Hesitant Fuzzy Multiple Criteria Decision Analysis Based on TOPSIS
HFE which allows the membership degree of an element to a set represented by several possible values is a powerful tool to describe and deal with uncertain data. This chapter develops the decision making approach based on TOPSIS and the maximizing deviati
- PDF / 364,288 Bytes
- 30 Pages / 439.37 x 666.142 pts Page_size
- 107 Downloads / 253 Views
Hesitant Fuzzy Multiple Criteria Decision Analysis Based on TOPSIS
Abstract HFE which allows the membership degree of an element to a set represented by several possible values is a powerful tool to describe and deal with uncertain data. This chapter develops the decision making approach based on TOPSIS and the maximizing deviation model for solving MCDM problems in which the evaluation information provided by the decision maker is expressed in HFEs and the information about criteria weights is incomplete. There are two key issues being addressed in this approach. The first one is to establish an optimization model based on the maximizing deviation method, which can be used to determine the weights of criteria. The second one is to calculate the revised closeness index of each alternative to the hesitant fuzzy PIS. The considered alternatives are ranked according to the revised closeness indices of alternatives and the most desirable one is selected. An important advantage of this proposed method is its ability to relieve the influence of subjectivity of the decision maker concerning the weights of criteria and at the same time to remain the original decision information sufficiently. Additionally, the extended results in the interval-valued hesitant fuzzy situations are also pointed out.
The TOPSIS method originally developed by Hwang and Yoon (1981) is a kind of simple and useful decision making method to handle the MCDM problems with crisp data. The basic idea of TOPSIS method is that the optimal alternative should have the shortest distance from the PIS and have the farthest distance from the NIS. The TOPSIS method has been successfully applied in various fields and a state-of the-art survey of TOPSIS applications can be found in the paper (Behzadian et al. 2012). Owing to the increasing complexity of decision making environment, the fuzzy sets and the generalizations of fuzzy sets are usually used by decision makers to express their imprecise and uncertain preference information (Chen and Chang 2015; Chen and Hong 2014). For this reason, lots of papers have recently been devoted to fuzzy extensions of the TOPSIS method in the literature, such as the fuzzy TOPSIS method (Chen 2000), interval-valued TOPSIS method (Chen and Tsao 2008), intuitionistic fuzzy TOPSIS method (Boran et al. 2009), hesitant fuzzy linguistic TOPSIS method (Beg and Rashid 2013), Pythagorean fuzzy TOPSIS method (Zhang and Xu 2014a), etc., have been developed. However, these © Springer International Publishing Switzerland 2017 X. Zhang and Z. Xu, Hesitant Fuzzy Methods for Multiple Criteria Decision Analysis, Studies in Fuzziness and Soft Computing 345, DOI 10.1007/978-3-319-42001-1_1
1
2
1 Hesitant Fuzzy Multiple Criteria Decision Analysis Based on TOPSIS
TOPSIS-based methods suffer from two limitations: (1) in many practical MCDM problems, the weights of criteria are usually completely unknown or partially known, while these methods under the hypothesis that the weights of criteria are completely known in advance fail to address the MC
Data Loading...
