# Analysis of Priority Scale for Watershed Reforestation Using Trapezoidal Fuzzy VIKOR Method: A Case Study in Semarang, Central Java Indonesia

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. Santawy and Ahmed [6] also used the VIKOR method as a project selection based on capital investment in every company. Several objectives are considered such as economic desires, environmental issues, and technical and social factors. The study showed that the VIKOR method can rank several projects and select one the appropriate one.

## 2. Literature Reviews

#### 2.1. Preliminaries

**Definition**

**1.**

**Definition**

**2.**

#### 2.2. Arithmetic Operations

#### 2.3. Concept of Fuzzy VIKOR

## 3. Criteria System

- Alternatives. Alternatives are different objects and have the same opportunity to be chosen by the decision maker.
- Attributes. Attributes are often also referred to as characteristics, components, or decision criteria. In most cases, one-level criteria are used, although there is a possibility of using sub-criteria related to the criteria that have been given.
- Conflict between criteria. Some criteria usually have conflicts between one another, for example the profit criteria will conflict with the cost criteria.
- Decision weight. Decision weight indicates the relative importance of each criterion, W = (${w}_{1},{w}_{2},\dots ,{w}_{n}$).

## 4. Methods

#### 4.1. VIKOR Method

**Step 1**. Evaluate the best rating ${f}_{i}^{*}$ and the worst rating ${f}_{i}^{-}$ for all the criteria,$i=1,2,\dots ,n$, if the function represents an advantage then

**Step 2**. Calculate the values of ${S}_{j}$ and ${R}_{j}$$\left(j=1,2,\dots ,m\right)$ as

**Step 3**. Compute the values of ${S}^{*}$, ${S}^{-}$, ${R}^{*}$, ${R}^{-}$, ${Q}_{j}$ for formulated:

**Step 4.**Perform ranking for the alternatives by categorizing each $S,R,Q$ values in decreasing order. The output is set in three ranking lists and denoted as ${S}_{[.]},{R}_{[.]}and{Q}_{[.]}$

**Step 5.**In this step, we conclude that the lower the VIKOR index (${Q}_{i}$), the better the alternative solution.

**Requirement**

**1.**

**Requirement**

**2.**

- (i)
- If condition 1 is not met, then ${A}^{(1)},{A}^{(2)},\dots ,{A}^{(n)}$ is the proposed solution.
- (ii)
- If condition 2 is not met, then ${A}^{(1)}$ and ${A}^{(2)}$ is the proposed solution.

#### 4.2. Data Analysis

## 5. Case Study

## 6. Results and Discussion

_{ij}of an alternative can be evaluated as [33,34]

_{i}is the value of maximum group utility and R

_{i}is a minimum individual regret of the opponent. These variables can be calculated as

_{j}is the weight given to each criterion c

_{j}. VIKOR index (Qi) can be obtained using the following formula

**C1**: DAS Preservation

**C2**: Prevention of soil erosion

**C3**: Cost saving

**C4**: Land availability

**C5**: Community Supporting Capacity

**C6**: Government involvement

_{i}and Ri using Equations (5) and (6)—and to determine the VIKOR index (Qi) using Equation (7) (Table 10).

**Condition**

**1.**

**Condition**

**2.**

## 7. Conclusions and Future Work

**Future work:**For further research, alternatives and criteria on the linguistic scale according to decision makers can be added, so that the data entered is more varied. In addition, the VIKOR method can be applied in other programs as a ranking method to provide an alternative model for integrated watershed management policies in the form of a framework that can be implemented within a certain timeframe, both general for all watersheds and those that are specific on the basis of their critical criterion criteria. Integrated watershed management is very important in order to preserve the environment for the welfare of the community. The VIKOR method can also be applied in other fields of study as a ranking or decision support method.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Study area of watershed boundaries in Semarang City, Central Java, Indonesia. Source: BPDAS-HL Pemali Jratun, 2019.

