# Implementation of Adjusted Fuzzy AHP Method in the Assessment for Reuse of Industrial Buildings

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Methodology

- Reciprocity axiom: If element A is n times more significant than element B, then the element B is 1/n times more significant than the element A.
- Homogeneity axiom: Comparison only makes sense if the elements are comparable.
- Dependency axiom: Allows the comparison among the group of criteria of one level with the criteria of a higher level. Comparisons at lower levels depend on the elements of a higher level.
- Axiom of expectations: Any change in the structure of the hierarchy requires recalculating priorities in the new hierarchy.

_{1}< M

_{2}; if ${I}_{T}^{\lambda}\left({M}_{1}\right)={I}_{T}^{\lambda}\left({M}_{2}\right)$, then M

_{1}≈ M

_{2.}If ${I}_{T}^{\lambda}\left({M}_{1}\right)>{I}_{T}^{\lambda}\left({M}_{2}\right)$, then M

_{1}> M

_{2}.

**Step 1****:**Step 1 is the same as in the crisp AHP method.**Step 2:**Obtaining the fuzzy comparison matrix.

**Step 3:**Examination of matrix consistency.

**Step 4:**The fuzzification and the defuzzification processes.

**Step 5**: Normalization of weight vector $\mathit{w}={\left({w}_{1},{w}_{2},\dots ,{w}_{n}\right)}^{T}$ and obtaining the vector for each criterion.$${w}_{i}^{*}={w}_{i}{\left({\displaystyle \sum}_{i=1}^{n}{w}_{i}\right)}^{-1}$$

#### 3.2. Indicators

## 4. Results

**X**and

_{1}**X**and their weights are shown in Table 9, Table 10 and Table 11.

_{2}**Y**–

_{1}**Y**and their weights are presented in Table 12, Table 13, Table 14 and Table 15.

_{4}**X**–

_{11}**X**as well as their weights, are presented in Table 16, Table 17, Table 18, Table 19, Table 20 and Table 21.

_{16},**X**–

_{21}**X**as well as their weights, are presented in Table 22, Table 23, Table 24 and Table 25.

_{26},_{152}), floor height of 3–5.5 m (X

_{112}), developed gross area 4500–15,000 ${\mathrm{m}}^{2}$ (X

_{153}), linear type of construction system (X

_{211}), with up to three floors (X

_{122}) and two access points (Y

_{42}).

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Maps of the Electronic Industry Complex with marked facilities, by letters A to S, as alternatives for future redevelopment.

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

Operators | Mathematical Expression | Results |
---|---|---|

Addition | ${\tilde{M}}_{1}\oplus {\tilde{M}}_{2}=\left({l}_{1},{m}_{1},{u}_{1}\right)\oplus \left({l}_{2},{m}_{2},{u}_{2}\right)$ | $\left({l}_{1}+{l}_{2},{m}_{1}+{m}_{2},{u}_{1}+{u}_{2}\right)$ |

Scalar multiplication | $k\cdot {\tilde{M}}_{1}=k\cdot \left({l}_{1},{m}_{1},{u}_{1}\right)$ | $\left(k\cdot {l}_{1},k\cdot {m}_{1},k\cdot {u}_{1}\right)$ |

Multiplication | ${\tilde{M}}_{1}\otimes {\tilde{M}}_{2}=\left({l}_{1},{m}_{1},{u}_{1}\right)\otimes \left({l}_{2},{m}_{2},{u}_{2}\right)$ | $\left({l}_{1}\cdot {l}_{2},{m}_{1}\cdot {m}_{2},{u}_{1}\cdot {u}_{2}\right)$ |

Inverse | ${\tilde{M}}_{1}^{-1}={\left({l}_{1},{m}_{1},{u}_{1}\right)}^{-1}$ | $\left(\frac{1}{{u}_{1}},\frac{1}{{m}_{1}},\frac{1}{{l}_{1}}\right)$ |

Denotation TFNs | TFNs | Denotation Inverse TFNs | Inverse TFNs |
---|---|---|---|

