.17432 | 0.179469 | 0.163424 |

**Table A14.**Triangular fuzzy comparison matrix of the sub-criteria N

_{3}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.016,CR=0.017$ ).

N_{31} | N_{32} | N_{33} | N_{34} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|

N_{31} | $\mathrm{E}$ | $\mathrm{W}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{WS}$ | 0.391579 | 0.331107 | 0.327465 | 0.319933 | 0.305571 |

N_{32} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\mathrm{EW}$ | 0.104125 | 0.144724 | 0.142439 | 0.137713 | 0.124793 |

N_{33} | $\mathrm{EW}$ | $\mathrm{WS}$ | $\mathrm{E}$ | $\mathrm{S}$ | 0.504296 | 0.449824 | 0.453298 | 0.460482 | 0.491839 |

N_{34} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\mathrm{E}$ | 0 | 0.074344 | 0.076798 | 0.081871 | 0.0777981 |

**Table A15.**Triangular fuzzy comparison matrix of the criteria H and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.024,CR=0.022$ ).

H_{1} | H_{2} | H_{3} | H_{4} | H_{5} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|---|---|

H_{1} | $\mathrm{E}$ | $\mathrm{W}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{EW}$ | $\mathrm{S}$ | 0.302687 | 0.278976 | 0.2728 | 0.259174 | 0.265205 |

H_{2} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{W}$ | 0.121185 | 0.132675 | 0.12679 | 0.113806 | 0.10256 |

H_{3} | $\mathrm{EW}$ | $\mathrm{WS}$ | $\mathrm{E}$ | $\mathrm{W}$ | $\mathrm{SV}$ | 0.375703 | 0.357825 | 0.366489 | 0.385604 | 0.420131 |

H_{4} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | $\mathrm{EW}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\mathrm{WS}$ | 0.200425 | 0.183401 | 0.185608 | 0.190476 | 0.163751 |

H_{5} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{SV}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\mathrm{E}$ | 0 | 0.047122 | 0.0483131 | 0.05094 | 0.048352 |

**Table A16.**Triangular fuzzy comparison matrix of the sub-criteria H

_{1}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.019,CR=0.033$ ).

H_{11} | H_{12} | H_{13} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

H_{11} | $\mathrm{E}$ | $\mathrm{W}$ | $\mathrm{S}$ | 0.573349 | 0.588534 | 0.591657 | 0.599821 | 0.636986 |

H_{12} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\mathrm{W}$ | 0.375448 | 0.307359 | 0.300366 | 0.282085 | 0.258285 |

H_{13} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | 0.0512038 | 0.104107 | 0.107977 | 0.118094 | 0.104729 |

**Table A17.**Triangular fuzzy comparison matrix of the H

_{2}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.009,CR=0.015$).

H_{21} | H_{22} | H_{23} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

H_{21} | $\mathrm{E}$ | $\mathrm{W}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0.423486 | 0.369599 | 0.35333 | 0.319177 | 0.319618 |

H_{22} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | 0 | 0.125255 | 0.127978 | 0.133695 | 0.121957 |

H_{23} | $\mathrm{EW}$ | $\mathrm{WS}$ | $\mathrm{E}$ | 0.576514 | 0.505146 | 0.518692 | 0.547127 | 0.558425 |

**Table A18.**Triangular fuzzy comparison matrix of the sub-criteria H

_{3}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.009,CR=0.015$ ).

H_{31} | H_{32} | H_{33} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

H_{31} | $\mathrm{E}$ | $\mathrm{WS}$ | $\mathrm{W}$ | 0.686499 | 0.603699 | 0.60215 | 0.598899 | 0.625013 |

H_{32} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ | 0 | 0.129365 | 0.135136 | 0.147250 | 0.1365 |

H_{33} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ | $\mathrm{EW}$ | $\mathrm{E}$ | 0.313501 | 0.266935 | 0.262714 | 0.253851 | 0.238487 |

**Table A19.**Triangular fuzzy comparison matrix of the sub-criteria H

_{4}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0,CR=0$ ).

