JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS J. Multi-Crit. Decis. Anal. (2014) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/mcda.1525
The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems WOJCIECH SAŁABUN* Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland ABSTRACT Multicriteria decision-making (MCDM) methods are concerned with the ranking of alternatives based on expert judgements made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for obtaining a final ranking. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind of MCDM method. The TOPSIS ranks the alternatives with respect to their geometric distance from the positive and negative ideal solutions. Unfortunately, two reference points are often insufficient, especially for nonlinear problems. As a consequence of this situation, the final result ranking is prone to errors, including the rank reversals phenomenon. This study proposes a new distance-based MCDM method: the characteristic objects method. In this approach, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, we have determined the domain and Fuzzy number set for all the considered criteria. The characteristic objects are obtained as the combination of the crisp values of all the Fuzzy numbers. The preference values of all the characteristic object are determined on the basis of the tournament method and the principle of indifference. Finally, the Fuzzy model is constructed and is used to calculate preference values of the alternatives, making it a multicriteria model that is free of rank reversal. The numerical example is used to illustrate the efficiency of the proposed method with respect to results from the TOPSIS method. The characteristic objects method results are more realistic than the TOPSIS results. Copyright © 2014 John Wiley & Sons, Ltd. KEY WORDS:
the characteristic objects method; TOPSIS; multicriteria making-decision method; decision-making; rank reversals free
1. INTRODUCTION The world around us is the extremely complex system, which is difficult to see in one-dimensional way in respect to what we see. The people always compare and rank objects with in order to various criteria of choice, but their decisions are not always successful and correct (Pedrycz et al. 2011). Therefore, the multicriteria decision-making (MCDM) methods were developed to cope with decision-making problems. The distance-based approach is one of the most popular manners to help the decision-maker make the correct decision. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind MCDM
*Correspondence to: Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland. E-mail:
[email protected]
Copyright © 2014 John Wiley & Sons, Ltd.
method. The TOPSIS was firstly proposed by Hwang and Yoon (1981). In no time, the TOPSIS method was applied in various scientific fields, and recently, the global interest in the TOPSIS method has exponentially grown (Behzadian et al., 2012). For instance, in supply chain management and logistics, the TOPSIS approach was used for supplier selection (Chen et al., 2006; Boran et al., 2009; Celik, 2010; Chen, 2011; Dalalah et al., 2011; Deng and Chan, 2011; Fazlollahtabar et al., 2011), the location problem (Chu, 2002; Yong, 2006; Ertuğrul, 2010; Kuo, 2011; Awasthi et al., 2011; Li et al., 2011) and the selecting service problems (Bottani and Rizzi, 2006; Kahraman et al., 2007; Lin and Tsai, 2009; Chamodrakas et al., 2011; Cheng et al., 2011). It was also used in energy management (Yan et al., 2011; Kaya and Kahraman, 2011; Boran et al., 2012), chemical engineering (Rao and Baral, 2011; Sun et al., 2011; Ramezani et al., 2011), health problem (Rahimi et al., 2007; Wang et al., 2010; La Scalia et al., 2011) and even for the new ground-air missile weapon system selection problem (Li et al., 2010). Received 24 December 2013 Accepted 14 April 2014