$\tilde{1}$ | (1, 1, 3) | $\tilde{1}$^{−1} | (1/3, 1, 1) |

$\tilde{2}$ | (1, 2, 3) | $\tilde{2}$^{−1} | (1/3, 1/2, 1) |

$\tilde{3}$ | (1, 3, 5) | $\tilde{3}$^{−1} | (1/5, 1/3, 1) |

$\tilde{4}$ | (3, 4, 5) | $\tilde{4}$^{−1} | (1/5, 1/4, 1/3) |

$\tilde{5}$ | (3, 5, 7) | $\tilde{5}$^{−1} | (1/7, 1/5, 1/3) |

$\tilde{6}$ | (5, 6, 7) | $\tilde{6}$^{−1} | (1/7, 1/6, 1/5) |

$\tilde{7}$ | (5, 7, 9) | $\tilde{7}$^{−1} | (1/9, 1/7, 1/5) |

$\tilde{8}$ | (7, 8, 9) | $\tilde{8}$^{−1} | (1/9, 1/8, 1/7) |

$\tilde{9}$ | (7, 9, 9) | $\tilde{9}$^{−1} | (1/9, 1/9, 1/7) |

FAHP Scale | Linguistic Statement | Explanation |
---|---|---|

$\tilde{1}$ | Equal importance | Two activities contribute equally to the objective |

$\tilde{3}$ | Weak Importance of one over another | Experience and judgment slightly favor one activity over another |

$\tilde{5}$ | Essential or strong importance | Experience and judgment strongly favor one activity over another |

$\tilde{7}$ | Very strong importance | Activity is strongly favored and its dominance demonstrated in practice |

$\tilde{9}$ | Absolute importance | The evidence favoring one activity over another is of the highest possible order or affirmation |

$\tilde{2},\tilde{4},\tilde{6},\tilde{8}$ | Intermediate values between the two adjacent judgments | When compromise is needed |

**Table 5.**Description of the criteria which affect the possibility of adaptive reuse of industrial buildings.

PHYSICAL INDICATORS (X) | |

X_{1}—Spatial-dimensional | |

X_{11}—Building floor height- X
_{111}—up to 3 m - X
_{112}—3–5.5 m - X
_{113}—5.5–8 m - X
_{114}—more than 8 m
| New purposes demand new requirements concerning the minimal floor height. The floor height indicates that the existing space in the vertical plane could be divided. |

- X
_{12}—Number of floors - X
_{121}—single floor - X
_{122}—up to 3 floors - X
_{123}—more floors
| The upper floors of high-rise buildings have limited connectivity with the surrounding for various purposes, making low-rise buildings more appropriate for conversion. |

- X
_{13}—Constructive span - X
_{131}—up to 15 m - X
_{132}—15–35 m - X
_{133}—more than 35 m
| The constructive span determines the dimensions of obstacle-free interior space. This paper defines three specific spans of industrial buildings, important for the potential adjustment of interior spaces. |

- X
_{14}—Minimal building depth - X
_{141}—up to 9 m - X
_{142}—9–16 m - X
_{143}—more than 16 m
| There is a direct correlation between the cross depth of the facilities and the potential for natural lighting and ventilation. It is more difficult to convert high-dept buildings, while the other ones, with small-depths, have narrow free interior space for reuse [72]. |

- X
_{15}—Developed gross area - X
_{151}—up to 1000 m^{2} - X
_{152}—1000–45,000 m^{2} - X
_{153}—4500–15,000 m^{2} - X
_{154}—more than 15,000 m^{2}
| From all building sizes, the most suitable ones are those in the range of 1000–4500 m^{2}. Extreme dimensions, the smallest, and the largest ones are inadequate for conversion [73]. |

- X
_{16}—Number of free facades - X
_{161}—self-standing - X
_{162}—leaning by 1 side - X
_{163}—bordered by 2 opposite sides - X
_{164}—bordered by 2 adjacent sides - X
_{165}—one free side
| We consider the characteristics of a redevelopment building in terms of its position in space relative to neighborhood buildings. Including all possible scenarios, self-standing buildings have the highest potential for adaptive reuse. |

X_{2}—Physical structures quality | |

- X
_{21}—Constructive system type - X
_{211}—linear - X
_{212}—surface
| The supporting elements of linear constructive systems do not create significant spatial obstacles as constraints in the conversion process, and therefore these systems have the advantage. [74]. |

- X
_{22}—Percentage of openings - X
_{221}—without/up to 30% - X
_{222}—30–70% - X
_{223}—more than 70%
| We define this criterion by dividing the total range of the value of the observed parameter into three parts. |

