# Solving Solar-Wind Power Station Location Problem Using an Extended Weighted Aggregated Sum Product Assessment (WASPAS) Technique with Interval Neutrosophic Sets

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. INs

**Definition**

**1.**

- ${a}_{1}+{a}_{2}=\left[{a}_{1}^{L}+{a}_{2}^{L},{a}_{1}^{U}+{a}_{2}^{U}\right]$,
- $\lambda {a}_{1}=\left[\lambda {a}_{1}^{L},\lambda {a}_{1}^{U}\right],\lambda >0.$

**Definition**

**2.**

#### 2.2. INSs

**Definition**

**3.**

**Definition**

**4.**

- (1)
- The complement of ${a}_{1}$ is ${\overline{a}}_{1}=\langle \left[{F}_{1}^{L},{F}_{1}^{U}\right],\left[1-{I}_{1}^{U},1-{I}_{1}^{L}\right],\left[{T}_{1}^{L},{T}_{1}^{U}\right]\rangle $,
- (2)
- ${a}_{1}+{a}_{2}=\langle \left[{T}_{1}^{L}+{T}_{2}^{L}-{T}_{1}^{L}{T}_{2}^{L},{T}_{1}^{U}+{T}_{2}^{U}-{T}_{1}^{U}{T}_{2}^{U}\right],\left[{I}_{1}^{L}{I}_{2}^{L},{I}_{1}^{U}{I}_{2}^{U}\right],\left[{F}_{1}^{L}{F}_{2}^{L},{F}_{1}^{U}{F}_{2}^{U}\right]\rangle ,$
- (3)
- ${a}_{1}\times {a}_{2}=\begin{array}{c}\langle \left[{T}_{1}^{L}{T}_{2}^{L},{T}_{1}^{U}{T}_{2}^{U}\right],\left[{I}_{1}^{L}+{I}_{2}^{L}-{I}_{1}^{L}{I}_{2}^{L},{I}_{1}^{U}+{I}_{2}^{U}-{I}_{1}^{U}{I}_{2}^{U}\right],\hfill \\ \left[{F}_{1}^{L}+{F}_{2}^{L}-{F}_{1}^{L}{F}_{2}^{L},{F}_{1}^{U}+{F}_{2}^{U}-{F}_{1}^{U}{F}_{2}^{U}\right]\rangle ,\hfill \end{array}$
- (4)
- $\eta {a}_{1}=\langle \left[1-{\left(1-{T}_{1}^{L}\right)}^{\eta},1-{\left(1-{T}_{1}^{U}\right)}^{\eta}\right],\left[{\left({I}_{1}^{L}\right)}^{\eta},{\left({I}_{1}^{U}\right)}^{\eta}\right],\left[{\left({F}_{1}^{L}\right)}^{\eta},{\left({F}_{1}^{U}\right)}^{\eta}\right]\rangle ,\text{\hspace{0.17em}}\eta >0$,
- (5)
- ${{a}_{1}}^{\eta}=\langle \left[{\left({T}_{1}^{L}\right)}^{\eta},{\left({T}_{1}^{U}\right)}^{\eta}\right],\left[1-{\left(1-{I}_{1}^{L}\right)}^{\eta},1-{\left(1-{I}_{1}^{U}\right)}^{\eta}\right],\left[1-{\left(1-{F}_{1}^{L}\right)}^{\eta},1-{\left(1-{F}_{1}^{U}\right)}^{\eta}\right]\rangle ,\text{\hspace{0.17em}}\eta >0.$

**Definition**

**5.**

**Theorem**

**1.**

**Definition**

**6.**

**Definition**

**7.**

- (1)
- $S\left(a\right)=\left[{T}^{L}+1-{I}^{U}+1-{F}^{U},{T}^{U}+1-{I}^{L}+1-{F}^{L}\right],$
- (2)
- $H\left(a\right)=\left[\mathrm{min}\left\{{T}^{L}-{F}^{L},{T}^{U}-{F}^{U}\right\},\mathrm{max}\left\{{T}^{L}-{F}^{L},{T}^{U}-{F}^{U}\right\}\right],$
- (3)
- $B\left(a\right)=\left[{T}^{L},{T}^{U}\right].$

