# Green Construction Grade Evaluation of Large Channels Based on Uncertain AHP-Multidimensional Cloud Model

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## Abstract

**:**

## 1. Introduction

## 2. Selection of Evaluation Indicators

## 3. Rating Method

#### 3.1. Uncertain AHP

- (1)
- Determine the comparison interval of evaluation indicators for individual experts

- (2)
- Determination of expert weights

- (3)
- Construction of uncertainty interval judgment matrix

- (4)
- Calculation of the weight interval

- (5)
- Calculate the weight value

#### 3.2. Multidimensional Linked Normal Cloud Model

- (1)
- Concept of multidimensional cloud model

- (2)
- Determination of numerical features of multidimensional cloud models

- (3)
- Multidimensional normal cloud model generated by multidimensional forward cloud generator

- Generate a $m$-dimensional normal random number ${{E}^{\prime}}_{n}({{E}^{\prime}}_{{n}_{1}},{{E}^{\prime}}_{{n}_{2}},\cdots ,{{E}^{\prime}}_{{n}_{m}})$ with ${E}_{n}({E}_{{n}_{1}},{E}_{{n}_{2}},\cdots ,{E}_{{n}_{m}})$ as the expectation and ${H}_{e}({H}_{{e}_{1}},{H}_{{e}_{2}},\cdots ,{H}_{{e}_{m}})$ as the variance.
- Generate a $m$-dimensional normal random number $x({x}_{1},{x}_{2},\cdots ,{x}_{m})$ with ${E}_{x}({E}_{{x}_{1}},{E}_{{x}_{2}},\cdots {E}_{{x}_{m}})$ as the expectation and ${{E}^{\prime}}_{n}({{E}^{\prime}}_{{n}_{1}},{{E}^{\prime}}_{{n}_{2}},\cdots ,{{E}^{\prime}}_{{n}_{m}})$ as the variance.
- Calculate the degree of certainty $\mu \{x({x}_{1},{x}_{2},\cdots ,{x}_{m})\}$ by means of Equation (15).
- $drop({x}_{1i},{x}_{2i},\cdots ,{x}_{mi},{\mu}_{i})$ denotes a cloud drop. where $({x}_{1i},{x}_{2i},\cdots ,{x}_{mi})$ denotes the primary counterpart of the qualitative concept in $U$ and ${\mu}_{i}$ is a measure of the qualitative concept to which $({x}_{1i},{x}_{2i},\cdots ,{x}_{mi})$ is subordinate.Repeat steps 1 to 4 until a cloud droplet is generated.

#### 3.3. Evaluation of Results

## 4. Large-Scale Channel Green Construction Example Application

- (1)
- Determination of expert weights

- (2)
- Determine the comparison interval of evaluation indicators for individual experts

- (3)
- Constructing uncertainty interval judgment matrix

- (4)
- Calculation of the weight interval

- (5)
- Calculate the exact weight value

- (6)
- Green construction index evaluation level classification

- (7)
- Multidimensional cloud model digital features

- (8)
- Multi-dimensional evaluation cloud model

- (9)
- Project evaluation results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Notation | Explanation |
---|---|

$A\text{~}E$ | Cloud model structure |

${A}_{ij}^{(k)}$ | Comparison interval of evaluation indicators |

${a}_{ij}^{(k)}$ | Lower limit of interval importance |

${b}_{ij}^{(k)}$ | Upper limit of interval importance |

${\gamma}^{(k)}$ | Expert Weights |

${a}_{ij},{b}_{ij}$ | Weight interval matrix |

$A={({A}_{ij})}_{n\times n}$ | Uncertainty interval judgment matrix |

$M=({m}_{ij}{)}_{n\times n}$ | Consistent approximation matrix satisfying mutual inverse |

${W}_{i}({w}_{1},{w}_{2},\cdots {w}_{n})$ | Weights of the consistency approximation matrix |

$\Delta M$ | Polar difference matrix |

${W}^{\prime}=({{w}^{\prime}}_{1},{{w}^{\prime}}_{2},\cdots ,{{w}^{\prime}}_{n})$ | The weight interval of the interval number judgment matrix |

${\mu}_{i}$ | Set to contact degree |

${a}_{i},{b}_{i},{c}_{i}$ | Interval Difference |

$i$ | Coefficient of variance |

$j$ | Contrast coefficient |

${p}_{i}$ | Relative weights of deterministic intervals |

${q}_{i}$ | Relative weights of uncertainty intervals |

${W}^{\ast}=({w}_{1}^{*},{w}_{2}^{*},\cdots {w}_{n}^{*})$ | Precise weighting values of evaluation indicators |