- X
_{23}—Facade envelope type - X
_{231}—masonry - X
_{232}—asbestos - X
_{233}—metal - X
_{234}—AB panels
| The criterion has defined based on the qualitative properties of the envelope structure. The range of values has derived from known materials used in the construction of industrial facilities [75,76]. |

- X
_{24}—Aesthetic values - X
_{241}—high - X
_{242}—medium - X
_{243}—low
| Aesthetic values are primary in this criterion. Buildings with high aesthetic values, by positive social acceptance, and appreciation, and with a strong identity, may have the advantage. |

SITE INDICATORS (Y) | |

Y_{1}—Distance from the road- Y
_{11}—up to 100 m - Y
_{12}—100–250 m - Y
_{13}—more than 250 m
| The optimum distance from a high traffic road indicates good traffic connections and easy accessibility to the building. It should take into account the negative aspects of short distances, such as noise and pollution. |

Y_{2}—Corresponding free area- Y
_{21}—up to 15%P - Y
_{22}—15–40%P - Y
_{23}—more than 40%P, - where P is a building projected surface
| The best possibility in the spot is when the occupancy level does not exceed 60% of the total area of the plot. The high occupancy level indicates the small free area for facilitating parking space, pedestrian space, and greenery [73]. |

Y_{3}—Distance from adjacent buildings - Y
_{31}—up to H - Y
_{32}—H - Y
_{33}—more than H, where H is the height of the higher facility
| The relation between the heights of the buildings is the essence of this criterion. Contributing with more solar power and better eyesight, higher buildings are more desirable. |

Y_{4}—Number of access- Y
_{41}—single - Y
_{42}—two - Y
_{43}—more
| The number of access points and evacuation gates determine the different purposes building adaptability degree. |

X | Y | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|

X | $\tilde{1}$ | $\tilde{3}$ | 0.75 | 0.739796 | 0.714286 |

Y | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.25 | 0.260204 | 0.285714 |

X_{1} | X_{2} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|

X_{1} | $\tilde{1}$ | $\tilde{4}$ | 0.810638 | 0.800928 | 0.787234 |

X_{2} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.189362 | 0.199072 | 0.212766 |

Y_{4} | Y_{1} | Y_{2} | Y_{3} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|

Y_{4} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ | $\tilde{7}$ | 0.439801 | 0.439298 | 0.438408 |

Y_{1} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{6}$ | 0.337632 | 0.333511 | 0.326212 |

Y_{2} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.177805 | 0.179049 | 0.181252 |

Y_{3} | $\tilde{7}$^{−1} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0447618 | 0.0481418 | 0.0541281 |

X_{15} | X_{11} | X_{12} | X_{16} | X_{14} | X_{13} | |
---|---|---|---|---|---|---|

X_{15} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{3}$ | $\tilde{4}$ | $\tilde{5}$ | $\tilde{6}$ |

X_{11} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{3}$ | $\tilde{4}$ | $\tilde{5}$ |

X_{12} | $\tilde{3}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{3}$ | $\tilde{4}$ |

X_{16} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{3}$ |

X_{14} | $\tilde{5}$^{−1} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{2}$ |

X_{13} | $\tilde{6}$^{−1} | $\tilde{5}$^{−1} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ |

λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|

X_{15} | 0.326206 | 0.333333 | 0.349591 |

X_{11} | 0.251322 | 0.250955 | 0.250118 |

X_{12} | 0.180591 | 0.178855 | 0.174893 |

X_{16} | 0.124978 | 0.120443 | 0.110092 |

X_{14} | 0.0740976 | 0.0732968 | 0.0714688 |

X_{13} | 0.0428056 | 0.0431201 | 0.0438381 |

X_{21} | X_{23} | X_{22} | X_{24} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|

X_{21} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{5}$ | $\tilde{7}$ | 0.487733 | 0.495091 | 0.512857 |

X_{23} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{5}$ | 0.302497 | 0.298662 | 0.289403 |

X_{22} | $\tilde{5}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | 0.15515 | 0.150053 | 0.137748 |

X_{24} | $\tilde{7}$^{−1} | $\tilde{5}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.0546197 | 0.0561933 | 0.0599926 |

Y_{12} | Y_{11} | Y_{13} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

Y_{12} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{6}$ | 0.601249 | 0.594416 | 0.582686 |