## 3. The Framework of an Extended WASPAS Technique

#### 3.1. Maximizing Deviation Method for Objective Weight Estimating

#### 3.2. G1 for Subjective Weight Estimating

**Step****1**- Determine the criteria ranking order relation.Let DMs provide the order relation of the set $C=\left\{{C}_{1},\cdots ,{C}_{j},\cdots ,{C}_{n}\right\}$ according to the importance of the criteria judging from their experience.
**Step****2**- Assign the relative importance degree index of adjacent criteria.Determine the relative importance degree index ${r}_{j}={\omega}_{j-1}^{\u2033}/{\omega}_{j}^{\u2033}$ of the adjacent criteria ${C}_{j-1}$ and ${C}_{j}$ according to Table 1.
**Step****3**- Calculate the subjective weights of criteria by Equations (18) and (19).$${\omega}_{n}^{\u2033}={\left(1+{\displaystyle \sum _{i=2}^{n}{\displaystyle \prod _{j=i}^{n}{r}_{j}}}\right)}^{-1},$$$${\omega}_{j}^{\u2033}={\displaystyle \prod _{k=j+1}^{n}{r}_{k}{\omega}_{n}^{\u2033}}.$$

#### 3.3. An Extended WASPAS Technique with Integrated Criteria Weight Information

**Step****1.**- Construct the decision matrix.Let a DM provide performance estimation of every alternative with respect to all the criteria, which is shown as$$A={\left({A}_{ij}\right)}_{m\times n}={\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \dots & {a}_{1n}\\ {a}_{21}& {a}_{22}& \dots & {a}_{2n}\\ & & \vdots & \\ {a}_{n1}& {a}_{n2}& \dots & {a}_{nn}\end{array}\right]}_{m\times n}$$
**Step****2.**- Derive the normalized decision matrix.Utilize Equation (1) in Definition 4 to convert the evaluation under cost criteria to benefit criteria. For convenience, the normalized evaluations for the $i$th alternative with respect to the $j$th cost criteria are also denoted by ${a}_{ij}=\langle \left[{T}_{ij}^{L},{T}_{ij}^{U}\right],\left[{I}_{ij}^{L},{I}_{ij}^{U}\right],\left[{F}_{ij}^{L},{F}_{ij}^{U}\right]\rangle $.
**Step****3.**- Calculate the objective criteria weight.Use Equations (16) and (17) to calculate the objective weight ${\omega}_{j}^{\prime *}$ for each criteria by the maximizing deviation method.
**Step****4.**- Estimate the subjective criteria weight.Conduct the procedures proposed in Section 3.2, and estimate the subjective criteria weight ${\omega}_{j}^{\u2033}$ for each criteria.
**Step****5.**- Compute the integrated criteria weight.Combine the objective and subjective weights generated from Step 3 and Step 4, the integrated criteria weight ${\omega}_{j}$ is shown as$${\omega}_{j}=\lambda {\omega}_{j}^{\prime *}+\left(1-\lambda \right){\omega}_{j}^{\u2033},$$
**Step****6.**- Calculate sum total relative importance of alternative.Incorporate the INPWA operator defined in Equation (9), the sum total relative importance of alternative $i$ is calculated by Equation (21).$${Q}_{i}^{\prime}=INPWA\left({a}_{1},{a}_{2},\cdots ,{a}_{n}\right).$$
**Step****7.**- Calculate product total relative importance of alternative.Refer to the INPGWA operator in Equation (8), the product total relative importance for alternative $i$ is defined as$${Q}_{i}^{\u2033}=INPGWA\left({a}_{1},{a}_{2},\cdots ,{a}_{n}\right).$$
**Step****8.**- Determine the aggregated WASPAS measure for each alternative.Aggregate ${Q}_{i}^{\prime}$ and ${Q}^{\u2033}$, the final WASPAS measure can be determined by the equation as follows:$${Q}_{j}=\theta {Q}_{i}^{\prime}+\left(1-\theta \right){Q}_{i}^{\u2033},$$
**Step****9.**- Generate the score, accuracy and certainty function values for each alternative.Obtain the score, accuracy and certainty function values $S\left({a}_{i}\right)$, $H\left({a}_{i}\right)$ and $B\left({a}_{i}\right)$ for each alternative utilizing Equation (1) in Definition 7.
**Step****10.**- Construct the likelihood matrix.Construct the possibility matrix of the score function value $S\left({a}_{i}\right)$ according to Equation (2), which is shown as follows:$${P}^{S}\left(S\left({a}_{i}\right)\ge S\left({a}_{j}\right)\right)={\left[\begin{array}{cccc}{p}_{11}^{S}& {p}_{12}^{S}& \cdots & {p}_{1n}^{S}\\ {p}_{21}^{S}& {p}_{22}^{S}& \cdots & {p}_{2n}^{S}\\ & & \vdots & \\ {p}_{n1}^{S}& {p}_{n2}^{S}& \cdots & {p}_{nn}^{S}\end{array}\right]}_{n\times n},$$
**Step****11.**- Rank the alternatives and select the good location.Rank all the alternatives and select the good location according to the descending order of ${p}_{i}\text{\hspace{0.17em}}(i=1,2,\cdots ,m)$.

