Research Article
BibTex RIS Cite

Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method

Year 2023, Volume: 7 Issue: 2, 293 - 307, 29.12.2023
https://doi.org/10.26650/acin.1224496

Abstract

In Analytic Hierarchy Process (AHP), which is a very common method in Multi Criteria Decision Making (MCDM) problems, the use of fuzzy set theory, which allows human judgment to be expressed more realistically, has gained popularity in recent years. However, this situation causes more computational complexity due to the way fuzzy numbers are expressed and the operators used. In this study, the results of real various problems in a hierarchical structure with the Magnitude Based Fuzzy Analytic Hierarchy Process (MFAHP) were compared with the results of the Modified Fuzzy Logarithmic Least Squares method (MFLLSM) and Buckley’s Geometric Means method (GM), which are two known methods to obtain accurate weight values. The results show that there is no statistically significant difference between MFAHP and the results of these two methods. In the performance comparison, although it is known that it produces incorrect results, unfortunately, the results of Chang’s Extent Analysis method on fuzzy AHP (FEA) are also included because it is a widely used method. As another important finding of this study, it can be said that MFAHP is faster than both methods when the running times are compared. Finally, software for the calculations of these methods mentioned in the study has been developed and link shared.

References

  • Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & Math. with Applications, 57(3), 413-419. google scholar
  • Ahmed, F., & Kilic, K. (2019). Fuzzy Analytic Hierarchy Process: A performance analysis of various algorithms. Fuzzy Sets and Systems, 362, 110-128. google scholar
  • Amiri, M. P. (2010). Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods. Expert systems with applications, 37(9), 6218-6224. google scholar
  • Arif, J. M., Ab Razak, M. F., Mat, S. R. T., Awang, S., Ismail, N. S. N., & Firdaus, A. (2021). Android mobile malware detection using fuzzy AHP. Journal of Information Security and Applications, 61, 102929. google scholar
  • Arikan, R., Dağdeviren, M., & Kurt, M. (2013). A fuzzy multi-attribute decision making model for strategic risk assessment. International Journal of Computational Intelligence Systems, 6(3), 487-502. google scholar
  • Aydogan, E. K., Delice, E. K., & Papajorgji, P. (2013). An effective approach for evaluating usability of Web sites. In Enterprise Business Modeling, Optimization Techniques, and Flexible Information Systems (pp. 97-107). IGI Global. google scholar
  • Aydogan, E. K., Demirtas, O., & Dagdeviren, M. (2015). A New Integrated Fuzzy Multi-Criteria Decision Model for Performance Evaluation. Business and Management Studies, 1(1), 38-55. google scholar
  • Ballı, S., & Karasulu, B. (2013). Bulanık karar verme sistemlerinde paralel hesaplama. Pamukkale Üniversitesi Mühendislik Bil. Dergisi, 19(2), 61-67. google scholar
  • Boender, C. G. E., De Graan, J. G., & Lootsma, F. (1989). Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets and Systems, 29(2), 133-143. google scholar
  • Bortolan, G., & Degani, R. (1985). A review of some methods for ranking fuzzy subsets. Fuzzy sets and systems, 15(1), 1-19. google scholar
  • Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy sets and systems, 17(3), 233-247. google scholar
  • Büyüközkan, G., Kahraman, C., & Ruan, D. (2004). A fuzzy multi-criteria decision approach for software development strategy selection. International journal of general systems, 33(2-3), 259-280. google scholar
  • Büyüközkan, G., Çifçi, G., & Güleryüz, S. (2011). Strategic analysis of healthcare service quality using fuzzy AHP methodology. Expert systems with applications, 38(8), 9407-9424. google scholar
  • Celik, M., Er, I. D., & Ozok, A. F. (2009). Application of fuzzy extended AHP methodology on shipping registry selection: The case of Turkish maritime industry. Expert Systems with Applications, 36(1), 190-198. google scholar
  • Chutia, R., & Chutia, B. (2017). A new method of ranking parametric form of fuzzy numbers using value and ambiguity. Applied Soft Comp., 52, 1154-1168. google scholar
  • Dong, M., Li, S., & Zhang, H. (2015). Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP. Expert Systems with Applications, 42(21), 7846-7857. google scholar