Y_{11} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.322622 | 0.323299 | 0.324461 |

Y_{13} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0761286 | 0.0822846 | 0.0928532 |

Y_{22} | Y_{23} | Y_{21} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

Y_{22} | $\tilde{1}$ | $\tilde{5}$ | $\tilde{6}$ | 0.702088 | 0.70579 | 0.712107 |

Y_{23} | $\tilde{5}$^{−1} | $\tilde{1}$ | $\tilde{2}$ | 0.196984 | 0.191583 | 0.182366 |

Y_{21} | $\tilde{6}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ | 0.100928 | 0.102627 | 0.105527 |

Y_{33} | Y_{32} | Y_{31} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

Y_{33} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ | 0.505146 | 0.518692 | 0.547127 |

Y_{32} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | 0.369599 | 0.35333 | 0.319177 |

Y_{31} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.125255 | 0.127978 | 0.133695 |

Y_{42} | Y_{43} | Y_{41} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

Y_{42} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ | 0.505146 | 0.518692 | 0.547127 |

Y_{43} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | 0.369599 | 0.35333 | 0.319177 |

Y_{41} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.125255 | 0.127978 | 0.133695 |

X_{112} | X_{113} | X_{111} | X_{114} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|

X_{112} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{5}$ | $\tilde{7}$ | 0.487733 | 0.495091 | 0.512857 |

X_{113} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{5}$ | 0.302497 | 0.298662 | 0.289403 |

X_{111} | $\tilde{5}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | 0.15515 | 0.150053 | 0.137748 |

X_{114} | $\tilde{7}$^{−1} | $\tilde{5}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.0546197 | 0.0561933 | 0.0599926 |

X_{122} | X_{121} | X_{123} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

X_{122} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{4}$ | 0.505146 | 0.518692 | 0.547127 |

X_{121} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | 0.369599 | 0.35333 | 0.319177 |

X_{123} | $\tilde{4}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | 0.125255 | 0.127978 | 0.133695 |

X_{131} | X_{132} | X_{133} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

X_{131} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{6}$ | 0.601249 | 0.594416 | 0.582686 |

X_{132} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.322622 | 0.323299 | 0.324461 |

X_{133} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0761286 | 0.0822846 | 0.0928532 |

X_{142} | X_{141} | X_{143} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

X_{142} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{5}$ | 0.550805 | 0.537017 | 0.511619 |

X_{141} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.360141 | 0.367572 | 0.381261 |

X_{143} | $\tilde{5}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0890539 | 0.0954105 | 0.10712 |

X_{152} | X_{153} | X_{151} | X_{154} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|

X_{152} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{5}$ | $\tilde{8}$ | 0.451062 | 0.44989 | 0.447971 |

X_{153} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | $\tilde{7}$ | 0.357641 | 0.354513 | 0.349394 |

X_{151} | $\tilde{5}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.151602 | 0.153332 | 0.156165 |

X_{154} | $\tilde{8}$^{−1} | $\tilde{7}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0396952 | 0.042265 | 0.0464702 |

X_{161} | X_{162} | X_{164} | X_{163} | X_{165} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|---|

X_{161} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{5}$ | $\tilde{6}$ | $\tilde{9}$ | 0.413656 | 0.420983 | 0.434561 |

X_{162} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{4}$ | $\tilde{7}$ | 0.286621 | 0.281378 | 0.271662 |

X_{164} | $\tilde{5}$^{−1} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{2}$ | $\tilde{5}$ | 0.165352 | 0.15933 | 0.148171 |

X_{163} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{2}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.105448 | 0.107575 | 0.111516 |

X_{165} | $\tilde{9}$^{−1} | $\tilde{7}$^{−1} | $\tilde{5}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0289223 | 0.0307332 | 0.0340893 |

X_{211} | X_{212} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|

X_{211} | $\tilde{1}$ | $\tilde{5}$ | 0.848684 | 0.836219 | 0.813596 |

X_{212} | $\tilde{5}$^{−1} | $\tilde{1}$ | 0.151316 | 0.163781 | 0.186404 |

X_{222} | X_{223} | X_{221} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

X_{222} | $\tilde{1}$ | $\tilde{4}$ | $\tilde{7}$ | 0.651202 | 0.644745 | 0.634569 |

X_{223} | $\tilde{4}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.27877 | 0.281051 | 0.284647 |

