[Home ] [Archive]   [ فارسی ]  
:: Search Submit Contact ::
:: Volume 8, Issue 2 (Vol. 8,No. 2, 2022) ::
2022, 8(2): 19-37 Back to browse issues page
Determination of weight vector by using a pairwise comparison matrix based on DEA and Shannon entropy
Hooshyar Azad1, Ali Asghar Foroughi
1- , h.azad86@yahoo.com
Abstract:   (707 Views)
Analytic hierarchy process (AHP) is a method of multiple criteria decision making (MCDM) that is used to select an alternative from a set of alternatives or to rank a set of alternatives, while data envelopment analysis (DEA) is a nonparametric method that is used based on linear programming to evaluate the performance of decision making units (DMUs) that have multiple inputs and multiple outputs. The relation between methods of MCDM and DEA is a topic of interest to researchers in this part of MCDM, e.g., one of the first works done in this field is the relation between data envelopment analysis and multiple objective linear programming by Golany. Ramanathan proposed a method (DEAHP method) based on DEA for weight generation in the AHP that his method had three main drawbacks: (1) producing irrational weights for inconsistent pairwise comparison matrices; (2) non-use all the information of the inconsistent pairwise comparison matrix; and (3) insensitivity to changing elements in some matrices of pairwise comparison. To solve the problems of DEAHP method, several methods were proposed that each one produces a weight vector in the AHP, e.g., we can mentioned to data envelopment analysis method of wang and chin (DEA method) and data envelopment analysis method with assurance region of wang and et al. (DEA/AR method). In this paper, we propose a new method, which is called E-DEAHP method for short, based on DEA and Shannon entropy, a concept used in information theory, to produce a weight vector in the AHP that does not have the problems of DEAHP method and is different from the mentioned methods.

Material and methods
In this approach, each row of the pairwise comparison matrix is considered as a decision making unit (DMU), so that in the normalized pairwise comparison matrix the arithmetic mean of the ith row and the entropy of ith column is considered as, respectively, output and input of the ith DMU and then with employed data envelopment analysis, we find the local weight vector of the elements (decision criteria or alternatives). Also, to aggregate the obtained local weights, we use the simple additive weighting (SAW) method in multiple criteria decision making.
Results and discussion
It is proved that if a pairwise comparison matrix is perfectly consistent, the entropy of all its columns are the same, so in this case all decision making units will have the same input and the method will produce true weight vector.
The results of the examined numerical examples show that the proposed method of this paper produces perfectly rational weights in comparison with the results of the methods known in the subject literature and can estimate a robust priority (weight) vector for a pairwise comparison matrix. Also, the results of the hierarchical problem survey show that the weights obtained from the method and their aggregation to obtain the global weight vector confirm the potential validity of the method.
In this paper, in relation to E-DEAHP method, we have achieved the following conclusions.
  • Generating true weight vector for perfectly consistent pairwise comparison matrices.
  • The method for ranking and selecting alternatives has a high resolution.
  • The weight vector obtained from this method is robust, In other words, it is not affected by possible errors, unusual and false observations (UFO) that appear because of inaccurate data entry random errors, in the pairwise comparison matrix.
  • In practice, the E-DEAHP method can be applied without the need to solve linear programming by using a simple relative relation.
Keywords: Multiple criteria decision making, Data envelopment analysis, Analytic hierarchy process, Shannon entropy, Pairwise comparison matrix, Robust estimation.
Full-Text [PDF 1074 kb]   (140 Downloads)    
Type of Study: S | Subject: Mat
Received: 2020/03/20 | Revised: 2022/11/16 | Accepted: 2020/10/11 | Published: 2022/05/21 | ePublished: 2022/05/21
Send email to the article author

Add your comments about this article
Your username or Email:


XML   Persian Abstract   Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Azad H, Foroughi A A. Determination of weight vector by using a pairwise comparison matrix based on DEA and Shannon entropy. Journal title 2022; 8 (2) :19-37
URL: http://mmr.khu.ac.ir/article-1-3070-en.html

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 8, Issue 2 (Vol. 8,No. 2, 2022) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
Persian site map - English site map - Created in 0.08 seconds with 33 queries by YEKTAWEB 4553