**Table 1.**Linguistics terms and appropriate fuzzy values among criteria [2].

Linguistic Variable | Fuzzy Number |
---|---|

Very poor (VP) | (0.0, 0.0, 0.1, 0.2) |

Poor (P) | (0.1, 0.2, 0.2, 0.3) |

Medium poor (MP) | (0.2, 0.3, 0.4, 0.5) |

Fair (F) | (0.4, 0.5, 0.5, 0.6) |

Medium good (MG) | (0.5, 0.6, 0.7, 0.8) |

Good (G) | (0.7, 0.8, 0.8, 0.9) |

Very good (VG) | (0.8, 0.9, 1.0,1.0) |

**Table 2.**Linguistic terms and appropriate fuzzy values among material [2].

Linguistic Variable | Fuzzy Number |
---|---|

Very low (VL) | (0.0, 0.0, 0.1, 0.2) |

Low (L) | (0.1, 0.2, 0.2, 0.3) |

Fairly low (FL) | (0.2, 0.3, 0.4, 0.5) |

Medium (M) | (0.4, 0.5, 0.5, 0.6) |

Fairly high (FH) | (0.5, 0.6, 0.7, 0.8) |

High (H) | (0.7, 0.8, 0.8, 0.9) |

Very high (VH) | (0.8, 0.9, 1.0,1.0) |

Decision | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

D1 | G | VG | MG | MG | F | MP |

D2 | VG | VG | G | MG | MP | MP |

**Table 4.**Pairwise comparisons among criteria according to decision makers in trapezoidal fuzzy numbers.

Decision | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

D1 | (0.7, 0.8, 0.8, 0.9) | (0.8, 0.9, 1.0, 1.0) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) | (0.4, 0.5, 0.5, 0.6) | (0.2, 0.3, 0.4,0.5) |

D2 | (0.8, 0.9, 1.0, 1.0) | (0.8, 0.9, 1.0, 1.0) | (0.7, 0.8, 0.8, 0.9) | (0.5, 0.6, 0.7, 0.8) | (0.2, 0.3, 0.4,0.5) | (0.2, 0.3, 0.4,0.5) |

**Table 5.**Pairwise comparisons of alternative with criteria according to decision makers on linguistic scale.

D1 | C1 | C2 | C3 | C4 | C5 | C6 |

A1 | H | H | FH | FH | H | FH |

A2 | FL | L | FL | L | FL | H |

A3 | FL | L | M | L | FL | FL |

A4 | FL | L | FL | L | FH | FH |

A5 | FH | M | L | M | FH | FH |

D2 | C1 | C2 | C3 | C4 | C5 | C6 |

A1 | M | M | M | H | FH | FH |

A2 | VL | VL | FL | VL | FH | FH |

A3 | FL | FL | M | H | FH | FH |

A4 | M | M | FL | VL | FH | FH |

A5 | FL | FL | L | FL | FH | FH |

**Table 6.**Pairwise comparisons of alternative with criteria according to decision makers on fuzzy numbers.

D1 | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

A1 | (0.7, 0.8, 0.8, 0.9) | (0.7, 0.8, 0.8, 0.9) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) | (0.7, 0.8, 0.8, 0.9) | (0.5, 0.6, 0.7, 0.8) |

A2 | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.2, 0.3, 0.4,0.5) | (0.7, 0.8, 0.8, 0.9) |

A3 | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.4, 0.5, 0.5, 0.6) | (0.1, 0.2, 0.2,0.3) | (0.2, 0.3, 0.4,0.5) | (0.2, 0.3, 0.4,0.5) |

A4 | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

A5 | (0.5, 0.6, 0.7, 0.8) | (0.4, 0.5, 0.5, 0.6) | (0.1, 0.2, 0.2,0.3) | (0.4, 0.5, 0.5, 0.6) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

D2 | C1 | C2 | C3 | C4 | C5 | C6 |

A1 | (0.4, 0.5, 0.5, 0.6) | (0.4, 0.5, 0.5, 0.6) | (0.4, 0.5, 0.5, 0.6) | (0.7, 0.8, 0.8, 0.9) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

A2 | (0.0, 0.0, 0.1, 0.2) | (0.0, 0.0, 0.1, 0.2) | (0.2, 0.3, 0.4,0.5) | (0.0, 0.0, 0.1, 0.2) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

A3 | (0.2, 0.3, 0.4,0.5) | (0.2, 0.3, 0.4,0.5) | (0.4, 0.5, 0.5, 0.6) | (0.7, 0.8, 0.8, 0.9) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

A4 | (0.4, 0.5, 0.5, 0.6) | (0.4, 0.5, 0.5, 0.6) | (0.2, 0.3, 0.4,0.5) | (0.0, 0.0, 0.1, 0.2) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

A5 | (0.2, 0.3, 0.4,0.5) | (0.2, 0.3, 0.4,0.5) | (0.1, 0.2, 0.2,0.3) | (0.2, 0.3, 0.4,0.5) | (0.5, 0.6, 0.7, 0.8) | (0.5, 0.6, 0.7, 0.8) |

**Table 7.**Weight of criteria and pairwise comparisons of alternative with criteria on trapezoidal fuzzy numbers.

C1 | C2 | C3 | C4 | C5 | C6 | |
---|---|---|---|---|---|---|

W | (0.7, 0.85, 0.9, 1.0) | (0.8, 0.9, 1.0, 1.0) | (0.5, 0.7, 0.75, 0.9) | (0.5,0.6, 0.7, 0.8) | (0.2, 0.4, 0.45, 0.6) | (0.2, 0.3, 0.4, 0.5) |