X_{221} | $\tilde{7}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0700282 | 0.074204 | 0.0807844 |

X_{231} | X_{234} | X_{233} | X_{232} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|---|

X_{231} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{6}$ | $\tilde{9}$ | 0.484025 | 0.486921 | 0.491541 |

X_{234} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | $\tilde{7}$ | 0.337062 | 0.330705 | 0.320564 |

X_{233} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.141467 | 0.142755 | 0.14481 |

X_{232} | $\tilde{9}$^{−1} | $\tilde{7}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0374457 | 0.0396189 | 0.0430859 |

X_{241} | X_{242} | X_{243} | λ = 1 | λ = 0.5 | λ = 0 | |
---|---|---|---|---|---|---|

X_{241} | $\tilde{1}$ | $\tilde{3}$ | $\tilde{6}$ | 0.601249 | 0.594416 | 0.582686 |

X_{242} | $\tilde{3}$^{−1} | $\tilde{1}$ | $\tilde{4}$ | 0.322622 | 0.323299 | 0.324461 |

X_{243} | $\tilde{6}$^{−1} | $\tilde{4}$^{−1} | $\tilde{1}$ | 0.0761286 | 0.0822846 | 0.0928532 |

Indicators | λ = 0 | λ = 0.5 | λ = 1 |
---|---|---|---|

X_{111} | 0.0194 | 0.0223 | 0.0237 |

X_{112} | 0.0721 | 0.0736 | 0.0745 |

X_{113} | 0.0407 | 0.0444 | 0.0462 |

X_{114} | 0.0084 | 0.0084 | 0.0083 |

X_{121} | 0.0314 | 0.0374 | 0.0406 |

X_{122} | 0.0538 | 0.0550 | 0.0555 |

X_{123} | 0.0131 | 0.0136 | 0.0138 |

X_{131} | 0.0144 | 0.0152 | 0.0156 |

X_{132} | 0.0080 | 0.0083 | 0.0084 |

X_{133} | 0.0023 | 0.0021 | 0.0020 |

X_{141} | 0.0153 | 0.0160 | 0.0162 |

X_{142} | 0.0206 | 0.0233 | 0.0248 |

X_{143} | 0.0043 | 0.0041 | 0.0040 |

X_{151} | 0.0307 | 0.0303 | 0.0301 |

X_{152} | 0.0881 | 0.0889 | 0.0895 |

X_{153} | 0.0687 | 0.0700 | 0.0709 |

X_{154} | 0.0091 | 0.0083 | 0.0079 |

X_{161} | 0.0269 | 0.0300 | 0.0314 |

X_{162} | 0.0168 | 0.0201 | 0.0218 |

X_{163} | 0.0069 | 0.0077 | 0.0080 |

X_{164} | 0.0092 | 0.0114 | 0.0126 |

X_{165} | 0.0021 | 0.0022 | 0.0022 |

X_{211} | 0.0634 | 0.0610 | 0.0588 |

X_{212} | 0.0145 | 0.0119 | 0.0105 |

X_{221} | 0.0017 | 0.0016 | 0.0015 |

X_{222} | 0.0133 | 0.0142 | 0.0143 |

X_{223} | 0.0060 | 0.0062 | 0.0061 |

X_{231} | 0.0216 | 0.0214 | 0.0208 |

X_{232} | 0.0019 | 0.0017 | 0.0016 |

X_{233} | 0.0064 | 0.0063 | 0.0061 |

X_{234} | 0.0141 | 0.0145 | 0.0145 |

X_{241} | 0.0053 | 0.0049 | 0.0047 |

X_{242} | 0.0030 | 0.0027 | 0.0025 |

X_{243} | 0.0008 | 0.0007 | 0.0006 |

Y_{11} | 0.0302 | 0.0281 | 0.0272 |

Y_{12} | 0.0543 | 0.0516 | 0.0508 |

Y_{13} | 0.0087 | 0.0071 | 0.0064 |

Y_{21} | 0.0055 | 0.0048 | 0.0045 |

Y_{22} | 0.0369 | 0.0329 | 0.0312 |

Y_{23} | 0.0094 | 0.0089 | 0.0088 |

Y_{31} | 0.0021 | 0.0016 | 0.0014 |

Y_{32} | 0.0049 | 0.0044 | 0.0041 |

Y_{33} | 0.0085 | 0.0065 | 0.0057 |

Y_{41} | 0.0167 | 0.0146 | 0.0138 |

Y_{42} | 0.0685 | 0.0593 | 0.0555 |

Y_{43} | 0.0400 | 0.0404 | 0.0406 |

**Table 27.**Review of requirements according to the characteristics of selected objects in the complex.

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

X_{111} | √ | x | √ | √ | x | √ | x | x | x | x | x | x | √ | x | √ | √ | √ | x | √ |

