# Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Waste Management Strategies

Technological Processes | I | II | III | IV | |
---|---|---|---|---|---|

Strategies | |||||

Secondary collection of secondary raw materials | + | + | + | + | |

Secondary collection and composting of garden wastes | + | + | + | + | |

Home composting | + | + | - | + | |

Mechanical biological treatment | - | - | + | + | |

Collection and separate treatment of a biodegradable fraction | + | + | - | + | |

Separation of a biodegradable fraction and production of biogas | - | - | + | - | |

Mechanical waste sorting plant (production of secondary raw materials) | + | + | + | + | |

Preparation of waste for incineration and incineration | + | - | - | + | |

Disposal of waste by landfill | + | + | + | + |

## 3. Possible Alternatives

_{1}–x

_{3}) cover a part of investments required for the project development. Residential, office, industrial, and public sector buildings cannot function without engineering communications. The analysis of industrial structures in general, and heat and electric power production facilities, in particular, revealed specific requirements, such as the need to be connected to electric power transmission grid or other systems to supply produced heat or power to end-users. Such supply also requires pipelines and electric lines. Additionally, local surface runoff cannot be directed to the city sewage as rainwater would mix with wastewater, and the mixture would put a strain on wastewater treatment facilities of the city.

_{2}) determines solutions to logistics problems. Clearly, a waste sorting base must be located further away from densely-populated territories as the waste sorting technology also includes waste warehousing, which often involves open-air storage. Such facilities are open to environmental processes and usually emit odors to surrounding territories. Certainly, open-air warehousing of waste also results in the visual pollution of residential areas.

Engineering Factors: | |||

x_{1} | x_{1–1} | Distance to a route of the centralized heat network, in km; | ∑x_{1} |

x_{1–2} | Distance to a high-pressure (12 bar) gas pipe, in km; | ||

x_{1–3} | Distance to 110 kW power transmission grid, in km; | ||

x_{1–4} | Distance to the water supply network, in km; | ||

x_{1–5} | Distance to industrial and domestic wastewater networks, in km; | ||

x_{1–6} | Distance to the surface water drain, in km; | ||

x_{2} | Distance to a complex of waste sorting bases, in km. | ||

x_{3} | Number of installations constructed on the site, in units; | ||

Environmental Factors: | |||

x_{4} | Distance to the center of the city of Vilnius, in km; | ||

x_{5} | Impact on air, in points; | ||

x_{6} | Level of noise, in points; | ||

x_{7} | Impact on entrails of the earth (soil) and groundwater in case of an accident, in points. | ||

Social Factors: | |||

x_{8} | Level of satisfaction among residents in relation to the site selection, in points; | ||

x_{9} | Mean population per 1 km^{2} in the territory of the analyzed alternative, in units; | ||

Economic Factors: | |||

x_{10} | Useful floor area of residential dwellings situated in the locality of the planned project, in m^{2}. |

_{3}) describes a possibility to install the planned waste management/incineration installations—a waste incineration plant, and/or waste sorting plant, and/or biodegradable waste treatment plant, which require 2.5 ha, 2.0 ha, and 1.0 ha in area, respectively—at a specific alternative site.

_{4}–x

_{7}) characterize the position of the incineration plant in terms of urban development and environmental effects. The distance to the center of the city (x

_{4}) assesses the location of the incineration plant and its possible impact on urban architecture, as a city center and surrounding quarters usually have a culturally-distinct style of architecture. Thus, such planned facilities should be kept away from culturally-important sites and located further away from residential areas. Such conclusions are determined by the power production technology, which may inconvenience residents of adjacent areas by noise, odors or aesthetics of the view.

_{5}), soil (x

_{6}), and the level of noise (x

_{7}) determine the impact of the waste incineration plant on the surrounding environment. The effect on air and soil results from warehousing of waste and byproducts that emerge either naturally or during the process of incineration; meanwhile, the level of noise is due to the intensified flow of transport to the plant. The intensified flow of transport results from delivery of waste from the entire Vilnius County.

_{8}) and the mean population per 1 km

^{2}in the territory of the analyzed alternative (x

_{9}) for the construction of the waste incineration plant consider the number of residents living next to the power production plant. Appropriate implementation of technological solutions during the construction of the waste incineration plant will prevent harmful effects and unpleasant odors during the exploitation of the plant. However, the negative stance of the public can bring the project implementation plans to a standstill. Assessment of the project from the point of view of public needs shows that the site of the project implementation should be chosen in the least densely populated territories. Assessment of the project on the level of the state or a private investor demonstrates that it is rational to construct the power production plant in densely populated areas to ensure the demand.

