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

Barış Tekin Tezel; Ayşe Övgü Kınay

Article Details

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

Authors:

Barış Tekin Tezel | Ayşe Övgü Kınay

Publisher:

Istanbul University

Main Topics:

Bilgisayar Yazılımı

Journal:

Acta Infologica Vol.7 Issue 2, pp.293-307

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001312780

pISSN:

2602-3563

Keywords:

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 Buckleys 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 Changs 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.

 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 Buckleys 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 Changs 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.

 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 Buckleys 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 Changs 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.

 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 Buckleynin 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 AHSde Changin Extent Analizi CEA yöntemi sonuçları da yer almaktadır. Bu çalışmanın bir diğer önemli bulgusu olarak çalışma süreleri karşılaştırıldığında da MBAHSnin her iki yöntemden daha hızlı olduğu söylenebilir. Son olarak çalışmada adı geçen bu yöntemlerin hesaplamalarınınyapılabileceği bir yazılım geliştirilmiş ve bağlantısı paylaşılmıştır.

Article Details

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

Authors:

Barış Tekin Tezel | Ayşe Övgü Kınay

Publisher:

Istanbul University

Main Topics:

Bilgisayar Yazılımı

Journal:

Acta Infologica Vol.7 Issue 2, pp.293-307

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001312780

pISSN:

2602-3563

Fuzzy multi-criteria decision making

fuzzy analytic hierarchy process

performance evaluationBulanık çok kriterli karar verme

bulanık analitik hiyerarşi süreci

performans değerlendirmesi.

Issues

Article Details

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

Authors: Barış Tekin Tezel | Ayşe Övgü Kınay

Publisher: Istanbul University

Main Topics: Bilgisayar Yazılımı

Journal: Acta Infologica Vol.7 Issue 2, pp.293-307

Document Type: Article

Publication Date: 12/2023

Document Language: English

Document ID (Org No.): 2001312780

pISSN: 2602-3563

Fuzzy multi-criteria decision making

fuzzy analytic hierarchy process

performance evaluationBulanık çok kriterli karar verme

bulanık analitik hiyerarşi süreci

performans değerlendirmesi.

Issues

Authors:

Barış Tekin Tezel | Ayşe Övgü Kınay

Publisher:

Istanbul University

Main Topics:

Bilgisayar Yazılımı

Journal:

Acta Infologica Vol.7 Issue 2, pp.293-307

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001312780

pISSN:

2602-3563