X_{112} | x | √ | x | x | x | x | √ | √ | √ | √ | √ | √ | x | x | x | x | x | x | x |

X_{113} | x | x | x | x | √ | x | x | x | x | x | x | x | x | √ | x | x | x | √ | x |

X_{114} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{121} | x | x | x | x | √ | x | x | x | x | √ | x | √ | x | √ | x | x | x | x | x |

X_{122} | √ | √ | √ | √ | x | x | x | x | √ | x | √ | x | x | x | √ | √ | √ | √ | x |

X_{123} | x | x | x | x | x | √ | √ | √ | x | x | x | x | √ | x | x | x | x | x | √ |

X_{131} | √ | x | x | √ | √ | √ | x | √ | x | √ | √ | x | √ | x | √ | √ | √ | √ | √ |

X_{132} | x | √ | √ | x | x | x | x | x | √ | x | x | √ | x | √ | x | x | x | x | x |

X_{133} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{141} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{142} | √ | x | x | x | √ | x | x | √ | x | √ | √ | x | √ | x | √ | √ | √ | x | √ |

X_{143} | x | √ | √ | √ | x | √ | √ | x | √ | x | x | √ | x | √ | x | x | x | √ | x |

X_{151} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{152} | √ | x | √ | √ | √ | √ | x | x | x | √ | x | x | x | √ | √ | x | x | x | x |

X_{153} | x | x | x | x | x | x | √ | x | √ | x | √ | x | √ | x | x | √ | √ | x | √ |

X_{154} | x | √ | x | x | x | x | x | √ | x | x | x | √ | x | x | x | x | x | √ | x |

X_{161} | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | x | x | x | √ | √ | x | √ | √ |

X_{162} | x | x | x | x | x | x | x | x | x | x | x | x | x | √ | x | x | √ | x | x |

X_{163} | x | x | x | x | x | x | x | x | x | x | x | √ | x | x | x | x | x | x | x |

X_{164} | x | x | x | x | x | x | x | x | x | x | x | x | √ | x | x | x | x | x | x |

X_{165} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{211} | √ | √ | √ | √ | √ | √ | √ | √ | √ | x | √ | x | √ | √ | √ | √ | √ | √ | √ |

X_{212} | x | x | x | x | x | x | x | x | x | √ | x | √ | x | x | x | x | x | x | x |

X_{221} | x | x | x | x | x | x | √ | x | x | x | x | x | x | x | x | x | x | x | x |

X_{222} | √ | √ | √ | √ | x | x | x | √ | √ | √ | x | x | √ | √ | √ | x | √ | √ | √ |

X_{223} | x | x | x | x | √ | √ | x | x | x | x | √ | √ | x | x | x | √ | x | x | x |

X_{231} | x | x | √ | √ | √ | x | x | √ | √ | √ | √ | √ | √ | x | √ | x | √ | x | √ |

X_{232} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x |

X_{233} | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | √ | x |

X_{234} | √ | √ | x | x | x | √ | √ | x | x | x | x | x | x | √ | x | √ | x | x | x |

X_{241} | x | x | x | √ | x | x | √ | √ | x | x | x | x | x | x | x | x | x | x | x |

X_{242} | √ | √ | x | x | √ | √ | x | x | √ | √ | √ | √ | x | x | √ | √ | √ | x | √ |

X_{243} | x | x | √ | x | x | x | x | x | x | x | x | x | √ | √ | x | x | x | √ | x |

Y_{11} | x | x | x | x | x | √ | x | x | x | x | x | x | x | x | x | x | x | x | x |

Y_{12} | √ | √ | √ | √ | √ | x | x | x | x | x | x | x | x | x | x | √ | x | x | √ |

Y_{13} | x | x | x | x | x | x | √ | √ | √ | √ | √ | √ | √ | √ | √ | x | √ | √ | x |

