A generalized model for prioritized multicriteria decision making systems

Abstract

In this paper, we present a generalized model for handling prioritized multicriteria decision making systems. First, we present a new method for handling prioritized multicriteria decision making problems, where the weights of the lower priority criteria of each alternative depend on whether each alternative satisfies the requirements of all the higher priority criteria or not. Then, we also present a generalized prioritized multicriteria decision making method for handling multicriteria decision making problems, where some criteria may have equal priority which can be aggregated by the ordered weighted averaging (OWA) operator or the weighted averaging method. The proposed methods can overcome the drawbacks of the methods presented in [Yager, R. R. (2004a). Modeling prioritized multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 34(6), 2396–2404]. The proposed methods can handle multicriteria decision making problems in a more intelligent and more flexible manner.

Introduction

In recent years, some methods have been presented for handling multicriteria decision making problems (Bellman and Zadeh, 1970, Beynon et al., 2001, Bordogna and Pasi, 1995, Chen, 1988, Chen and Chen, 2005, Fu, 2008, Filev and Yager, 1995, Filev and Yager, 1999a, Filev and Yager, 1999b, Fullér and Majlender, 2003, Kulak, 2005, Kwon et al., 2007, Kwon and Kim, 2004, Lin et al., 2007, Liu, 2006, Tacker and Silvia, 1991, Torra, 1997, Wang and Chen, 2007, Yager, 1988, Yager, 1991, Yager, 1992, Yager, 1996, Yager, 1998, Yager, 2004a, Yager, 2004b). Some methods have been presented for handling prioritized multicriteria decision making problems (Chen and Chen, 2005, Wang and Chen, 2007, Yager, 1991, Yager, 1992, Yager, 1998, Yager, 2004b). Yager (1991) presented a prioritized intersection operator, called the non-monotonic intersection operator, for default and other common-sense reasoning systems. Yager (1992) used the non-monotonic intersection operator to deal with multicriteria decision making problems and presented a type of criterion, called the second order criterion. A statement shown in (Yager, 1992), such as “I want a good job, near my house if possible”, involves the first criterion (i.e., a good job) and the second criterion (i.e., near my house if possible). A second order criterion acts as an additional selector on these alternatives which satisfy the first order criteria. If none of the elements which satisfy the first order criteria also satisfy the second order criteria, then we do not need to consider the requirements of the second order criteria. Bordogna and Pasi (1995) regarded the process of information retrieval as a multicriteria decision making activity. They used the prioritized intersection operator to deal with fuzzy information retrieval problems. Yager (1998) used the weighted conjunction of fuzzy sets and fuzzy modeling to develop the operators in fuzzy information fusion structures. Chen and Chen (2005) extended the non-monotonic intersection operator (Yager, 1991) to present a prioritized information fusion method for handling prioritized multicriteria fuzzy decision making problems based on the similarity measure of generalized fuzzy numbers. Yager (2004a) presented some methods for handling prioritized multicriteria decision making problems, based on the Bellman–Zadeh paradigm for multicriteria decision making and the ordered weighted averaging operator (OWA). In prioritized multicriteria decision making problems, some criteria may be necessary to be satisfied. An example shown in Yager (2004a) is the case of air travel, where the passengers’ safety is necessary to be satisfied. In this case, the passengers’ safety has a higher priority than saving gasoline. Tradeoffs between saving gasoline and jeopardizing the passengers’ safety are unacceptable. Yager (2004a) found that the weights associated with the lower priority criteria are related to the degree of satisfaction of the alternatives with respect to the higher priority criteria.

In this paper, we present a generalized model for prioritized multicriteria decision making systems. First, we present a new method for prioritized multicriteria decision making, where the weights of the lower priority criteria of each alternative depend on whether each alternative satisfies the requirements of all the higher priority criteria or not. If the requirements of all the higher priority criteria can not be satisfied by the alternative, then the weights of the lower priority criteria are all zero. That is, the degrees of satisfaction with respect to the lower priority criteria do not affect the overall degree of satisfaction. Then, we present a generalized prioritized multicriteria decision making method for handling multicriteria decision making problems in which some criteria may have equal priority and the criteria with equal priority are aggregated by using the ordered weighted averaging (OWA) operator or the weighted averaging method. The proposed methods can overcome the drawbacks of the methods presented in (Yager, 2004a). They can handle multicriteria decision making problems in a more intelligent and more flexible manner.

The rest of this paper is organized as follows. In Section 2, we briefly review some multicriteria decision making methods (Bellman and Zadeh, 1970, Yager, 1988, Yager, 1996, Yager, 2004a, Yager, 2004b) and point out the drawbacks of the methods presented in (Yager, 2004a). In Section 3, we present a new method for handling prioritized multicriteria decision making problems. We also show that the proposed method can overcome the drawbacks of the methods presented in Yager (2004a). In Section 4, we present a generalized prioritized multicriteria decision making method. We also show that it can overcome the drawbacks of the methods presented in Yager (2004a). In Section 5, an example is used to illustrate how the proposed generalized prioritized multicriteria decision making method can handle multicriteria decision making problems with respect to different decision maker’s requests. We also make a comparison of the experimental results of the proposed generalized prioritized multicriteria decision making method with Yager’s methods (2004a). The conclusions are discussed in Section 6.