# Fuzzy AHP Application for Supporting Contractors’ Bidding Decision

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Decision Making Processes in Construction Management

## 3. Bidding Decision Support Systems Based on Fuzzy AHP—Methodology

**Step 1:**Computation of synthetic fuzzy values for each object of the analysis.

**Step 2:**Comparison of the degree of possibility that ${M}_{2}\ge {M}_{1}$.

**Step 3:**Computation of the smallest degree of possibility ${M}_{2}\ge {M}_{1}$ .

## 4. Project Selection for Bidding—Model Application

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Method Name | Aim of Analysis | Number of Criterion Used | Source |
---|---|---|---|

Analytic Hierarchy Process (AHP) + PROMETHEE | subcontractor selection for main contractor | 13 | [8] |

Data Envelopment Analysis (DEA) | subcontractor selection at short-listing stage | 5–6 selected depending on the specific tender | [9] |

Fuzzy AHP; The method of entropy; Method of criterion impact loss (CILOS); Integrated Determination of Objective CRIteria Weights (IDOCRIW) method; The SAW method; The TOPSIS method; The COPRAS method | comparing quality assurance in different contractor contracts | 7 | [10] |

The EDAS method | comparing quality assurance in different contractor contracts | 7 | [11] |

hybrid MCDM model of discrete zero-sum two-person matrix games with grey numbers | delays in Design-Bid-Build projects | 8 | [12] |

Integration of intuitionistic fuzzy sets I(FS) theory, ELECTRE and VIKOR along with Grey Relational Analysis (GRA | contractor selection problem | 20 | [13] |

Weighted Aggregated Sum Product Assessment with Grey Values (WASPAS-G) | evaluating and selecting contractors | 6 | [14] |

**Table 2.**A fuzzy scheme of preference evaluation [41].

Qualitative Evaluation | Fuzzy Evaluation | AHP Equivalent |
---|---|---|

Extreme preference | (2; 5/2; 3) | 9 |

Very strong preference | (3/2; 2; 5/2) | 7 |

Strong preference | (1; 3/2; 2) | 5 |

Moderate preference | (1; 1; 3/2) | 3 |

Equal preference | (1; 1; 1) | 1 |

Moderate inferiority | (2/3; 1; 1) | 1/3 |

Strong inferiority | (1/2; 2/3; 1) | 1/5 |

Very strong inferiority | (2/5; ½; 2/3) | 1/7 |

Extreme inferiority | (1/3; 2/5; 1/2) | 1/9 |

**Table 3.**Average evaluation of the criteria involved in the decision process of selecting a project.

Criterion/Sub-Criterion | Name of the Criterion/Factor | Average Evaluation of Criterion/Factor * |
---|---|---|

C1 | Company’s capabilities | 5.14 |

C1_1 | Need of work | 5.21 |

C1_2 | Past experience with similar projects | 5.95 |

C1_3 | Location of the project | 4.25 |

C2 | Investment characteristics | 4.48 |

C2_1 | Size of the project (e.g., cubic measure) | 4.95 |

C2_2 | Time of project duration | 4.49 |

C2_3 | Type of works | 5.98 |

C2_4 | Degree of works complexity | 3.25 |

C2_5 | Necessity for specialized equipment | 3.51 |

C2_6 | Possible subcontractors | 3.87 |

C2_7 | Owner’s reputation | 5.31 |

C3 | Financial conditions | 5.35 |

C3_1 | Value of the project | 5.30 |

C3_2 | Contract conditions | 5.89 |

C3_3 | Profits from similar past projects | 4.87 |

C4 | Tender characteristics | 4.14 |

C4_1 | Time for the preparation of the bid | 3.89 |

C4_2 | Criteria of bid selection | 4.38 |

Sub-Criterion/Factor | Project | |||
---|---|---|---|---|

P1 | P2 | P3 | P4 | |

C1_1 | 7 | 5 | 7 | 5 |

C1_2 | 4 | 7 | 7 | 7 |

C1_3 | 4 | 5 | 6 | 6 |

C2_1 | 3 | 3 | 5 | 2 |

C2_2 | 3 | 4 | 6 | 5 |

C2_3 | 5 | 7 | 7 | 6 |

C2_4 | 4 | 6 | 7 | 7 |

C2_5 | 4 | 6 | 6 | 6 |

C2_6 | 6 | 6 | 6 | 3 |

C2_7 | 6 | 4 | 7 | 4 |

C3_1 | 4 | 3 | 4 | 2 |

C3_2 | 5 | 4 | 6 | 4 |

C3_3 | 4 | 4 | 5 | 4 |

C4_1 | 6 | 5 | 7 | 6 |

C4_2 | 4 | 5 | 4 | 4 |

Names | Priority Weight Vector for Each Individual Project | |||||
---|---|---|---|---|---|---|

Criteria | Sub-Criteria | P1 | P2 | P3 | P4 | |

C1_1 | 0.4045 | 0.3381 | 0.5000 | 0.0000 | 0.5000 | 0.0000 |

C1_2 | 0.6619 | 0.0000 | 0.3333 | 0.3333 | 0.3333 | |

C1_3 | 0.0000 | 0.0309 | 0.2253 | 0.3719 | 0.3719 | |

C2_1 | 0.1026 | 0.1990 | 0.0264 | 0.0264 | 0.9472 | 0.0000 |

C2_2 | 0.1287 | 0.0000 | 0.1086 | 0.5586 | 0.3329 | |

C2_3 | 0.3544 | 0.0309 | 0.3719 | 0.3719 | 0.2253 | |

C2_4 | 0.0000 | 0.0000 | 0.1870 | 0.4065 | 0.4065 | |

C2_5 | 0.0028 | 0.0000 | 0.3333 | 0.3333 | 0.3333 | |

C2_6 | 0.0547 | 0.3333 | 0.3333 | 0.3333 | 0.0000 | |

C2_7 | 0.2603 | 0.3119 | 0.0000 | 0.6881 | 0.0000 | |

C3_1 | 0.4928 | 0.2692 | 0.3719 | 0.2253 | 0.3719 | 0.0309 |

C3_2 | 0.7308 | 0.3694 | 0.0333 | 0.5640 | 0.0333 | |

C3_3 | 0.0000 | 0.1688 | 0.1688 | 0.4937 | 0.1688 | |

C4_1 | 0.0000 | 0.0000 | 0.2474 | 0.0809 | 0.4244 | 0.2474 |

C4_2 | 1.0000 | 0.1688 | 0.4937 | 0.1688 | 0.1688 | |

Solution | 0.2627 | 0.1486 | 0.4707 | 0.1180 |

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**MDPI and ACS Style**

Leśniak, A.; Kubek, D.; Plebankiewicz, E.; Zima, K.; Belniak, S.
Fuzzy AHP Application for Supporting Contractors’ Bidding Decision. *Symmetry* **2018**, *10*, 642.
https://doi.org/10.3390/sym10110642

**AMA Style**

Leśniak A, Kubek D, Plebankiewicz E, Zima K, Belniak S.
Fuzzy AHP Application for Supporting Contractors’ Bidding Decision. *Symmetry*. 2018; 10(11):642.
https://doi.org/10.3390/sym10110642

**Chicago/Turabian Style**

Leśniak, Agnieszka, Daniel Kubek, Edyta Plebankiewicz, Krzysztof Zima, and Stanisław Belniak.
2018. "Fuzzy AHP Application for Supporting Contractors’ Bidding Decision" *Symmetry* 10, no. 11: 642.
https://doi.org/10.3390/sym10110642