_{10}) determines the floor area of buildings to be supplied with energy from the future power production plant. This factor is useful from the social point of view as well as in terms of the plant design: the knowledge of the useful floor area of buildings facilitates the planning of the plant capacity required to supply the power to all accessible consumers.

Criteria | Optimum | Alternatives | ||||||
---|---|---|---|---|---|---|---|---|

A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | A_{6} | A_{7} | ||

x_{1} | min | 1.50 | 3.50 | 0.80 | 4.80 | 5.50 | 0.60 | 0.30 |

0.60 | 1.20 | 0.50 | 1.20 | 1.00 | 0.70 | 0.40 | ||

2.50 | 4.50 | 3.00 | 1.60 | 1.60 | 2.00 | 2.00 | ||

1.37 | 0.50 | 0.10 | 2.00 | 0.30 | 0.60 | 0.60 | ||

1.25 | 0.50 | 0.10 | 0.50 | 0.50 | 0.60 | 0.50 | ||

1.31 | 1.00 | 2.90 | 1.50 | 0.50 | 0.50 | 0.50 | ||

∑x_{1} | 8.53 | 11.20 | 7.40 | 11.60 | 9.40 | 5.00 | 4.30 | |

x_{2} | min | 1.5 | 14.5 | 13.5 | 6.2 | 13.1 | 15 | 14.5 |

x_{3} | max | 3 | 3 | 1 | 1 | 3 | 2 | 1 |

x_{4} | max | 9.26 | 8.64 | 6.44 | 11.19 | 5.9 | 6.09 | 5.72 |

x_{5} | max | 4 | 5 | 5 | 8 | 5 | 2 | 2 |

x_{6} | max | 6 | 6 | 5 | 8 | 5 | 3 | 2 |

x_{7} | max | 8 | 6 | 6 | 4 | 6 | 4 | 4 |

x_{8} | max | 10 | 9 | 6 | 10 | 8 | 2 | 1 |

x_{9} | min | 3188.6 | 497.5 | 2484 | 2676.5 | 3291 | 6490 | 5946.7 |

x_{10} | max | 55,269 | 9327 | 50,798 | 56,206 | 66,807 | 13,2136 | 123,314 |

## 4. Sustainable Assessment of Waste Incineration Plant Construction Site Alternatives by MCDM

#### 4.1. An Extension of the WASPAS Method with Single-Valued Neutrosophic Set (WASPAS-SVNS)

**Step 1.**In this step, the evaluations concerning the ratings of the alternatives with respect to the attributes and the attribute weights are presented. It can be expressed by ${x}_{ij},i=1,2,\mathrm{...},m;j=1,2,\mathrm{...},n$, which is the aggregated experts evaluation of the ${i}^{th}$ alternative by the ${j}^{th}$ criterion. Thus, the aggregated decision matrix can be constructed:

**Step 2.**Normalization of the decision $X$ is performed applying vector normalization approach applying division by the norm as follows:

**Step 3.**Neutrosophication of the normalizated aggregated decision matrix $\tilde{X}$ and the aggregated weight vector $w$ is performed. In the neutrosophication step we perform conversion of all crisp initial information into the single valued neutrosophic set. In this step, the neutrosophic aggregated decision matrix ${\tilde{X}}^{n}$ is determined. For this purpose we apply relationships between normalized terms of the alternatives and single-valued neutrosophic numbers. This evaluation is expressed in linguistic terms presented in the Table 4.