H_{41} | H_{42} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|

H_{41} | $\mathrm{E}$ | $\mathrm{S}$ | 1 | 0.848684 | 0.836219 | 0.813596 | 0.833333 |

H_{42} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ | 0 | 0.151316 | 0.163781 | 0.186404 | 0.151316 |

**Table A20.**Triangular fuzzy comparison matrix of the sub-criteria H

_{5}and its weights for Chang’s approach (EAM), different degrees of optimism in FAHP, and crisp AHP ($CI=0.038,CR=0.065$ ).

H_{51} | H_{52} | H_{53} | ${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathit{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | ${\mathit{\omega}}_{\mathit{A}\mathit{H}\mathit{P}}$ | |
---|---|---|---|---|---|---|---|---|

H_{51} | $\mathrm{E}$ | $\mathrm{WS}$ | $\mathrm{V}$ | 0.904283 | 0.651202 | 0.644745 | 0.634569 | 0.695523 |

H_{52} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ | $\mathrm{E}$ | $\mathrm{WS}$ | 0.0957168 | 0.27877 | 0.281051 | 0.284647 | 0.229048 |

H_{53} | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{V}$}\right.$ | $\mathrm{WS}$ | $\mathrm{E}$ | 0 | 0.070028 | 0.074204 | 0.080784 | 0.0754292 |

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**Figure 3.**Intersection between membership functions ${\mu}_{{\tilde{T}}_{1}}$ and ${\mu}_{{\tilde{T}}_{2}}$.

**Figure 4.**Corresponding weights for Chang’s approach, different degrees of optimism in FAHP and crisp AHP ($CI=0.006,CR=0.007)$.

**Figure 5.**Graphical representation of final weights of influential indicators by AHP and FAHP with Chang approach and different degrees of optimism.

S—Strengthening participation in the development [40] | |

S_{1}—Economic development strategybased on knowledge and innovation [41,42] | S_{11}—Development of a stimulating entrepreneurial environment [43]S _{12}—Targeted investment attraction [44]S _{13}—Development of potentials for the needs of the labor market |

S_{2}—Sustainable mobilityand interactive city development [45,46] | S_{21}—Increased accessibility of the cityS _{22}—Sustainable mobility of the central city zone [47]S _{23}—Development of economic zones and logisticsS _{24}—Compliance of the traffic system with the needs of citizensS _{25}—Increasing the share of pedestrians in cyclists as road users [48]S _{26}—Improved safety conditions for all road users |

S_{3}—Improvement and developmentinfrastructure services of citizens [49] | S_{31}—Improving the quality of communal infrastructureS _{32}—Creating a framework for high-quality utilitiesS _{33}—Improving the level of information and communication with citizens |

S_{4}—Energy capital as a development opportunity [50] | S_{34}—Increased efficiency coefficient of all PUCs individuallyS _{41}—Improvement of energy infrastructureS _{42}—Improving energy efficiencyS _{43}—Institutional environment for the development of energy systems and the provision of quality services [51] |

S_{5}—Improved social cohesion [52] | S_{44}—Achieved in the billing system according to the energy consumedS _{51}—Diversified, accessible, and quality social servicesS _{52}—Improving the content of culture, sports, and tourismS _{53}—Improving social development infrastructureS _{54}—A single record system for users of social rights and services has been establishedS _{55}- City Housing Strategy adoptedS _{56}—Implementation of investment plans in facilities and equipment of primary health care institutions |

E—Economic potentials [53] | |

E_{1}—Increasing competitiveness [54,55] | E_{11}—Stability of business environment and business sector [56]E _{12}—Global response to the COVID-19 pandemic [57] |

E_{2}—Suppression of the gray economy [58] | E_{21}—Reducing the degree of the gray economy in GDP [59]E _{22}—Reduction of the share of unregistered economic entitiesE _{23}—Relative reduction of VAT |

E_{3}—Public-private partnership in support of local economic development and foreign direct investment (FDI) [60] | E_{31}- Increase in efficiency and economy [61]E _{32}- Reducing the pressure of public investment on the budget [62]E _{33}- Increasing the level of foreign direct investment (FDI) |

N—Natural resources [63] | |

N_{1}—Use and protection of natural resources in planning [64] | N_{11}—Implementation of the National Strategy on the Use and Protection of Natural Resources and GoodsN _{12}—Strategic environmental impact assessment of plans and programs N _{13}—Environmental impact assessment of projectsN _{14}—Integrated prevention and control of environmental pollution |