  • Dweiri, F., Kumar, S., Khan, S. A., & Jain, V. (2016). Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Systems with Applications, 62, 273-283. google scholar
  • Isaai, M. T., Kanani, A., Tootoonchi, M., & Afzali, H. R. (2011). Intelligent timetable evaluation using fuzzy AHP. Expert systems with App., 38(4), 3718-3723. google scholar
  • Jaganathan, S., Erinjeri, J. J., & Ker, J. I. (2007). Fuzzy analytic hierarchy process based group decision support system to select and evaluate new manufacturing technologies. The International Journal of Advanced Manufacturing Technology, 32(11), 1253-1262. google scholar
  • Kahraman, C., Cebeci, U., & Ruan, D. (2004). Multi-attribute comparison of catering service companies using fuzzy AHP: The case of Turkey. International journal of production economics, 87(2), 171-184. google scholar
  • Kinay, A. O., & Tezel, B. T. (2022). Modification of the fuzzy analytic hierarchy process via different ranking methods. International Journal of Intelligent Systems, 37(1), 336-364. google scholar
  • Korkmaz, I., Gökçen, H., & Çetinyokuş, T. (2008). An analytic hierarchy process and two-sided matching based decision support system for military personnel assignment. Information Sciences, 178(14), 2915-2927. google scholar
  • 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 Systems with Applications, 65, 398-422. google scholar
  • Kwiesielewicz, M. (1996). The logarithmic least squares and the generalized pseudoinverse in estimating ratios. European Journal of Operational Research, 93(3), 611-619. google scholar
  • Liu, Y., Eckert, C. M., & Earl, C. (2020). A review of fuzzy AHP methods for decision-making with subjective judgements. Expert Systems with Applications, 161, 113738. google scholar
  • Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of mathematical psychology, 15(3), 234-281. google scholar
  • Saaty, T.L. (1980) The Analytic Hierarchy Process: Planning, Priority Setting, Resources Allocation. Mcgraw-Hill, New York. google scholar
  • Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of operational research, 169(1), 1-29. google scholar
  • Xu, Z., & Liao, H. (2013). Intuitionistic fuzzy analytic hierarchy process. IEEE transactions on fuzzy systems, 22(4), 749-761. google scholar
  • Wang, Y. M., Elhag, T. M., & Hua, Z. (2006). A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and systems, 157(23), 3055-3071. google scholar
  • Chang, D. Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649-655. google scholar
  • Mardani, A., Jusoh, A., & Zavadskas, E. K. (2015). Fuzzy multiple criteria decision-making techniques and applications–Two decades review from 1994 to 2014. Expert Systems with Applications, 42(8), 4126-4148. google scholar
  • Van Laarhoven, P. J., & Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy sets and Systems, 11(1-3), 229-241. google scholar
  • Ruoning, X., & Xiaoyan, Z. (1996). Fuzzy logarithmic least squares ranking method in analytic hierarchy process. Fuzzy Sets and Systems, 77(2), 175-190. google scholar
  • Wang, Y. M., Luo, Y., & Hua, Z. (2008). On the extent analysis method for fuzzy AHP and its applications. European Journal of Operational Research, 186(2), 735-747. google scholar
  • Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. google scholar
  • Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy sets and systems, 118(3), 375-385. google scholar
  • Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy sets and systems, 118(3), 387-405. google scholar
  • Wang, Y. M., & Elhag, T. M. (2006). On the normalization of interval and fuzzy weights. Fuzzy sets and systems, 157(18), 2456-2471. google scholar
  • Praščević, N., & Praščević, Ž. (2016). Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehnički vjesnik/Technical Gazette, 23(1), 57-64. google scholar
  • Sehra, S. K., Brar, D., Singh, Y., & Kaur, D. (2013). Multi criteria decision making approach for selecting effort estimation model. arXiv preprint arXiv:1310.5220. google scholar
  • Tyagi, S., Agrawal, S., Yang, K., & Ying, H. (2017). An extended Fuzzy-AHP approach to rank the influences of socialization-externalizationcombination- internalization modes on the development phase. Applied Soft Computing, 52, 505-518. google scholar
  • Yuen, K. K., & Lau, H. C. (2008). Software vendor selection using fuzzy analytic hierarchy process with ISO/IEC 9126. IAENG International journal of computer science, 35(3). google scholar