Crisp Normalized Terms | Single-Valued Neutrosophic Numbers |
---|---|

Extremely good (EG)/1.0 | (1.00, 0.00, 0.00) |

Very very good (VVG)/0.9 | (0.90, 0.10, 0.10) |

Very good (VG )/0.8 | (0.80, 0.15, 0.20) |

Good (G)/0.7 | (0.70, 0.25, 0.30) |

Medium good (MG)/0.6 | (0.60, 0.35, 0.40) |

Medium (M)/0.5 | (0.50, 0.50, 0.50) |

Medium bad (MB)/0.4 | (0.40, 0.65, 0.60) |

Bad (B)/0.3 | (0.30, 0.75, 0.70) |

Very bad (VB)/0.2 | (0.20, 0.85, 0.80) |

Very very bad (VVB)/0.1 | (0.10, 0.90, 0.90) |

Extremely bad (EB)/0.0 | (0.00, 1.00, 1.00) |

**Step 4.**Following the WASPAS-SVNS approach, the sum of the total relative importance of the alternative i is calculated by the following equation:

**Step.5.**The second criteria of the WASPAS-SVNS methodology is determined by applying the framework of the product total relative importance of the alternative i and is calculated by the following equation:

**Step 6.**A joint generalized criteria for the ranking alternatives by the proposed WASPAS-SVNS approach is determined as follows:

**Step 7.**In the last step, the score function $S\left({\tilde{Q}}_{i}\right)$ is determined for i = 1, 2,…, m applying Equation (S7) and the final rankings of the alternatives are calculated considering the descending order of the ${\tilde{Q}}_{i}$, i = 1, 2, …, m.

#### 4.2. Numerical Example

_{1}. If analysis of the aggregated decision matrix is performed, it is not difficult to observe that alternative A

_{1}possesses the best results for C

_{2}, C

_{3}, C

_{7}, C

_{8,}and reasonably good results for C

_{4}, C

_{6}. Comparing A

_{1}and A

_{3}(they are the first and the second ones in the ranking queue) we state that the alternative A

_{1}is better for the criteria C

_{2}, C

_{3}, C

_{4}, C

_{6}, C

_{7}, C

_{8}, and C

_{10}.

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

I | II | III | IV | V | VI | VII | |

C_{1} min | (0.3743, 0.6757, 0.6257) | (0.4914, 0.5128, 0.5086) | (0.3247, 0.7253, 0.6753) | (0.5090, 0.4865, 0.4910) | (0.4125, 0.6313, 0.5875) | (0.2194, 0.8306, 0.7806) | (0.1887, 0.8557, 0.8113) |

C_{2} min | (0.0465, 0.9535, 0.9535) | (0.4496, 0.5756, 0.5504) | (0.4186, 0.6221, 0.5814) | (0.1922, 0.8539, 0.8078) | (0.4062, 0.6407, 0.5938) | (0.4651, 0.5523, 0.5349) | (0.4496, 0.5756, 0..5504) |

C_{3} max | (0.5145, 0.4783, 0.4855) | (0.5145, 0.4783, 0.4855) | (0.1715, 0.8643, 0.8285) | (0.1715, 0.8643, 0.8285) | (0.5145, 0.4783, 0.4855) | (0.3430, 0.7070, 0.6570) | (0.1715, 0.8643, 0.8285) |

C_{4} max | (0.4457, 0.5815, 0.5543) | (0.4158, 0.6262, 0.5842) | (0.3100, 0.7400, 0.6900) | (0.5386, 0.4422, 0.4614) | (0.2840, 0.7660, 0.7160) | (0.2931, 0.7569, 0.7069) | (0.2753, 0.7747, 0.7247) |

C_{5} max | (0.3133, 0.7367, 0.6867) | (0.3916, 0.6584, 0.6084) | (0.3916, 0.6584, 0.6084) | (0.6266, 0.3234, 0.3734) | (0.3916, 0.6584, 0.6084) | (0.1567, 0.8717, 0.8433) | (0.1567, 0.8717, 0.8433) |

C_{6} max | (0.4253, 0.6120, 0.5747) | (0.4253, 0.6120, 0.5747) | (0.3544, 0.6956, 0.6456) | (0.5671, 0.3993, 0.4329) | (0.3544, 0.6956, 0.6456) | (0.2127, 0.8373, 0.7873) | (0.1418, 0.8791, 0.8582) |

C_{7} max | (0.5394, 0.4410, 0.4606) | (0.4045, 0.6432, 0.5955) | (0.4045, 0.6432, 0.5955) | (0.2697, 0.7803, 0.7303) | (0.4045, 0.6432, 0.5955) | (0.2697, 0.7803, 0.7303) | (0.2697, 0.7803, 0.7303) |

C_{8} max | (0.5090, 0.4865, 0.4910) | (0.4581, 0.5629, 0.5419) | (0.3054, 0.7446, 0.6946) | (0.5090, 0.4865, 0.4910) | (0.4072, 0.6392, 0.5928) | (0.1018, 0.8991, 0.8982) | (0.0509, 0.9491, 0.9491) |