N_{2}—Management of renewable natural resources andnon-renewable natural resources [65] | N_{21}—Reconciliation of the relationship between the degree of exhaustion of natural resources and their regeneration rate [66]N _{22}—Design of available resources by quality, structure, amount, and capital investmentsN _{23}—Direction of ecological aspects in the interest of the population of the local area |

N_{3}—Protection of resources and ecosystems through the principles of sustainable development [67] | N_{31}—Creating ability of the environment to accept a certain amount of pollutants per unit of time and space so that there is no irreversible damage to the environment; N _{32}—The impact of a product/service or system on the environmentN _{33}—Effective preservation of ecosystems and resources themselves [68]N _{34}—Transparency-information of the wider local community |

H—Human resources [69] | |

H_{1}—Employment and labor market [70] | H_{11}—Support for the development of local and inter-municipal employment policiesH _{12}—Increasing the impact of employment policy measures on the hard-to-employH _{13}—Suppression of the informal economy |

H_{2}—Improving the quality and accessibility of health services [71] | H_{21}—Promoting the health and well-being of all citizensH _{22}—Preventive careH _{23}—Strengthening the operational capacity of the health system in line with EU standards data |

H_{3}—Education [72] | H_{31}—Improving the quality and importance of secondary vocational education and adult education within the National Qualifications FrameworkH _{32}—Ensuring access to and reaching higher levels of education for children at risk [73]H _{33}—Education for all |

H_{4}—Social inclusion [74] | H_{41}—Support for social inclusion through a more diverse offer of social services in the local communityH _{42}—Support for the transition from social assistance to work (“welfare-to-work”) through activation |

H_{5}—Technical assistance | H_{51}—Announcement of new calls for cross-border cooperation programsH _{52}—Finalization of the Operational Program Human Resources DevelopmentH _{53}—Negotiations with individual bilateral donors, discussions on a new EU financial perspective [75] |

Description TFNs | TFNs | Inverse TFNs | Denotation of TFNs | Denotation of Inverse TFNs |
---|---|---|---|---|

Equally important | $\tilde{1}=\left(1,1,3\right)$ | $\tilde{1}-1$ = $\left(1/3,1,1\right)$ | $\mathrm{E}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{E}$}\right.$ |

Equally to weakly important | $\tilde{2}=\left(1,2,3\right)$ | $\tilde{2}-1$ = $\left(1/3,1/2,1\right)$ | $\mathrm{EW}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{EW}$}\right.$ |

Weakly important | $\tilde{3}=\left(1,3,5\right)$ | $\tilde{3}-1$ = $\left(1/5,1/3,1\right)$ | $\mathrm{W}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.$ |

Weakly to strong important | $\tilde{4}$ $=\left(3,4,5\right)$ | $\tilde{4}-1$ = $\left(1/5,1/4,1/3\right)$ | $\mathrm{WS}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{WS}$}\right.$ |

Strong important | $\tilde{5}$ $=\left(3,5,7\right)$ | $\tilde{5}-1$ = $\left(1/7,1/5,1/3\right)$ | $\mathrm{S}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{S}$}\right.$ |

Strong to very strongly important | $\tilde{6}$ $=\left(5,6,7\right)$ | $\tilde{6}-1$ = $\left(1/7,1/6,1/5\right)$ | $\mathrm{SV}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{SV}$}\right.$ |

Very strongly important | $\tilde{7}=\left(5,7,9\right)$ | $\tilde{7}-1$ = $\left(1/9,1/7,1/5\right)$ | $\mathrm{V}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{V}$}\right.$ |

Very strongly to absolutely important | $\tilde{8}$ $=\left(7,8,9\right)$ | $\tilde{8}-1$ = $\left(1/9,1/8,1/7\right)$ | $\mathrm{VA}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{VA}$}\right.$ |

Absolutely important | $\tilde{9}$ $=\left(7,9,9\right)$ | $\tilde{9}-1$ = $\left(1/9,1/9,1/7\right)$ | $\mathrm{A}$ | $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{A}$}\right.$ |

F | S | N | H | |
---|---|---|---|---|

F | $\tilde{1}$ | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ |

S | $\tilde{1}-1$ | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ |

N | $\tilde{2}-1$ | $\tilde{2}-1$ | $\tilde{1}$ | $\tilde{3}$ |

H | $\tilde{4}-1$ | $\tilde{4}-1$ | $\tilde{3}-1$ | $\tilde{1}$ |

**Table 4.**Ranking of indicators with final weights by triangular fuzzy AHP method, AHP method and IAHP method $(I\omega $ is interval weight, p is probability).