Y_{21} | x | √ | √ | x | x | x | x | x | √ | √ | x | √ | √ | √ | x | x | √ | √ | x |

Y_{22} | x | x | x | √ | √ | √ | x | x | x | x | x | x | x | x | √ | x | x | x | x |

Y_{23} | √ | x | x | x | x | x | √ | √ | x | x | √ | x | x | x | x | √ | x | x | √ |

Y_{31} | x | x | x | √ | x | √ | √ | √ | √ | √ | x | √ | √ | x | x | x | √ | √ | x |

Y_{32} | x | x | x | x | √ | x | x | x | x | x | √ | x | x | x | x | x | x | x | x |

Y_{33} | √ | √ | √ | x | x | x | x | x | x | x | x | x | x | √ | √ | √ | x | x | √ |

Y_{41} | x | x | x | √ | x | x | x | x | x | x | x | √ | √ | √ | √ | x | x | x | √ |

Y_{42} | √ | x | x | x | x | x | x | x | √ | x | x | x | x | x | x | √ | √ | x | x |

Y_{43} | x | √ | √ | x | √ | √ | √ | √ | x | √ | √ | x | x | x | x | x | x | √ | x |

Buildings | Final Weight | Buildings | Final Weight | Buildings | Final Weight |
---|---|---|---|---|---|

A | 0.4577 | E | 0.4598 | E | 0.4630 |

E | 0.4522 | A | 0.4534 | A | 0.4514 |

P | 0.4310 | P | 0.4265 | P | 0.4246 |

D | 0.4205 | K | 0.4192 | K | 0.4208 |

I | 0.4199 | D | 0.4177 | D | 0.4155 |

K | 0.4135 | I | 0.4131 | I | 0.4089 |

C | 0.4079 | C | 0.4092 | C | 0.4086 |

O | 0.3953 | O | 0.3951 | O | 0.3940 |

Q | 0.3798 | Q | 0.3780 | J | 0.3774 |

B | 0.3763 | B | 0.3750 | Q | 0.3765 |

J | 0.3622 | J | 0.3725 | B | 0.3734 |

F | 0.3619 | F | 0.3615 | F | 0.3603 |

R | 0.3533 | S | 0.3553 | S | 0.3557 |

G | 0.3442 | G | 0.3465 | G | 0.3469 |

N | 0.3203 | N | 0.3266 | N | 0.3291 |

H | 0.3200 | H | 0.3235 | H | 0.3238 |

S | 0.2894 | R | 0.2931 | R | 0.2933 |

M | 0.2775 | M | 0.2812 | M | 0.2820 |

L | 0.2099 | L | 0.2097 | L | 0.2094 |

Value of Increasing for Y | Change of Position for λ = 0 | Change of Position for λ = 0.5 | Change of Position for λ = 1 |
---|---|---|---|

0.01 | J falls from 11. to 12. | ||

0.02 | N falls from 15. to 16. | ||

0.03 | D jumps from 5. to 4. | ||

0.04 | S falls from 12. to 13. | ||

0.05 | J falls from 9. to 11. | ||

0.06 | F falls from 12. to 11. | F falls from 12. to 13. | |

0.07 | |||

0.08 | |||

0.09 | S falls from 13. to 14. | J falls from 11. to 13. | |

N falls from 15. to 16. | |||

0.10 | S falls from 13. to 14. | D jumps from 4. to 3. | |

0.11 | D jumps from 4. to 3. | D jumps from 4. to 3. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Milošević, D.M.; Milošević, M.R.; Simjanović, D.J.
Implementation of Adjusted Fuzzy AHP Method in the Assessment for Reuse of Industrial Buildings. *Mathematics* **2020**, *8*, 1697.
https://doi.org/10.3390/math8101697

**AMA Style**

Milošević DM, Milošević MR, Simjanović DJ.
Implementation of Adjusted Fuzzy AHP Method in the Assessment for Reuse of Industrial Buildings. *Mathematics*. 2020; 8(10):1697.
https://doi.org/10.3390/math8101697

**Chicago/Turabian Style**

Milošević, Dušan M., Mimica R. Milošević, and Dušan J. Simjanović.
2020. "Implementation of Adjusted Fuzzy AHP Method in the Assessment for Reuse of Industrial Buildings" *Mathematics* 8, no. 10: 1697.
https://doi.org/10.3390/math8101697