## 4. Case Study

#### 4.1. Problem Description

#### 4.2. The Selection of Solar-Wind Power Station Location

**Step****1.**- Construct the decision matrix.The decision matrix is constructed by the illustration in Section 4.1, which is shown as $A={\left({A}_{ij}\right)}_{4\times 5}$ above.
**Step****2.**- Derive the normalized decision matrix.Referring to the criteria description in Table 2, ${C}_{2}$ and ${C}_{4}$ are cost criteria. Utilize Equation (1) in Definition 4, the normalized decision matrix can be obtained as$$\begin{array}{l}A={\left({A}_{ij}\right)}_{4\times 5}=[\begin{array}{cc}\langle \left[0.7,0.8\right],\left[0.5,0.7\right],\left[0.1,0.2\right]\rangle & \langle \left[0.2,0.3\right],\left[0.2,0.8\right],\left[0.3,0.5\right]\rangle \\ \langle \left[0.6,0.8\right],\left[0.4,0.5\right],\left[0.3,0.3\right]\rangle & \langle \left[0.1,0.3\right],\left[0.5,0.7\right],\left[0.5,0.7\right]\rangle \\ \langle \left[0.8,0.8\right],\left[0.4,0.6\right],\left[0.1,0.2\right]\rangle & \langle \left[0.4,0.5\right],\left[0.7,0.8\right],\left[0.6,0.6\right]\rangle \\ \langle \left[0.7,0.9\right],\left[0.3,0.4\right],\left[0.2,0.2\right]\rangle & \langle \left[0.2,0.4\right],\left[0.6,0.6\right],\left[0.6,0.8\right]\rangle \end{array}\\ {\begin{array}{ccc}\langle \left[0.4,0.6\right],\left[0.2,0.2\right],\left[0.2,0.4\right]\rangle & \langle \left[0.4,0.4\right],\left[0.4,0.5\right],\left[0.4,0.5\right]\rangle & \langle \left[0.6,0.7\right],\left[0.4,0.5\right],\left[0.4,0.5\right]\rangle \\ \langle \left[0.6,0.7\right],\left[0.4,0.6\right],\left[0.3,0.4\right]\rangle & \langle \left[0.4,0.5\right],\left[0.6,0.7\right],\left[0.5,0.6\right]\rangle & \langle \left[0.8,0.9\right],\left[0.3,0.4\right],\left[0.1,0.2\right]\rangle \\ \langle \left[0.7,0.8\right],\left[0.6,0.7\right],\left[0.1,0.2\right]\rangle & \langle \left[0.2,0.3\right],\left[0.2,0.3\right],\left[0.6,0.7\right]\rangle & \langle \left[0.7,0.8\right],\left[0.5,0.6\right],\left[0.1,0.2\right]\rangle \\ \langle \left[0.5,0.6\right],\left[0.5,0.6\right],\left[0.2,0.3\right]\rangle & \langle \left[0.1,0.2\right],\left[0.6,0.7\right],\left[0.8,0.9\right]\rangle & \langle \left[0.5,0.7\right],\left[0.5,0.6\right],\left[0.2,0.3\right]\rangle \end{array}]}_{4\times 5}\end{array}$$
**Step****3.**- Calculate the objective criteria weight.Use Equations (16) and (17), then the objective weight ${\omega}_{j}^{\prime *}$ for each criteria can be calculated as$${\omega}_{1}^{\prime *}=0.1259,\text{}{\omega}_{2}^{\prime *}=0.2122,\text{}{\omega}_{3}^{\prime *}=0.2086,\text{}{\omega}_{4}^{\prime *}=0.2698,\text{}{\omega}_{5}^{\prime *}=0.1835.$$
**Step****4.**- Estimate the subjective criteria weight.Assume that the aggregation parameter $\lambda =0.5$, and the order relation of all the criteria is ${C}_{4}\succ {C}_{2}\succ {C}_{1}\succ {C}_{5}\succ {C}_{3}$ judging from DMs’ subjective experience. Referring to the relative importance degree index among adjacent criteria in Table 1, the subjective criteria weight for each criteria is estimated as ${\omega}_{1}^{\u2033}=0.3533$, ${\omega}_{2}^{\u2033}=0.2945$, ${\omega}_{3}^{\u2033}=0.1840$, ${\omega}_{4}^{\u2033}=0.1022$ and ${\omega}_{5}^{\u2033}=0.0639$.