${\mathit{\omega}}_{\mathit{E}\mathit{A}\mathit{M}}$ | ${\mathit{\omega}}_{\mathit{\nu}=1}$ | ${\mathit{\omega}}_{\mathsf{\nu}=0.5}$ | ${\mathit{\omega}}_{\mathit{\nu}=0}$ | $\mathit{I}\mathit{\omega}$ | p | $\mathit{\omega}\left(\mathit{A}\mathit{H}\mathit{P}\right)$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

E_{11} | 0.100666 | E_{11} | 0.095156 | E_{11} | 0.094012 | E_{11} | 0.091420 | S_{11} | [8.63826,19.0926] | 0.959395 | E_{11} | 0.095807 |

E_{32} | 0.068298 | E_{32} | 0.060143 | S_{11} | 0.077816 | S_{11} | 0.077491 | S_{12} | [4.75382,10.9277] | 0.66159 | S_{11} | 0.088968 |

S_{11} | 0.064537 | N_{33} | 0.056326 | E_{32} | 0.062224 | E_{32} | 0.066205 | E_{21} | [4.70912,8.97667] | 0.871921 | E_{32} | 0.077548 |

N_{33} | 0.062361 | E_{12} | 0.047578 | N_{33} | 0.053412 | E_{12} | 0.050789 | N_{33} | [3.92281,6.33196] | 0.520358 | N_{33} | 0.053058 |

E_{31} | 0.048790 | S_{12} | 0.043947 | E_{12} | 0.048828 | S_{12} | 0.048970 | S_{26} | [3.17891,6.9234] | 0.816068 | S_{12} | 0.048961 |

N_{31} | 0.048423 | N_{31} | 0.041460 | S_{12} | 0.045329 | N_{33} | 0.047105 | S_{22} | [2.92868,4.77265] | 0.558448 | E_{12} | 0.047903 |

S_{12} | 0.046103 | N_{21} | 0.037358 | N_{31} | 0.038585 | E_{31} | 0.041838 | S_{13} | [2.07642,5.25352] | 0.513292 | E_{31} | 0.042676 |

E_{12} | 0.044741 | E_{31} | 0.033894 | E_{31} | 0.036246 | E_{21} | 0.033955 | S_{34} | [2.80168,4.4438] | 0.5 | E_{21} | 0.035341 |

N_{21} | 0.041493 | S_{11} | 0.032996 | N_{21} | 0.035811 | N_{31} | 0.032727 | S_{33} | [2.80168,4.4438] | 0.747129 | N_{31} | 0.032964 |

E_{21} | 0.039108 | E_{21} | 0.028827 | E_{21} | 0.030422 | N_{21} | 0.032503 | E_{11} | [2.64639,3.76592] | 0.550364 | N_{21} | 0.032035 |

S_{33} | 0.030624 | S_{13} | 0.025371 | S_{13} | 0.025999 | S_{13} | 0.027660 | S_{43} | [1.81144,4.34561] | 0.5 | S_{13} | 0.026944 |

S_{34} | 0.030624 | S_{33} | 0.025188 | S_{33} | 0.025013 | S_{33} | 0.024555 | S_{42} | [1.81144,4.34561] | 0.520348 | S_{33} | 0.023801 |

E_{22} | 0.030367 | S_{34} | 0.022304 | S_{34} | 0.022765 | E_{33} | 0.023632 | E_{32} | [2.69886,3.35506] | 0.730681 | S_{34} | 0.023801 |

N_{22} | 0.029641 | E_{22} | 0.021219 | E_{22} | 0.021977 | S_{34} | 0.023616 | H_{31} | [1.88112,3.4493] | 0.512562 | E_{33} | 0.023486 |

