تصمیم گیری گروه با روابط اولویت زبانشناختی و کاربرد آن در انتخاب تامین کننده

Linguistic preference relation is a useful tool for expressing preferences of decision makers in group decision making according to linguistic scales. But in the real decision problems, there usually exist interactive phenomena among the preference of decision makers, which makes it difficult to aggregate preference information by conventional additive aggregation operators. Thus, to approximate the human subjective preference evaluation process, it would be more suitable to apply non-additive measures tool without assuming additivity and independence. In this paper, based on λ-fuzzy measure, we consider dependence among subjective preference of decision makers to develop some new linguistic aggregation operators such as linguistic ordered geometric averaging operator and extended linguistic Choquet integral operator to aggregate the multiplicative linguistic preference relations and additive linguistic preference relations, respectively. Further, the procedure and algorithm of group decision making based on these new linguistic aggregation operators and linguistic preference relations are given. Finally, a supplier selection example is provided to illustrate the developed approaches.

Group decision-making problems generally involve the following two phases: (1) Aggregation phase: It combines individual preferences to obtain a collective preference value for each alternative; (2) Exploitation phase: It orders collective preference values to obtain the best alternative(s). But in some real-life situations, decision makers (DMs) may not possess a precise or sufficient level of knowledge of the problem, or is unable to discriminate explicitly the degree to which one alternative are better than others. In such cases, it is very suitable to express DM’s preference values with the use of linguistic variable rather than exact numerical values (Bordogna et al., 1997, Kacprzyk, 1986 and Zadeh, 1975). In other words, human beings are constantly making decisions under linguistic environment. For example, when evaluating the “comfort” or “design” of a car, linguistic terms like “good”, “fair”, “poor” are usually be used. Recently group decision making based on linguistic preference relations, which are usually used by decision makers (DMs) to express their linguistic preference information based on pairwise comparisons of alternatives with respect to a single criterion, has received a great deal of attention (Dickson, 1966, Figueira et al., 2005, Grabisch, 1995a, Grabisch, 1995b, Grabisch, 1996, Grabisch et al., 2003, Grabisch et al., 2000, Grabisch and Nicolas, 1994, Herrera and Herrera-Viedma, 2000 and Herrera and Herrera-Viedma, 2003). At present, many aggregation operators have been developed to aggregate linguistic preference information in aggregation phase, such as the linguistic ordered weighted averaging (LOWA) operators (Bordogna et al., 1997 and Herrera and Herrera-Viedma, 2000), linguistic weighted geometric averaging (LWGA) operator (Xu, 2004a), linguistic ordered weighted geometric averaging (LOWGA) operator (Wu, 2009, Xu, 2004a and Xu, 2004b), and linguistic hybrid geometric averaging (LHGA) operator (Xu, 2004a). Although there has been progress in group decision making with linguistic preference information, most of the work has assumed preferences of decision makers are independent. And these aggregation operators are linear operators based on additive measures, which is characterized by an independence axiom (Keeney and Raiffa, 1976 and Wakker, 1999), that is, the operator is based on the implicit assumption that preference of DMs are independent of one another; their effects are viewed as additive. This property is too strong to match group decision behaviors in the real world. DM’s subjective preference evaluation often shows non-linearity. There usually exists interaction among preference of DMs. The independence axiom generally can not be satisfied. Thus, it is more reasonable and appropriate to use a non-additive measure instead of traditional additive aggregation operators to approximate DM’s subjective preference evaluation processes for group decision making problems. In 1974, Sugeno (1974) introduced the concept of fuzzy measure (non-additive measure), which only make a monotonicity instead of additivity property. For decision making problems, it does not need assumption that criteria or preferences are independent of one another, which make it an effective tool for modeling interaction phenomena (Grabisch, 1996, Ishii and Sugeno, 1985 and Kojadinovic, 2002). As an extension of the additive aggregation operators, such as the weighted average and Ordered Weighted Averaging (OWA)(Yager, 1988) operator, the Choquet integral (Choquet, 1954) with respect to fuzzy measure can be used to mimic human being decision process, and deal with decision making problems (Figueira et al., 2005, Grabisch, 1995a, Grabisch et al., 2000 and Marichal, 2000). In this paper, based on λ-fuzzy measure ( Sugeno, 1974), we develop a practical method for group decision making with linguistic preference relations. In order to do this, the paper is organized as follows. In Section 2, we review fuzzy measure. Based on λ-fuzzy measure, some new aggregation operator are proposed. In Section 3, we introduce the multiplicative linguistic preference relations and additive linguistic preference relations according to corresponding linguistic scales. In order to aggregate these linguistic preferences information, we developed some new linguistic aggregation operators such as linguistic ordered geometric averaging based on fuzzy measure (F-LOGA) operator and extended linguistic Choquet integral (ELC) operator, respectively. Some properties of these linguistic aggregation operators are shown. Further, the procedure and algorithm of group decision making based on these new linguistic aggregation operators and linguistic preference relations are given. In Section 4, a supplier selection example is given to illustrate the concrete application of the method and to demonstrate its feasibility and practicality. Conclusions are made in Section 5.

Linguistic preference relation is a useful tool in expressing decision makers’ preferences over alternatives. In general, there are always interactive phenomena among preference of experts in the real decision problems. It is not suitable for us to aggregate preference information by conventional additive linear operators. In order to overcome the limitation, in this paper, we have defined some operational laws for the multiplicative linguistic scales and additive linguistic scales, respectively. Based on the λ-fuzzy measure, we developed some new linguistic aggregation operators such as linguistic ordered geometric averaging based on (F-LOGA) operator and extended linguistic Choquet integral operator to aggregate the given linguistic preference relations. Based on F-LOGA operator and multiplicative linguistic preference relations, we have proposed a practical group decision making method for supplier selection. The prominent characteristic of the developed approach is not only that all the aggregated preference information is also expressed by the linguistic scales, but also the interactive phenomena among preference of experts are considered in the aggregation process, which approximates to the truth of real decision making problems, and has no any loss of information in the process of aggregation.