Magnitüde Bağlı Bulanık Analitik Hiyerarşi Süreci (MBAHS) Yöntemi Performans Değerlendirmesi

Year 2023, Volume: 7 Issue: 2, 293 - 307, 29.12.2023
https://doi.org/10.26650/acin.1224496

Abstract

Çok Kriterli Karar Verme (ÇKKV) problemlerinde oldukça yaygın bir yöntem olan Analitik Hiyerarşi Sürecinde (AHS), insan yargısının daha gerçekçi bir şekilde ifade edilmesini sağlayan bulanık küme teorisinin kullanımı son yıllarda önem kazanmıştır. Ancak bu durum, bulanık sayıların ifade edilme şekli ve kullanılan operatörler nedeniyle daha fazla hesaplama karmaşıklığına neden olmaktadır. Bu çalışmada, hiyerarşik yapıdaki çeşitli gerçek hayat problemlerinin Magnitüde Bağlı Bulanık Analitik Hiyerarşi Süreci (MBAHS) ile elde edilen sonuçların doğruluğu, doğru ağırlıkdeğerleri elde etmekte kullanılan iki yöntem olan Modifiye Bulanık Logaritmik En Küçük Kareler yöntemi (MFLLSM) ve Buckley’nin Geometrik Ortalamalar yöntemi (GM) sonuçları ile karşılaştırılmıştır. Sonuçlar, MBAHS ile bu iki yöntemin sonuçları arasında istatistiksel olarak anlamlı bir fark olmadığını göstermektedir. Performans karşılaştırmasında hatalı sonuçlar ürettiği bilinse de ne yazık ki yaygın olarak kullanılan bir yöntem olduğu için bulanık AHS’de Chang’in Extent Analizi (CEA) yöntemi sonuçları da yer almaktadır. Bu çalışmanın bir diğer önemli bulgusu olarak çalışma süreleri karşılaştırıldığında da MBAHS’nin her iki yöntemden daha hızlı olduğu söylenebilir. Son olarak çalışmada adı geçen bu yöntemlerin hesaplamalarınınyapılabileceği bir yazılım geliştirilmiş ve bağlantısı paylaşılmıştır.