E_{33} | 0.028319 | N_{22} | 0.021053 | N_{22} | 0.020861 | E_{22} | 0.023591 | N_{31} | [2.17212,3.1189] | 0.774858 | E_{22} | 0.021957 |

S_{13} | 0.026760 | S_{22} | 0.020602 | E_{33} | 0.020789 | N_{22} | 0.020540 | S_{52} | [1.64082,2.90676] | 0.552408 | H_{31} | 0.021409 |

S_{31} | 0.021887 | E_{33} | 0.019567 | S_{22} | 0.020150 | H_{31} | 0.020205 | S_{25} | [1.73775,2.67714] | 0.5 | S_{22} | 0.018137 |

S_{22} | 0.021309 | S_{26} | 0.019114 | S_{26} | 0.018968 | S_{22} | 0.018909 | S_{21} | [1.73775,2.67714] | 0.662139 | S_{26} | 0.018137 |

S_{26} | 0.021309 | N_{32} | 0.018122 | H_{31} | 0.018368 | S_{26} | 0.018462 | S_{31} | [1.55898,2.51796] | 0.739001 | N_{22} | 0.017630 |

N_{11} | 0.018888 | H_{31} | 0.017541 | N_{32} | 0.016783 | S_{42} | 0.014893 | E_{22} | [1.46285,2.14209] | 0.646789 | H_{11} | 0.013773 |

N_{12} | 0.018888 | S_{31} | 0.016464 | S_{31} | 0.015616 | S_{43} | 0.014236 | E_{31} | [1.48524,1.92029] | 0.675224 | N_{32} | 0.013462 |

N_{23} | 0.017205 | S_{42} | 0.014756 | S_{42} | 0.014808 | N_{32} | 0.014087 | E_{12} | [1.3232,1.88296] | 0.73459 | S_{42} | 0.013400 |

S_{21} | 0.016776 | N_{11} | 0.014742 | N_{11} | 0.014240 | S_{31} | 0.013822 | H_{11} | [1.21722,1.7032] | 0.513748 | S_{43} | 0.013400 |

S_{25} | 0.016015 | S_{21} | 0.013937 | H_{11} | 0.013434 | H_{11} | 0.013601 | S_{51} | [1.04206,1.85598] | 0.588416 | S31 | 0.013244 |

N_{13} | 0.013499 | H_{11} | 0.013332 | S_{43} | 0.013270 | H_{41} | 0.013558 | S_{41} | [0.9555,1.78963] | 0.577056 | N_{11} | 0.011738 |

S_{42} | 0.013147 | N_{12} | 0.013053 | S_{21} | 0.013236 | N_{11} | 0.013197 | S_{24} | [1.03337,1.58321] | 0.618407 | N_{12} | 0.011738 |

S_{43} | 0.013147 | S_{43} | 0.012920 | N_{12} | 0.012960 | N_{12} | 0.012693 | N_{22} | [1.1401,1.34627] | 0.5 | H_{41} | 0.011126 |

N_{32} | 0.012876 | H_{41} | 0.012639 | H_{41} | 0.012918 | N_{23} | 0.011602 | N_{21} | [1.1401,1.34627] | 0.718915 | S_{21} | 0.010174 |

S_{24} | 0.010677 | S_{25} | 0.012449 | S_{25} | 0.012054 | S_{21} | 0.011464 | H_{33} | [0.71778,1.44861] | 0.602178 | S_{25} | 0.010174 |

S_{41} | 0.009492 | N_{23} | 0.012154 | N_{23} | 0.011965 | S_{25} | 0.011017 | N_{11} | [0.759,1.25804] | 0.540678 | N_{23} | 0.009702 |

E_{23} | 0.008075 | N_{13} | 0.009635 | E_{23} | 0.009559 | E_{23} | 0.010155 | N_{34} | [0.83114,1.1453] | 0.5 | E_{23} | 0.008967 |

S_{44} | 0.006231 | N_{34} | 0.009309 | N_{34} | 0.009049 | S_{41} | 0.008886 | N_{32} | [0.83114,1.1453] | 0.661054 | S_{52} | 0.008699 |