**Step****5.**- Compute the integrated criteria weight.Combine the objective and subjective weights generated from Step 3 and Step 4, the integrated weight of criteria is shown as ${\omega}_{1}=0.2396$, ${\omega}_{2}=0.2534$, ${\omega}_{3}=0.1963$, ${\omega}_{4}=0.1860$ and ${\omega}_{5}=0.1237$.
**Step****6.**- Calculate sum total relative importance of alternative.Incorporate the INPWA operator defined in Equation (9), the sum total relative importance of all alternatives are$${Q}_{1}^{\prime}=\langle \left[0.4986,0.6171\right],\left[0.3084,0.6468\right],\left[0.1866,0.3342\right]\rangle ,$$$${Q}_{2}^{\prime}=\langle \left[0.4236,0.6255\right],\left[0.4479,0.5977\right],\left[0.3746,0.4618\right]\rangle ,$$$${Q}_{3}^{\prime}=\langle \left[0.6136,0.6642\right],\left[0.5212,0.6680\right],\left[0.2643,0.3665\right]\rangle $$$${Q}_{4}^{\prime}=\langle \left[0.4867,0.7214\right],\left[0.4433,0.5128\right],\left[0.3468,0.4122\right]\rangle $$
**Step****7.**- Calculate product total relative importance of alternative.Refer to the INPGWA operator in Equation (8), the product total relative importance for alternatives are$${Q}_{1}^{\u2033}=\langle \left[0.3816,0.4983\right],\left[0.3562,0.7138\right],\left[0.2219,0.3815\right]\rangle ,$$$${Q}_{2}^{\u2033}=\langle \left[0.2638,0.4970\right],\left[0.4566,0.6189\right],\left[0.4046,0.5409\right]\rangle ,$$$${Q}_{3}^{\u2033}=\langle \left[0.5184,0.6005\right],\left[0.5784,0.7099\right],\left[0.4203,0.4605\right]\rangle $$$${Q}_{4}^{\u2033}=\langle \left[0.3533,0.5616\right],\left[0.4852,0.5355\right],\left[0.4509,0.6134\right]\rangle $$
**Step****8.**- Determine the aggregated WASPAS measure for each alternative.Let $\theta =0.5$, then the final WASPAS measure can be derived as$${Q}_{1}=\langle \left[0.4401,0.5577\right],\left[0.3323,0.6803\right],\left[0.2043,0.3579\right]\rangle ,$$$${Q}_{2}=\langle \left[0.3437,0.5613\right],\left[0.4523,0.6083\right],\left[0.3896,0.5014\right]\rangle ,$$$${Q}_{3}=\langle \left[0.5660,0.6324\right],\left[0.5498,0.6889\right],\left[0.3423,0.4135\right]\rangle $$$${Q}_{4}=\langle \left[0.4200,0.6415\right],\left[0.4643,0.5241\right],\left[0.3989,0.5129\right]\rangle $$
**Step****9.**- Generate the score, accuracy and certainty function values for each alternative.For each alternative, the score, accuracy and certainty function values $S\left({a}_{i}\right)$, $H\left({a}_{i}\right)$ and $B\left({a}_{i}\right)$ are shown in Table 3.
**Step****10.**- Construct the likelihood matrix.Construct the possibility matrix of the score function value $S\left({a}_{i}\right)$ according to Equation (2), which is shown as follows:$${P}^{S}\left(S\left({a}_{i}\right)\ge S\left({a}_{j}\right)\right)={\left[\begin{array}{cccc}0.5& 0.7126& 0.6224& 0.6290\\ 0.7126& 0.5& 0.3358& 0.3820\\ 0.6224& 0.3358& 0.5& 0.5315\\ 0.6290& 0.3820& 0.5315& 0.5\end{array}\right]}_{4\times 4}.$$
**Step****11.**- Rank the alternatives and select the good location.The ranking order of all the alternatives is ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ and the good location is ${A}_{1}$.