A1 | (0.4, 0.65, 0.65, 0.9) | (0.4, 0.65, 0.65, 0.9) | (0.4, 0.55, 0.6, 0.8) | (0.5, 0.7, 0.75, 0.9) | (0.5, 0.7, 0.75, 0.9) | (0.5,0.6, 0.7, 0.8) |

A2 | (0.0, 0.15, 0.25, 0.5) | (0.0, 0.1, 0.15, 0.3) | (0.2, 0.3, 0.4, 0.5) | (0.0, 0.1, 0.15, 0.3) | (0.2, 0.45, 0.55, 0.8) | (0.5, 0.7, 0.75, 0.9) |

A3 | (0.2, 0.3, 0.4, 0.5) | (0.1, 0.25, 0.3, 0.5) | (0.4, 0.5, 0.5, 0.6) | (0.1, 0.5, 0.5, 0.9) | (0.2, 0.45, 0.55, 0.8) | (0.2, 0.45, 0.55, 0.8) |

A4 | (0.2, 0.4, 0.45, 0.6) | (0.1, 0.35, 0.35,0.6) | (0.2, 0.3, 0.4, 0.5) | (0.0, 0.1, 0.15, 0.3) | (0.5,0.6, 0.7, 0.8) | (0.5,0.6, 0.7, 0.8) |

A5 | (0.2, 0.45, 0.55, 0.8) | (0.2, 0.4, 0.45, 0.6) | (0.1, 0.2, 0.2, 0.3) | (0.2, 0.4, 0.45, 0.6) | (0.5,0.6, 0.7, 0.8) | (0.5,0.6, 0.7, 0.8) |

C1 | C2 | C3 | C4 | C5 | C6 | |
---|---|---|---|---|---|---|

W | 0.86 | 0.92 | 0.71 | 0.65 | 0.41 | 0.35 |

A1 | 0.65 | 0.65 | 0.59 | 0.71 | 0.71 | 0.65 |

A2 | 0.23 | 0.14 | 0.35 | 0.14 | 0.50 | 0.71 |

A3 | 0.35 | 0.29 | 0.50 | 0.50 | 0.50 | 0.50 |

A4 | 0.41 | 0.35 | 0.35 | 0.14 | 0.65 | 0.65 |

A5 | 0.50 | 0.41 | 0.20 | 0.41 | 0.65 | 0.65 |

C1 | C2 | C3 | C4 | C5 | C6 | |
---|---|---|---|---|---|---|

${f}_{i}^{*}$ | 0.65 | 0.65 | 0.59 | 0.71 | 0.71 | 0.71 |

${f}_{i}^{-}$ | 0.23 | 0.14 | 0.20 | 0.14 | 0.50 | 0.50 |

S | R | Q(0.5) | |
---|---|---|---|

A1 | 0.10 | 0.10 | 0.00 |

A2 | 3.28 | 0.92 | 1.00 |

A3 | 2.43 | 0.65 | 0.70 |

A4 | 2.34 | 0.65 | 0.69 |

A5 | 2.01 | 0.71 | 0.67 |

1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|

S | A1 | A5 | A4 | A3 | A2 |

R | A1 | A3 | A4 | A5 | A2 |

Q(0.5) | A1 | A5 | A4 | A3 | A2 |

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**MDPI and ACS Style**

Sunarsih, S.; Pamurti, R.D.; Khabibah, S.; Hadiyanto, H.
Analysis of Priority Scale for Watershed Reforestation Using Trapezoidal Fuzzy VIKOR Method: A Case Study in Semarang, Central Java Indonesia. *Symmetry* **2020**, *12*, 507.
https://doi.org/10.3390/sym12040507

**AMA Style**

Sunarsih S, Pamurti RD, Khabibah S, Hadiyanto H.
Analysis of Priority Scale for Watershed Reforestation Using Trapezoidal Fuzzy VIKOR Method: A Case Study in Semarang, Central Java Indonesia. *Symmetry*. 2020; 12(4):507.
https://doi.org/10.3390/sym12040507

**Chicago/Turabian Style**

Sunarsih, Sunarsih, Rahayuning Dwi Pamurti, Siti Khabibah, and Hadiyanto Hadiyanto.
2020. "Analysis of Priority Scale for Watershed Reforestation Using Trapezoidal Fuzzy VIKOR Method: A Case Study in Semarang, Central Java Indonesia" *Symmetry* 12, no. 4: 507.
https://doi.org/10.3390/sym12040507