C_{9} min | (0.3012, 0.7488, 0.6988) | (0.0470, 0.9530, 0.9530) | (0.2347, 0.8153, 0.7653) | (0.2528, 0.7972, 0.7472) | (0.3109, 0.7391, 0.6891) | (0.6131, 0.3369, 0.3869) | (0.5618, 0.4074, 0.4382) |

C_{10} max | (0.2577, 0.7923, 0.7423) | (0.0435, 0.9565, 0.9565) | (0.2368, 0.8132, 0.7632) | (0.2620, 0.7880, 0.7380) | (0.3115, 0.7385, 0.6885) | (0.6160, 0.3340, 0.3840) | (0.5749, 0.3877, 0.4251) |

Alternatives | |||||||
---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | |

${\tilde{Q}}^{(1)}$ | (0.9603, 0.0375, 0.449) | (0.9423, 0.0603, 0.0619) | (0.9508, 0.0491, 0.0594) | (0.9416, 0.0549, 0,0581) | (0.9431, 0.0570, 0.0666) | (0.9186, 0.0910, 0.0894) | (0.9239, 0.0821, 0.0836) |

${\tilde{Q}}^{(2)}$ | (0.1108, 0.8959, 0.8892) | (0.0923, 0.9157, 0.9077) | (0.0865, 0.9260, 0.9135) | (0.1081, 0.8964, 0.8919) | (0.1006, 0.9114, 0.8994) | (0.0591, 0.9486, 0.9409) | (0.0482, 0.9577, 0.9518) |

$\tilde{Q}$ | (0.6500, 0.3459, 0.3441) | (0.6029, 0.4049, 0.4025) | (0.6198, 0.3837, 0.3800) | (0.6062, 0.3879, 0.3865) | (0.6071, 0.3967, 0.3931) | (0.5485, 0.4695, 0.4669) | (0.5539, 0.4582, 0.4563) |

$S\left(\tilde{Q}\right)$ | 0.6535 | 0.5976 | 0.6181 | 0.6110 | 0.6052 | 0.5356 | 0.5453 |

Rank | 1 | 5 | 2 | 3 | 4 | 7 | 6 |

Alternatives | |||||||
---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | |

${\tilde{Q}}^{(1)}$ | 0.7550 | 0.7023 | 0.5816 | 0.7025 | 0.6416 | 0.4625 | 0.4238 |

${\tilde{Q}}^{(2)}$ | 0.6578 | 0.5780 | 0.5077 | 0.5980 | 0.5578 | 0.3411 | 0.2874 |

$\tilde{Q}$ | 0.7064 | 0.6402 | 0.5446 | 0.6502 | 0.5997 | 0.4028 | 0.3556 |

Rank | 1 | 3 | 5 | 2 | 4 | 6 | 7 |

Method | Alternatives | ||||||
---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | |

Original crisp WASPAS | 1 | 3 | 5 | 2 | 4 | 6 | 7 |

Proposed WASPAS-SVNS | 1 | 5 | 2 | 3 | 4 | 7 | 6 |

ARAS-F | 1 | 2 | 5 | 3 | 4 | 6 | 7 |

COPRAS | 1 | 3 | 5 | 2 | 4 | 6 | 7 |

_{4}, A

_{1}and A

_{2}, A

_{3}, A

_{5}) and one zone in densely populated parts of the city (A

_{6}, A

_{7}).

## 5. Conclusions

_{4}, A

_{1}and A

_{2}, A

_{3}, A

_{5}) and one zone in densely populated parts of the city (A

_{6}, A

_{7}).

_{2}, A

_{3}, and A

_{5}have challenges related to the connection to engineering communications and construction of access roads. The airport of Vilnius is the key challenge for the design of the flue-gas stack of the incineration plant in this particular zone. Thus, from the point of view of rational development, requirements of stakeholder groups can be satisfied by choosing the alternative a

_{1}, which is selected based on calculated results. This site is technologically fit for the construction of waste incineration, waste sorting, and biodegradable waste treatment plants.