## 5. Sensitivity Analysis and Comparison Analysis

#### 5.1. Sensitivity Analysis and Discussion

#### 5.2. Comparison Analysis and Discussion

- (1)
- The method in [62] generates the selection result by implementing two steps. Firstly, confirm the ideal alternatives for different type of criteria. Subsequently, derive the result by similarity measures. According to the first similarity measure in that literature, the similarity measures are obtained as ${S}_{1}^{*}\left({A}^{*},{A}_{1}\right)=0.8178$, ${S}_{1}^{*}\left({A}^{*},{A}_{2}\right)=0.8705$, ${S}_{1}^{*}\left({A}^{*},{A}_{3}\right)=0.8692$ and ${S}_{1}^{*}\left({A}^{*},{A}_{4}\right)=0.9057$.
- (2)
- In the method of [69], maximizing deviation method is utilized to derive objective weights. Then, based on the ideal of TOPSIS method, alternatives are ranked by the relative closeness coefficient. Conduct these procedures, relative closeness coefficient can be calculated as $RC{C}_{1}=0.5226$, $RC{C}_{2}=0.5186$, $RC{C}_{3}=0.5190$ and $RC{C}_{4}=0.5189$.
- (3)
- The procedure of the method in [68] can be briefly classified into aggregation process and ranking process. The ranking procedure in [68] is identical with our proposed method. Based on weighted arithmetic aggregation operator or weighted geometric aggregation operator, the total score are obtained as ${p}_{s}=\left[2.2997,2.0098,2.0589,2.5926\right]$ or ${p}_{s}=\left[2.5804,2.2751,2.3728,2.9288\right]$ with the same ranking order ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$.
- (4)
- Classical WASPAS method in [34] generates the final WASPAS measure by aggregating weighted arithmetic aggregation operator and weighted geometric aggregation operator. To better compare the classical WASPAS method with our method, the alternatives are ranked by the ranking procedure in our paper. Then, ranking vector can be obtained as ${p}_{1}=2.4449$, ${p}_{2}=2.1483$, ${p}_{3}=2.2189$ and ${p}_{4}=2.7681$.

- (1)
- It can effectively manage the solar-wind power station location problem via embedding three procedures into the newly extended WASPAS technique. During the WASPAS technique implement process, a rational location selection result will be generated by incorporating the advantages of relevant methods in these procedures.
- (2)
- With the maximizing derivation method, objective criteria weights can be simply determined no matter under the criteria weights completely unknown or incomplete circumstances. Apart from the objective criteria weights, subjective weights, which fully reflect the subjective preference under practice, can be obtained with G1. The integrated criteria weight is the combination of the objective and subjective weights, and can adequately represent more realistic situation.
- (3)
- Different aggregation parameter $\lambda $ and the proportion adjustment parameter $\theta $ facilitate the whole procedures a dynamic selection. The parameter setting is based on the requirement of real application and subjective preference of DMs, which makes the extended WASPAS technique feasible in dealing with the reality.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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${\mathit{r}}_{\mathit{j}}$ | Description |
---|---|

