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

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.

Keywords

• Fuzzy multi-criteria decision making
• fuzzy analytic hierarchy process
• performance evaluation

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

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.

Keywords

• Bulanık çok kriterli karar verme
• bulanık analitik hiyerarşi süreci
• performans değerlendirmesi.

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