دانلود رایگان مقاله انگلیسی فرآیند سلسله مراتبی تحلیلی فازی: تجزیه و تحلیل عملکرد الگوریتم های مختلف - الزویر 2018

Abstract

Analytical Hierarchical Process (AHP) along with fuzzy set theory has been used extensively in the Multi-Criteria Decision Making (MCDM) process in which fuzzy numbers are utilized to represent human judgments more realistically. Over the past couple of decades, numerous articles have been published proposing algorithms through which priority vector (or weight vector) can be calculated from fuzzy comparison matrices. The aim of this study is to conduct a comprehensive performance analysis of the most popular algorithms proposed in this domain in terms of accuracy of weights calculated from fuzzy comparison matrices. Such an analysis is much needed by the researchers and practitioners. However none is available. An experimental analysis is conducted and the performance of various algorithms are evaluated with varying three parameters i.e., the size of the comparison matrix, the level of fuzziness and the level of inconsistency. We found that modified Logarithmic Least Squares Method and Fuzzy Inverse of Column Sum Method (FICSM) generally outperformed other algorithms, while Fuzzy Extent Analysis (FEA) which is the most frequently used algorithm in the literature provides the least accurate results. Furthermore, it was observed that a modified version of FEA method significantly improved its performance.

Conclusions and future research

In this research we compared performance of nine FAHP methods among which five FAHP methods are the most popular ones in the literature. Compatibility Index Value (CIV) is used as a performance metrics to evaluate all nine FAHP methods. Three experimental conditions are considered as part of the analysis, namely, size of the matrix (n), fuzzification level (α) and inconsistency (C.R). For the fuzzification parameter four levels are assumed as 0.25, 0.50, 0.75 and 1.00. The fuzzification parameter is not inherent to the problem that the decision maker is facing but more a decision variable as part of the process. That is to say, the decision analysts can set the fuzzification level and conduct FAHP accordingly. On the other hand the inconsistency parameter refers to the inconsistency of the decision maker and is not a decision variable but depends on the fuzzy comparison matrices elicited from the experts. For the analysis three levels are considered for the inconsistency which is low, medium and high based on the consistency ratio (C.R) values as explained before. Finally, four different matrix sizes are considered which are 3, 7, 11 and 15. Note that one can consider 3 as the representative of small sized problems, 7 and 11 are for medium sized problems and 15 for larger cases. As a result of this set up total of 48 (= 4 ∗ 3 ∗ 4) different experimental conditions are constructed. For each condition 13 replications are created randomly. Hence the total dataset is composed of six hundred and twenty four matrices with varying parameters for size of the matrix, fuzzification levels and inconsistency.