Abstract
Fuzzy analytic hierarchy process (FAHP) has been extensively applied to multi-criteria decision making (MCDM). However, the computational burden resulting from the calculation of fuzzy eigenvalue and eigenvector is heavy. As a result, a FAHP problem is usually solved using approximation techniques such as fuzzy geometric mean (FGM) and fuzzy extent analysis (FEA) instead of exact methods. Therefore, the FAHP results are subject to considerable inaccuracy. To solve this problem, in this study, a FAHP method based on the combination of α-cut operations (ACO), center-of-gravity (COG) defuzzification and defuzzification convergence mechanism (DCM) is proposed. First, ACO is applied to derive the near-exact fuzzy maximal eigenvalue and fuzzy weights. Subsequently, the α cuts of the fuzzy maximal eigenvalue and fuzzy weights are interpolated to generate samples that are uniformly distributed along the x-axis so that COG can be correctly applied to defuzzify the fuzzy maximal eigenvalue and fuzzy weights. To accelerate the computation process, DCM is applied to terminate the enumeration process if the defuzzified values of fuzzy weights have converged. The ACO–COG–DCM method has been applied to a real case to illustrate its applicability. In addition, a simulation study was also conducted to perform a parametric analysis. According to the experimental results, the proposed ACO–COG–DCM method improved the accuracy of estimating fuzzy weights by up to 56%. Furthermore, the experimental results also showed that the inaccuracy of estimating fuzzy weights was mostly owing to the deficiency of the FAHP method rather than the inconsistency of fuzzy pairwise comparison results.
Similar content being viewed by others
References
Ahmed F, Kilic K (2015) Modification to fuzzy extent analysis and its performance analysis. In: 6th international conference on industrial engineering and systems management (IESM), Seville, Spain
Buckley JJ (1985) Fuzzy hierarchical analysis. Fuzzy Sets Syst 17(3):233–247
Business Performance Management Singapore (2013) AHP—high consistency ratio. https://bpmsg.com/ahp-high-consistency-ratio/
Chang DY (1996) Applications of the extent analysis method on fuzzy AHP. Eur J Oper Res 95(3):649–655
Chen TCT (2020) Guaranteed-consensus posterior-aggregation fuzzy analytic hierarchy process method. Neural Comput Appl 32:7057–7068
Cheng CH, Mon DL (1994) Evaluating weapon system by analytical hierarchy process based on fuzzy scales. Fuzzy Sets Syst 63(1):1–10
Csutora R, Buckley JJ (2001) Fuzzy hierarchical analysis: the Lambda-Max method. Fuzzy Sets Syst 120(2):181–195
Donais FM, Abi-Zeid I, Waygood EOD, Lavoie R (2019) A review of cost–benefit analysis and multicriteria decision analysis from the perspective of sustainable transport in project evaluation. EURO J Decis Process 7(3):327–358
Gnanavelbabu A, Arunagiri P (2018) Ranking of MUDA using AHP and Fuzzy AHP algorithm. Mater Today Proc 5(5–2):13406–13412
Gu X, Zhu Q (2006) Fuzzy multi-attribute decision-making method based on eigenvector of fuzzy attribute evaluation space. Decis Support Syst 41(2):400–410
Güran A, Uysal M, Ekinci Y, Güran CB (2017) An additive FAHP based sentence score function for text summarization. Inf Technol Control 46(1):53–69
Junior FRL, Osiro L, Carpinetti LCR (2014) A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection. Appl Soft Comput 21:194–209
Kaewfak K, Huynh VN, Ammarapala V, Charoensiriwath C (2019) A fuzzy AHP-TOPSIS approach for selecting the multimodal freight transportation routes. In: International symposium on knowledge and systems sciences. Springer, Singapore, pp 28–46
Kubler S, Robert J, Derigent W, Voisin A, Le Traon Y (2016) A state-of the-art survey & testbed of fuzzy AHP (FAHP) applications. Expert Syst Appl 65:398–422
Lima-Junior FR, Carpinetti LCR (2020) Dealing with the problem of null weights and scores in Fuzzy Analytic Hierarchy Process. Soft Comput 24:9557–9573
Ljubojević S, Pamučar D, Jovanović D, Vešović V (2019) Outsourcing transport service: a fuzzy multi-criteria methodology for provider selection based on comparison of the real and ideal parameters of providers. Oper Res 19:399–433
López JCL, Carrillo PAÁ, Chavira DAG, Noriega JJS (2017) A web-based group decision support system for multicriteria ranking problems. Oper Res Int J 17(2):499–534
Pramono PP, Surjandari I, Laoh E (2019) Estimating customer segmentation based on customer lifetime value using two-stage clustering method. In: 2019 16th international conference on service systems and service management, pp 1–5
Promentilla MAB, Furuichi T, Ishii K, Tanikawa N (2008) A fuzzy analytic network process for multi-criteria evaluation of contaminated site remedial countermeasures. J Environ Manage 88(3):479–495
Saaty TL (1996) Decision making with dependence and feedback: the analytic network process. RWS Publications, Pittsburgh
Satty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
Schito J, Jullier J, Raubal M (2019) A framework for integrating stakeholder preferences when deciding on power transmission line corridors. EURO J Decis Process 7(3–4):159–195
Sirisawat P, Kiatcharoenpol T (2018) Fuzzy AHP-TOPSIS approaches to prioritizing solutions for reverse logistics barriers. Comput Ind Eng 117:303–318
Van Laarhoven PJM, Pedrycz W (1983) A fuzzy extension of Saaty’s priority theory. Fuzzy Sets Syst 11(1–3):229–241
Wang YC, Chen TCT (2019) A partial-consensus posterior-aggregation FAHP method—supplier selection problem as an example. Mathematics 7(2):179
Wang L, Chu J, Wu J (2007) Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process. Int J Prod Econ 107(1):151–163
Wedley WC (1993) Consistency prediction for incomplete AHP matrices. Math Comput Model 17(4–5):151–161
Zheng G, Zhu N, Tian Z, Chen Y, Sun B (2012) Application of a trapezoidal fuzzy AHP method for work safety evaluation and early warning rating of hot and humid environments. Saf Sci 50(2):228–239
Zhü K (2014) Fuzzy analytic hierarchy process: fallacy of the popular methods. Eur J Oper Res 236(1):209–217
Acknowledgements
The author would like to thank the valuable comments of the editor and reviewers for improving the quality of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, T. Enhancing the efficiency and accuracy of existing FAHP decision-making methods. EURO J Decis Process 8, 177–204 (2020). https://doi.org/10.1007/s40070-020-00115-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40070-020-00115-8
Keywords
- Fuzzy analytic hierarchy process
- Fuzzy geometric mean
- Fuzzy extent analysis
- Alpha-cut operations
- Accuracy
- Center-of-gravity