${E}_{x}$ | Expected Value |

${E}_{n}$ | Entropy value |

${H}_{e}$ | Hyperentropy value |

$x$ | Measured value |

$\mu \{x({x}_{1},{x}_{2},\cdots ,{x}_{m})\}$ | Degree of certainty |

${C}_{\mathrm{min}}$ | Constraint interval small value |

${C}_{\mathrm{max}}$ | Constraint interval large value |

${E}_{n}^{(1)}$ | $\mathrm{Cloud}\text{}\mathrm{entropy}\text{}\mathrm{based}\text{}\mathrm{on}\text{}\u201c3{E}_{n}\u201d$ rule |

${E}_{n}^{(2)}$ | Cloud entropy based on “50% association degree” rule |

Sub-Indicators | Expert Title | Years in Channel Construction and Management (Years) | Familiarity with Engineering Green Construction | Understanding of This Channel Project | Sub-Index Score | Relative Weighting Values of Sub-Indicators |

Positive senior | >20 | Very familiar | Very familiar | 10 | 0.323 | |

Associate senior | 10~20 | Familiarity | Familiarity | 8 | 0.258 | |

Intermediate | 5~10 | More familiar | More familiar | 6 | 0.193 | |

Primary | 2~5 | Understanding | Understanding | 4 | 0.129 | |

Other | <2 | Better understanding | Better understanding | 3 | 0.097 |

Experts | Title | Number of Years Engaged in Channel Construction (Years) | Familiarity with Engineering Green Construction | Understanding of This Channel Project | Cumulative Weighting | Normalized Weights |
---|---|---|---|---|---|---|

1 | Positive senior (0.323) | 22 (0.323) | Very familiar (0.323) | Familiarity (0.258) | 1.227 | 0.284 |

2 | Associate senior (0.258) | 18 (0.258) | Very familiar (0.323) | Familiarity (0.258) | 1.097 | 0.254 |

3 | Intermediate (0.193) | 9 (0.193) | Familiarity (0.258) | More familiar (0.193) | 0.837 | 0.194 |

4 | Positive senior (0.258) | 19 (0.258) | Very familiar (0.323) | Very familiar (0.323) | 1.162 | 0.268 |

Primary Indexes | Single Weighting | Secondary Indexes | Single Weighting | Total Weighting | Tertiary Indexes | Single Weighting | Total Weighting |
---|---|---|---|---|---|---|---|

${A}_{}$ | 0.2660 | ${A}_{1}$ | 0.6014 | 0.1600 | $A{\text{}}_{1-1}$ | 0.5570 | 0.0891 |