S_{52} | 0.004730 | E_{23} | 0.009275 | N_{13} | 0.008890 | H_{33} | 0.008564 | H_{41} | [0.70149,1.13498] | 0.603941 | N_{34} | 0.008393 |

S_{23} | 0.004462 | S_{52} | 0.008171 | S_{52} | 0.008215 | N_{34} | 0.008375 | S_{54} | [0.61831,1.11409] | 0.5 | H_{33} | 0.008169 |

S_{51} | 0.003829 | S_{24} | 0.008006 | H_{33} | 0.008014 | S_{52} | 0.008284 | S_{53} | [0.61831,1.11409] | 0.661846 | S_{41} | 0.007220 |

S_{53} | 0.002731 | H_{33} | 0.007756 | S_{41} | 0.007970 | N_{13} | 0.007429 | E_{33} | [0.64874,0.92318] | 0.56956 | N_{13} | 0.006531 |

S_{54} | 0.002429 | S_{41} | 0.007645 | S_{24} | 0.007702 | S_{24} | 0.006919 | N_{12} | [0.672,0.86174] | 0.550236 | S_{24} | 0.005896 |

S_{55} | 0.001546 | H_{12} | 0.006962 | H_{12} | 0.006820 | H_{12} | 0.006396 | S_{23} | [0.5046,0.98125] | 0.501867 | E_{24} | 0.005590 |

S_{32} | 0.000000 | S_{51} | 0.006134 | S_{51} | 0.005987 | E_{24} | 0.006037 | S_{32} | [0.52952,0.95455] | 0.58258 | H_{12} | 0.005585 |

S_{56} | 0.000000 | S_{32} | 0.005652 | S_{32} | 0.005756 | S_{32} | 0.005944 | S_{44} | [0.33614,1.03286] | 0.513851 | S_{51} | 0.005525 |

E_{24} | 0.000000 | H_{23} | 0.005442 | H_{23} | 0.005474 | S_{51} | 0.005637 | E_{23} | [0.49956,0.85014] | 0.700636 | S_{32} | 0.005401 |

N_{14} | 0.000000 | S_{44} | 0.004830 | E_{24} | 0.005154 | H_{23} | 0.005448 | H_{12} | [0.49356,0.7153] | 0.716183 | H_{32} | 0.004676 |

N_{34} | 0.000000 | E_{24} | 0.004764 | S_{44} | 0.004904 | S_{44} | 0.005098 | S_{55} | [0.37522,0.69381] | 0.663563 | H_{23} | 0.004669 |

H_{11} | 0.000000 | S_{23} | 0.004646 | S_{23} | 0.004527 | H_{32} | 0.004968 | H_{32} | [0.28485,0.65808] | 0.544825 | S_{44} | 0.004167 |

H_{12} | 0.000000 | S_{53} | 0.004210 | S_{53} | 0.004165 | S_{23} | 0.004209 | H_{23} | [0.40115,0.50832] | 0.595829 | S_{23} | 0.003729 |

H_{13} | 0.000000 | H_{21} | 0.003982 | H_{32} | 0.004122 | S_{53} | 0.004051 | N_{13} | [0.40942,0.47951] | 0.586548 | S_{53} | 0.003278 |

H_{21} | 0.000000 | S_{54} | 0.003780 | S_{54} | 0.003825 | S_{54} | 0.003912 | E_{24} | [0.32312,0.53] | 0.558802 | S_{54} | 0.003278 |

H_{22} | 0.000000 | H_{32} | 0.003759 | H_{21} | 0.003729 | N_{14} | 0.003195 | N_{23} | [0.38003,0.44876] | 0.840303 | H_{51} | 0.002742 |

H_{23} | 0.000000 | N_{14} | 0.003308 | N_{14} | 0.003277 | H_{21} | 0.003178 | H_{51} | [0.23827,0.44786] | 0.89211 | H_{21} | 0.002673 |

H_{31} | 0.000000 | S_{55} | 0.002765 | S_{55} | 0.002636 | H_{42} | 0.003106 | H_{21} | [0.2296,0.29094] | 0.898511 | N_{14} | 0.002664 |

H_{32} | 0.000000 | H_{51} | 0.002492 | H_{51} | 0.002593 | H_{51} | 0.002828 | H_{13} | [0.17111,0.26352] | 0.500174 | H_{13} | 0.002265 |