References

  • Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & Math. with Applications, 57(3), 413-419. google scholar
  • Ahmed, F., & Kilic, K. (2019). Fuzzy Analytic Hierarchy Process: A performance analysis of various algorithms. Fuzzy Sets and Systems, 362, 110-128. google scholar
  • Amiri, M. P. (2010). Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods. Expert systems with applications, 37(9), 6218-6224. google scholar
  • Arif, J. M., Ab Razak, M. F., Mat, S. R. T., Awang, S., Ismail, N. S. N., & Firdaus, A. (2021). Android mobile malware detection using fuzzy AHP. Journal of Information Security and Applications, 61, 102929. google scholar
  • Arikan, R., Dağdeviren, M., & Kurt, M. (2013). A fuzzy multi-attribute decision making model for strategic risk assessment. International Journal of Computational Intelligence Systems, 6(3), 487-502. google scholar
  • Aydogan, E. K., Delice, E. K., & Papajorgji, P. (2013). An effective approach for evaluating usability of Web sites. In Enterprise Business Modeling, Optimization Techniques, and Flexible Information Systems (pp. 97-107). IGI Global. google scholar
  • Aydogan, E. K., Demirtas, O., & Dagdeviren, M. (2015). A New Integrated Fuzzy Multi-Criteria Decision Model for Performance Evaluation. Business and Management Studies, 1(1), 38-55. google scholar
  • Ballı, S., & Karasulu, B. (2013). Bulanık karar verme sistemlerinde paralel hesaplama. Pamukkale Üniversitesi Mühendislik Bil. Dergisi, 19(2), 61-67. google scholar
  • Boender, C. G. E., De Graan, J. G., & Lootsma, F. (1989). Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets and Systems, 29(2), 133-143. google scholar
  • Bortolan, G., & Degani, R. (1985). A review of some methods for ranking fuzzy subsets. Fuzzy sets and systems, 15(1), 1-19. google scholar
  • Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy sets and systems, 17(3), 233-247. google scholar
  • Büyüközkan, G., Kahraman, C., & Ruan, D. (2004). A fuzzy multi-criteria decision approach for software development strategy selection. International journal of general systems, 33(2-3), 259-280. google scholar
  • Büyüközkan, G., Çifçi, G., & Güleryüz, S. (2011). Strategic analysis of healthcare service quality using fuzzy AHP methodology. Expert systems with applications, 38(8), 9407-9424. google scholar
  • Celik, M., Er, I. D., & Ozok, A. F. (2009). Application of fuzzy extended AHP methodology on shipping registry selection: The case of Turkish maritime industry. Expert Systems with Applications, 36(1), 190-198. google scholar
  • Chutia, R., & Chutia, B. (2017). A new method of ranking parametric form of fuzzy numbers using value and ambiguity. Applied Soft Comp., 52, 1154-1168. google scholar
  • Dong, M., Li, S., & Zhang, H. (2015). Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP. Expert Systems with Applications, 42(21), 7846-7857. google scholar
  • Dweiri, F., Kumar, S., Khan, S. A., & Jain, V. (2016). Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Systems with Applications, 62, 273-283. google scholar
  • Isaai, M. T., Kanani, A., Tootoonchi, M., & Afzali, H. R. (2011). Intelligent timetable evaluation using fuzzy AHP. Expert systems with App., 38(4), 3718-3723. google scholar
  • Jaganathan, S., Erinjeri, J. J., & Ker, J. I. (2007). Fuzzy analytic hierarchy process based group decision support system to select and evaluate new manufacturing technologies. The International Journal of Advanced Manufacturing Technology, 32(11), 1253-1262. google scholar
  • Kahraman, C., Cebeci, U., & Ruan, D. (2004). Multi-attribute comparison of catering service companies using fuzzy AHP: The case of Turkey. International journal of production economics, 87(2), 171-184. google scholar
  • Kinay, A. O., & Tezel, B. T. (2022). Modification of the fuzzy analytic hierarchy process via different ranking methods. International Journal of Intelligent Systems, 37(1), 336-364. google scholar
  • Korkmaz, I., Gökçen, H., & Çetinyokuş, T. (2008). An analytic hierarchy process and two-sided matching based decision support system for military personnel assignment. Information Sciences, 178(14), 2915-2927. google scholar
  • 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 Systems with Applications, 65, 398-422. google scholar
  • Kwiesielewicz, M. (1996). The logarithmic least squares and the generalized pseudoinverse in estimating ratios. European Journal of Operational Research, 93(3), 611-619. google scholar
  • Liu, Y., Eckert, C. M., & Earl, C. (2020). A review of fuzzy AHP methods for decision-making with subjective judgements. Expert Systems with Applications, 161, 113738. google scholar
  • Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of mathematical psychology, 15(3), 234-281. google scholar
  • Saaty, T.L. (1980) The Analytic Hierarchy Process: Planning, Priority Setting, Resources Allocation. Mcgraw-Hill, New York. google scholar
  • Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of operational research, 169(1), 1-29. google scholar
  • Xu, Z., & Liao, H. (2013). Intuitionistic fuzzy analytic hierarchy process. IEEE transactions on fuzzy systems, 22(4), 749-761. google scholar
  • Wang, Y. M., Elhag, T. M., & Hua, Z. (2006). A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and systems, 157(23), 3055-3071. google scholar
  • Chang, D. Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649-655. google scholar
  • Mardani, A., Jusoh, A., & Zavadskas, E. K. (2015). Fuzzy multiple criteria decision-making techniques and applications–Two decades review from 1994 to 2014. Expert Systems with Applications, 42(8), 4126-4148. google scholar
  • Van Laarhoven, P. J., & Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy sets and Systems, 11(1-3), 229-241. google scholar
  • Ruoning, X., & Xiaoyan, Z. (1996). Fuzzy logarithmic least squares ranking method in analytic hierarchy process. Fuzzy Sets and Systems, 77(2), 175-190. google scholar
  • Wang, Y. M., Luo, Y., & Hua, Z. (2008). On the extent analysis method for fuzzy AHP and its applications. European Journal of Operational Research, 186(2), 735-747. google scholar
  • Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. google scholar
  • Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy sets and systems, 118(3), 375-385. google scholar
  • Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy sets and systems, 118(3), 387-405. google scholar
  • Wang, Y. M., & Elhag, T. M. (2006). On the normalization of interval and fuzzy weights. Fuzzy sets and systems, 157(18), 2456-2471. google scholar
  • Praščević, N., & Praščević, Ž. (2016). Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehnički vjesnik/Technical Gazette, 23(1), 57-64. google scholar
  • Sehra, S. K., Brar, D., Singh, Y., & Kaur, D. (2013). Multi criteria decision making approach for selecting effort estimation model. arXiv preprint arXiv:1310.5220. google scholar
  • Tyagi, S., Agrawal, S., Yang, K., & Ying, H. (2017). An extended Fuzzy-AHP approach to rank the influences of socialization-externalizationcombination- internalization modes on the development phase. Applied Soft Computing, 52, 505-518. google scholar
  • Yuen, K. K., & Lau, H. C. (2008). Software vendor selection using fuzzy analytic hierarchy process with ISO/IEC 9126. IAENG International journal of computer science, 35(3). google scholar
There are 43 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section Research Article
Authors