${A}_{\text{}1-2}$ | 0.2705 | 0.0433 | |||||

${A}_{\text{}1-3}$ | 0.1725 | 0.0276 | |||||

${A}_{2}$ | 0.3986 | 0.1060 | $A{\text{}}_{2-1}$ | 0.7942 | 0.0842 | ||

$A{\text{}}_{2-2}$ | 0.2058 | 0.0218 | |||||

$B$ | 0.0650 | ${B}_{1}$ | 0.3795 | 0.0247 | ${B}_{1-1}$ | 0.3573 | 0.0088 |

${B}_{1-2}$ | 0.6427 | 0.0159 | |||||

${B}_{2}$ | 0.6205 | 0.0403 | ${B}_{2-1}$ | 0.3993 | 0.0161 | ||

${B}_{2-2}$ | 0.6007 | 0.0242 | |||||

$C$ | 0.2207 | ${C}_{1}$ | 0.2822 | 0.0623 | ${C}_{1-1}$ | 0.6725 | 0.0419 |

${C}_{1-2}$ | 0.3275 | 0.0204 | |||||

${C}_{2}$ | 0.4253 | 0.0939 | ${C}_{2-1}$ | 0.1924 | 0.0181 | ||

${C}_{2-2}$ | 0.3058 | 0.0287 | |||||

${C}_{2-3}$ | 0.5018 | 0.0471 | |||||

${C}_{3}$ | 0.2241 | 0.0495 | ${C}_{3-1}$ | 0.6047 | 0.0299 | ||

${C}_{3-2}$ | 0.2548 | 0.0126 | |||||

${C}_{3-3}$ | 0.1405 | 0.0070 | |||||

${C}_{4}$ | 0.0684 | 0.0151 | ${C}_{4-1}$ | 0.6061 | 0.0091 | ||

${C}_{4-2}$ | 0.2399 | 0.0036 | |||||

${C}_{4-3}$ | 0.1540 | 0.0023 | |||||

${D}_{}$ | 0.3624 | ${D}_{1}$ | 0.6063 | 0.2197 | ${D}_{1-1}$ | 0.2306 | 0.0508 |

${D}_{1-2}$ | 0.2635 | 0.0579 | |||||

${D}_{1-3}$ | 0.5059 | 0.1111 | |||||

${D}_{2}$ | 0.2402 | 0.0870 | ${D}_{2-1}$ | 0.7330 | 0.0638 | ||

${D}_{2-2}$ | 0.2670 | 0.0232 | |||||

${D}_{3}$ | 0.1535 | 0.0556 | ${D}_{3-1}$ | 0.6616 | 0.0368 | ||

${D}_{3-2}$ | 0.3384 | 0.0188 | |||||

$E$ | 0.0859 | ${E}_{1}$ | 0.3573 | 0.0307 | ${E}_{1-1}$ | 0.3617 | 0.0111 |

${E}_{1-2}$ | 0.6383 | 0.0196 | |||||

${E}_{2}$ | 0.6427 | 0.0552 | ${E}_{2-1}$ | 0.7149 | 0.0395 | ||

${E}_{2-2}$ | 0.2851 | 0.0157 |

Indicators | Green Level | ||||
---|---|---|---|---|---|

Failure | Basic Level | One-Star | Two-Star | Three-Star | |

$A{\text{}}_{1-1}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${A}_{\text{}1-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${A}_{\text{}1-3}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

$A{\text{}}_{2-1}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

$A{\text{}}_{2-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${B}_{1-1}$ | [0,5) | [5,10) | [10,15) | [15,20) | [20,25] |

${B}_{1-2}$ | [0,2) | [2,3) | [3,4) | [4,5) | [5,6] |

${B}_{2-1}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${B}_{2-2}$ | [0,4) | [4,5) | [5,7) | [7,9) | [9,10] |

${C}_{1-1}$ | [0,1) | [1,2) | [2,3) | [3,4) | [4,5] |

${C}_{1-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{2-1}$ | [0,60) | [60,70) | [70,80) | [80,90) | [90,100] |

${C}_{2-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{2-3}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{3-1}$ | [0,5) | [5,10) | [10,15) | [15,20) | [20,25] |

${C}_{3-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{3-3}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{4-1}$ | [0,60) | [60,70) | [70,80) | [80,90) | [90,100] |

${C}_{4-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${C}_{4-3}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${D}_{1-1}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${D}_{1-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${D}_{1-3}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${D}_{2-1}$ | [0,60) | [60,70) | [70,80) | [80,90) | [90,100] |

${D}_{2-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${D}_{3-1}$ | [0,300) | [300,350) | [350,400) | [400,450) | [450,600] |

${D}_{3-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${E}_{1-1}$ | [0,60) | [60,70) | [70,80) | [80,90) | [90,100] |

${E}_{1-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${E}_{2-1}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

${E}_{2-2}$ | [0,6) | [6,7) | [7,8) | [8,9) | [9,10] |

Indicators | Green Level | ||||
---|---|---|---|---|---|

Failure | Basic Level | One-Star | Two-Star | Three-Star | |

${A}_{1-1}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${A}_{1-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${A}_{1-3}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${A}_{2-1}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${A}_{2-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${B}_{1-1}$ | (2.5,0.83,0.08) | (7.5,2.12,0.08) | (12.5,2.12,0.08) | (17.5,2.12,0.08) | (22.5,2.12,0.08) |

${B}_{1-2}$ | (1,0.33,0.08) | (2.5,0.42,0.08) | (3.5,0.42,0.08) | (4.5,0.42,0.08) | (5.5,0.42,0.08) |

${B}_{2-1}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${B}_{2-2}$ | (2,0.67,0.08) | (4.5,0.42,0.08) | (6,0.85,0.08) | (8,0.85,0.08) | (9.5,0.42,0.08) |

${C}_{1-1}$ | (0.5,0.17,0.08) | (1.5,0.42,0.08) | (2.5,0.42,0.08) | (3.5,0.42,0.08) | (4.5,0.42,0.08) |

${C}_{1-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{2-1}$ | (30,10,0.08) | (65,4.25,0.08) | (75,4.25,0.08) | (85,4.25,0.08) | (95,4.25,0.08) |