H_{33} | 0.000000 | H_{13} | 0.002358 | H_{42} | 0.002530 | H_{13} | 0.002678 | S_{56} | [0.13099,0.30358] | 0.794194 | H_{42} | 0.002020 |

H_{41} | 0.000000 | H_{42} | 0.002253 | H_{13} | 0.002452 | S_{55} | 0.002339 | N_{14} | [0.13746,0.19556] | 0.778545 | S_{55} | 0.001989 |

H_{42} | 0.000000 | H_{22} | 0.001349 | H_{22} | 0.001351 | H_{22} | 0.001331 | H_{42} | [0.11091,0.17946] | 0.999997 | H_{22} | 0.001020 |

H_{51} | 0.000000 | H_{52} | 0.001067 | H_{52} | 0.001130 | H_{52} | 0.001269 | H_{22} | [0.08761,0.11101] | 0.615939 | S_{56} | 0.000952 |

H_{52} | 0.000000 | S_{56} | 0.000987 | S_{56} | 0.001011 | S_{56} | 0.001063 | H_{52} | [0.06855,0.11849] | 1 | H_{52} | 0.000903 |

H_{53} | 0.000000 | H_{53} | 0.000268 | H_{53} | 0.000298 | H_{53} | 0.000360 | H_{53} | [0.02376,0.03902] | H_{53} | 0.00029 |

FAHP $\mathit{\nu}=1$ | FAHP $\mathit{\nu}=0.5$ | FAHP $\mathit{\nu}=0$ | FAHP Chang | AHP | IAHP | |
---|---|---|---|---|---|---|

$\mathrm{FAHP}\nu =1$ | $Sc=0.997\phantom{\rule{0ex}{0ex}}WS=0.964$ | $Sc=0.988\phantom{\rule{0ex}{0ex}}WS=0.964$ | $Sc=0.877\phantom{\rule{0ex}{0ex}}WS=0.991$ | $Sc=0.989\phantom{\rule{0ex}{0ex}}WS=0.964$ | $Sc=0.836\phantom{\rule{0ex}{0ex}}Ws=0.837$ | |

$\mathrm{FAHP}\nu =0.5$ | $Sc=0.995\phantom{\rule{0ex}{0ex}}WS=0.997$ | $Sc=0.871\phantom{\rule{0ex}{0ex}}WS=0.991$ | $Sc=0.995\phantom{\rule{0ex}{0ex}}WS=0.999$ | $Sc=0.845\phantom{\rule{0ex}{0ex}}WS=0.877$ | ||

$\mathrm{FAHP}\nu =0$ | $Sc=0.852\phantom{\rule{0ex}{0ex}}WS=0.986$ | $Sc=0.996\phantom{\rule{0ex}{0ex}}WS=0.997$ | $Sc=0.838\phantom{\rule{0ex}{0ex}}WS=0.865$ | |||

FAHP Chang | $Sc=0.847\phantom{\rule{0ex}{0ex}}WS=0.991$ | $Sc=0.836\phantom{\rule{0ex}{0ex}}WS=0.837$ | ||||

AHP | $Sc=0.850\phantom{\rule{0ex}{0ex}}WS=0.882$ |

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Milošević, M.R.; Nikolić, M.M.; Milošević, D.M.; Dimić, V.
Managing Resources Based on Influential Indicators for Sustainable Economic Development: A Case Study in Serbia. *Sustainability* **2022**, *14*, 4795.
https://doi.org/10.3390/su14084795

**AMA Style**

Milošević MR, Nikolić MM, Milošević DM, Dimić V.
Managing Resources Based on Influential Indicators for Sustainable Economic Development: A Case Study in Serbia. *Sustainability*. 2022; 14(8):4795.
https://doi.org/10.3390/su14084795

**Chicago/Turabian Style**

Milošević, Mimica R., Miloš M. Nikolić, Dušan M. Milošević, and Violeta Dimić.
2022. "Managing Resources Based on Influential Indicators for Sustainable Economic Development: A Case Study in Serbia" *Sustainability* 14, no. 8: 4795.
https://doi.org/10.3390/su14084795