1.0 | ${C}_{j-1}$ is equally important as ${C}_{j}$ |

1.2 | ${C}_{j-1}$ is slightly more important than ${C}_{j}$ |

1.4 | ${C}_{j-1}$ is obviously more important than ${C}_{j}$ |

1.6 | ${C}_{j-1}$ is strongly more important than ${C}_{j}$ |

1.8 | ${C}_{j-1}$ is extremely more important than ${C}_{j}$ |

Criteria ${\mathit{C}}_{\mathit{j}}$ | Description |
---|---|

Natural resources ${C}_{1}$ | Natural resources include various indicators related to wind and solar resources in the location. |

Economic factors ${C}_{2}$ | Economic factors briefly measure the cost during the engineering construction, operation and maintenance procedures. |

Traffic conditions ${C}_{3}$ | Traffic conditions reflect the traffic convenience to the location during the engineering construction, operation and maintenance procedures. |

Environmental factors ${C}_{4}$ | Environmental factors reflect the environment destruction during the engineering construction and operation procedures. |

Social factors ${C}_{5}$ | Social factors reflect the attitude of the local residents to the engineering. |

${\mathit{A}}_{\mathit{i}}$ | $\mathit{S}\left({\mathit{a}}_{\mathit{i}}\right)$ | $\mathit{H}\left({\mathit{a}}_{\mathit{i}}\right)$ | $\mathit{B}\left({\mathit{a}}_{\mathit{i}}\right)$ |
---|---|---|---|

${A}_{1}$ | $\left[1.4020,2.0212\right]$ | $\left[0.1998,0.2359\right]$ | $\left[0.4401,0.5577\right]$ |

${A}_{2}$ | $\left[1.2341,1.7194\right]$ | $\left[-0.0459,0.0599\right]$ | $\left[0.3437,0.5613\right]$ |

${A}_{3}$ | $\left[1.4636,1.7402\right]$ | $\left[0.2189,0.2237\right]$ | $\left[0.5660,0.6324\right]$ |

${A}_{4}$ | $\left[1.3831,1.7783\right]$ | $\left[0.0212,0.1286\right]$ | $\left[0.4200,0.6415\right]$ |

$\mathit{\lambda}$ | $\mathit{\theta}=0$ | $\mathit{\theta}=0.2$ | $\mathit{\theta}=0.5$ | $\mathit{\theta}=0.8$ | $\mathit{\theta}=1$ |
---|---|---|---|---|---|

$0$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ |

$0.2$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ |

$0.5$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ |

$0.8$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ |

$1$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ |

Methods | Ranking Results |
---|---|

Similarity measure in [62] | ${A}_{4}\succ {A}_{2}\succ {A}_{3}\succ {A}_{1}$ |

An extended TOPSIS method in [69] | ${A}_{3}\succ {A}_{4}\succ {A}_{2}\succ {A}_{1}$ |

Method used weighted arithmetic aggregation operator in [68] | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ |

Method used weighted geometric aggregation operator in [68] | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ |

Classical WASPAS method in [34] | ${A}_{4}\succ {A}_{1}\succ {A}_{3}\succ {A}_{2}$ |

The proposed method | ${A}_{1}\succ {A}_{4}\succ {A}_{3}\succ {A}_{2}$ |

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## Share and Cite

**MDPI and ACS Style**

Nie, R.-x.; Wang, J.-q.; Zhang, H.-y.
Solving Solar-Wind Power Station Location Problem Using an Extended Weighted Aggregated Sum Product Assessment (WASPAS) Technique with Interval Neutrosophic Sets. *Symmetry* **2017**, *9*, 106.
https://doi.org/10.3390/sym9070106

**AMA Style**

Nie R-x, Wang J-q, Zhang H-y.
Solving Solar-Wind Power Station Location Problem Using an Extended Weighted Aggregated Sum Product Assessment (WASPAS) Technique with Interval Neutrosophic Sets. *Symmetry*. 2017; 9(7):106.
https://doi.org/10.3390/sym9070106

**Chicago/Turabian Style**

Nie, Ru-xin, Jian-qiang Wang, and Hong-yu Zhang.
2017. "Solving Solar-Wind Power Station Location Problem Using an Extended Weighted Aggregated Sum Product Assessment (WASPAS) Technique with Interval Neutrosophic Sets" *Symmetry* 9, no. 7: 106.
https://doi.org/10.3390/sym9070106