${C}_{2-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{2-3}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{3-1}$ | (2.5,0.83,0.08) | (7.5,2.12,0.08) | (12.5,2.12,0.08) | (17.5,2.12,0.08) | (22.5,2.12,0.08) |

${C}_{3-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{3-3}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{4-1}$ | (30,10,0.08) | (65,4.25,0.08) | (75,4.25,0.08) | (85,4.25,0.08) | (95,4.25,0.08) |

${C}_{4-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${C}_{4-3}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${D}_{1-1}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${D}_{1-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${D}_{1-3}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${D}_{2-1}$ | (30,10,0.08) | (65,4.25,0.08) | (75,4.25,0.08) | (85,4.25,0.08) | (95,4.25,0.08) |

${D}_{2-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${D}_{3-1}$ | (150,50,0.08) | (325,21.23,0.08) | (375,21.23,0.08) | (425,21.23,0.08) | (525,63.7,0.08) |

${D}_{3-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${E}_{1-1}$ | (30,10,0.08) | (65,4.25,0.08) | (75,4.25,0.08) | (85,4.25,0.08) | (95,4.25,0.08) |

${E}_{1-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${E}_{2-1}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

${E}_{2-2}$ | (3,1,0.08) | (6.5,0.42,0.08) | (7.5,0.42,0.08) | (8.5,0.42,0.08) | (9.5,0.42,0.08) |

Green evaluation indicators | ${A}_{1-1}$ | ${A}_{1-2}$ | ${A}_{1-3}$ | ${A}_{2-1}$ | ${A}_{2-2}$ | ${B}_{1-1}$ | ${B}_{1-2}$ | ${B}_{2-1}$ |

Actual value | 8.732 | 9.347 | 9.635 | 9.986 | 9.451 | 17.845 | 5.298 | 9.171 |

Green evaluation indicators | ${B}_{2-2}$ | ${C}_{1-1}$ | ${C}_{1-2}$ | ${C}_{2-1}$ | ${C}_{2-2}$ | ${C}_{2-3}$ | ${C}_{3-1}$ | ${C}_{3-2}$ |

Actual value | 9.617 | 3.687 | 8.947 | 98.199 | 9.491 | 9.249 | 18.267 | 8.115 |

Green evaluation indicators | ${C}_{3-3}$ | ${C}_{4-1}$ | ${C}_{4-2}$ | ${C}_{4-3}$ | ${D}_{1-1}$ | ${D}_{1-2}$ | ${D}_{1-3}$ | ${D}_{2-1}$ |

Actual value | 9.333 | 97.442 | 9.777 | 9.713 | 9.911 | 8.336 | 9.633 | 93.147 |

Green evaluation indicators | ${D}_{2-2}$ | ${D}_{3-1}$ | ${D}_{3-2}$ | ${E}_{1-1}$ | ${E}_{1-2}$ | ${E}_{2-1}$ | ${E}_{2-2}$ | |

Actual value | 10.000 | 437.116 | 9.525 | 91.478 | 7.663 | 8.797 | 9.211 |

Affiliation | Evaluation Results of This Paper | AHP-Cloud Model | ||||
---|---|---|---|---|---|---|

I | II | III | IV | V | ||

${\mu}_{1}=0$ | ${\mu}_{2}=0$ | ${\mu}_{3}=0$ | ${\mu}_{4}=0.0746$ | ${\mu}_{5}=0.3119$ | V | V |

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## Share and Cite

**MDPI and ACS Style**

Ma, Q.; Lu, L.; Li, Q.; Wang, Z.
Green Construction Grade Evaluation of Large Channels Based on Uncertain AHP-Multidimensional Cloud Model. *Sustainability* **2022**, *14*, 6143.
https://doi.org/10.3390/su14106143

**AMA Style**

Ma Q, Lu L, Li Q, Wang Z.
Green Construction Grade Evaluation of Large Channels Based on Uncertain AHP-Multidimensional Cloud Model. *Sustainability*. 2022; 14(10):6143.
https://doi.org/10.3390/su14106143

**Chicago/Turabian Style**

Ma, Qiang, Linfang Lu, Qingfu Li, and Zhipeng Wang.
2022. "Green Construction Grade Evaluation of Large Channels Based on Uncertain AHP-Multidimensional Cloud Model" *Sustainability* 14, no. 10: 6143.
https://doi.org/10.3390/su14106143