Barış Tekin Tezel 0000-0003-4873-7848

Ayşe Övgü Kınay 0000-0001-9908-8652

Publication Date December 29, 2023
Submission Date December 26, 2022
Published in Issue Year 2023 Volume: 7 Issue: 2

Cite

APA Tezel, B. T., & Kınay, A. Ö. (2023). Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method. Acta Infologica, 7(2), 293-307. https://doi.org/10.26650/acin.1224496
AMA Tezel BT, Kınay AÖ. Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method. ACIN. December 2023;7(2):293-307. doi:10.26650/acin.1224496
Chicago Tezel, Barış Tekin, and Ayşe Övgü Kınay. “Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method”. Acta Infologica 7, no. 2 (December 2023): 293-307. https://doi.org/10.26650/acin.1224496.
EndNote Tezel BT, Kınay AÖ (December 1, 2023) Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method. Acta Infologica 7 2 293–307.
IEEE B. T. Tezel and A. Ö. Kınay, “Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method”, ACIN, vol. 7, no. 2, pp. 293–307, 2023, doi: 10.26650/acin.1224496.
ISNAD Tezel, Barış Tekin - Kınay, Ayşe Övgü. “Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method”. Acta Infologica 7/2 (December 2023), 293-307. https://doi.org/10.26650/acin.1224496.
JAMA Tezel BT, Kınay AÖ. Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method. ACIN. 2023;7:293–307.
MLA Tezel, Barış Tekin and Ayşe Övgü Kınay. “Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method”. Acta Infologica, vol. 7, no. 2, 2023, pp. 293-07, doi:10.26650/acin.1224496.
Vancouver Tezel BT, Kınay AÖ. Performance Evaluation of Magnitude-Based Fuzzy Analytic Hierarchy Process (MFAHP) Method. ACIN. 2023;7(2):293-307.