## Author Contributions

## Conflicts of Interest

## Appendix

#### Neutrosophic Sets

**Definition 1.**Let X be space of the objects and $x\in X$. A neutrosophic set A in X is defined by three functions: truth-membership function ${T}_{A}\left(x\right)$, an indeterminacy-membership function ${I}_{A}\left(x\right)$ and falsity-membership function ${F}_{A}\left(x\right)$. These functions ${T}_{A}\left(x\right)$, ${I}_{A}\left(x\right)$ and ${F}_{A}\left(x\right)$ are defined on real standard or real non-standard subsets of $\left]{0}^{-},{1}^{+}\right[$. That is ${T}_{A}\left(x\right):X\to \left]{0}^{-},{1}^{+}\right[$, ${I}_{A}\left(x\right):X\to \left]{0}^{-},{1}^{+}\right[$ and ${F}_{A}\left(x\right):X\to \left]{0}^{-},{1}^{+}\right[$. We have no any restriction on the sum of ${T}_{A}\left(x\right)$, ${I}_{A}\left(x\right)$ and ${F}_{A}\left(x\right)$, so ${0}^{-}\le \mathrm{sup}{T}_{A}\left(x\right)+\mathrm{sup}{I}_{A}\left(x\right)+\mathrm{sup}{F}_{A}\left(x\right)\le {3}^{+}$.

**Definition 2.**A single-valued neutrosophic set (SVNS) has been defined as described in Wang et al., scientific work [38]. Let X be a universal space of the objects and $x\in X$. A single-valued neutrosophic set (SVNS) $\tilde{N}\subset X$ can be expressed as

**Definition 3.**If ${\tilde{N}}_{1}=\left({t}_{1},{i}_{1},{f}_{1}\right)$ and ${\tilde{N}}_{2}=\left({t}_{2},{i}_{2},{f}_{2}\right)$ are two single-valued neutrosophic numbers (SVNN), then the summation between ${\tilde{N}}_{1}$ and ${\tilde{N}}_{2}$ can be expressed as follows

**Definition 4.**If ${\tilde{N}}_{1}=\left({t}_{1},{i}_{1},{f}_{1}\right)$ and ${\tilde{N}}_{2}=\left({t}_{2},{i}_{2},{f}_{2}\right)$ are two single-valued neutrosophic numbers, then multiplication between ${\tilde{N}}_{1}$ and ${\tilde{N}}_{2}$ can be expressed as follows

**Definition 5.**If ${\tilde{N}}_{1}=\left({t}_{1},{i}_{1},{f}_{1}\right)$ is a single-valued neutrosophic number and $\mathsf{\lambda}\in \Re $ is an arbitrary positive real number then

**Definition 6.**If ${\tilde{N}}_{1}=\left({t}_{1},{i}_{1},{f}_{1}\right)$ is a single-valued neutrosophic number and $\mathsf{\lambda}\in \Re $ is an arbitrary positive real number then

**Definition 7.**If ${\tilde{N}}_{1}=\left({t}_{1},{i}_{1},{f}_{1}\right)$ is a single-valued neutrosophic number then the complementary component of this single valued neutrosophic number is determined as follows

**Definition 8.**If ${\tilde{N}}_{A}=\left({t}_{A},{i}_{A},{f}_{A}\right)$ is a single-valued neutrosophic number, a score function is mapped ${\tilde{N}}_{A}$ into the single crisp output $S\left({\tilde{N}}_{A}\right)$ as follows

**Definition 9.**Let ${\tilde{N}}_{1}$ and ${\tilde{N}}_{2}$ be any two SVNNs. Therefore, if $S\left({\tilde{N}}_{1}\right)<S\left({\tilde{N}}_{2}\right)$ then ${\tilde{N}}_{1}$ is smaller than ${\tilde{N}}_{2}$, ${\tilde{N}}_{1}<{\tilde{N}}_{2}$.

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**MDPI and ACS Style**

Kazimieras Zavadskas, E.; Baušys, R.; Lazauskas, M. Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set. *Sustainability* **2015**, *7*, 15923-15936.
https://doi.org/10.3390/su71215792

**AMA Style**

Kazimieras Zavadskas E, Baušys R, Lazauskas M. Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set. *Sustainability*. 2015; 7(12):15923-15936.
https://doi.org/10.3390/su71215792

**Chicago/Turabian Style**

Kazimieras Zavadskas, Edmundas, Romualdas Baušys, and Marius Lazauskas. 2015. "Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set" *Sustainability* 7, no. 12: 15923-15936.
https://doi.org/10.3390/su71215792