ارزیابی جایگزین اضطراری تحت تصمیم گیرندگان گروه : با استفاده از روش ترکیب DS / تحلیل سلسله مراتبی با TOPSIS توسعه یافته

How to select suitable emergency alternative is critical to emergency management and has attracted much attention for both researchers and practitioners. In the process of evaluating emergency alternative problems, there usually exists incomplete and uncertain information, and the decision makers can not easily express their judgments on the candiates with exact and crisp values. The Dempster–Shafer theory (DST) is well suited for dealing with such problems and can generate comprehensive assessments for different alternatives. In this paper, the DS/AHP method and extended TOPSIS method are incorporated to solve group multi-criteria decision making (GMCDM) problems with incomplete information. The proposed method involves three steps: (1) Identify the focal elements of each decision maker according to the group decision matrix. (2) Construct the group weighted normalized belief interval decision matrix using Dempster’s rule of combination. (3) Propose the Extended TOPSIS approach for group interval data to rank the emergency alternatives. In this method, the positive ideal solution vector is defined as the maximum plausibility of all emergency alternatives with respect to each criterion, and the negative ideal solution vector is defined as the minimum belief of all emergency alternatives with respect to each criterion. An emergency alternative evaluation selection problem is taken as an illustrative example to demonstrate the feasibility and practicability of the proposed methods for group decision making in emergency management.

In the process of emergency management, a major issue is to evaluate the emergency alternative, and it has attracted much research attention recently (Georgiadoua, Papazogloub, Kiranoudisc, & Markatos, 2007). Emergency alternative evaluation (EAE) in a fuzzy group setting is a very important strategic decision involving decisions balancing within a number of criteria and opinions from different decision maker. Moreover, these criteria usually conflict with each other and there may be no solution satisfying all criteria simultaneously. Different decision makers have different knowledge about emergency alternatives, and they may make different contributions to different emergency alternatives. Therefore, emergency alternative evaluation select problem (EAESP) belongs to a multi-criteria decision making (MCDM) problem which involve both quantitative and qualitative criteria with various kinds of uncertainties such as ignorance, fuzziness, interval data, and interval belief degrees. Many MCDM approaches have been proposed to help decision makers to solve problems in uncertain environment. Amongst these methods, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method, presented in Chen and Hwang (1992) and with reference to Hwang and Yoon (1981) has been widely used in many areas. Recently, Abo-Sinna and Amer (2005) extended TOPSIS approach to solve multi-objective nonlinear programming problems. Chen (2000) extended the concept of TOPSIS to develop a methodology for solving multi-person multi-criteria decision making problems in fuzzy environment. Ye (2010) extended the TOPSIS method with interval-valued intuitionistic fuzzy numbers to solve virtual enterprise partner selection. Jahanshahloo, Lotfi, and Izadikhah (2006) proposes an algorithmic method to extend TOPSIS for decision making problems with interval data. Saremi, Mousavi, and Sanayei (2009) used TOPSIS to select total quality management consultant in small- and medium-sized enterprises under fuzzy environment. The analytic hierarchy process (AHP) is another important MCDM approach, which was originally proposed by Saaty, 1977 and Saaty, 1980. The AHP has been widely used by both researchers and practitioners. Amiri (2010) used the AHP and fuzzy TOPSIS methods to select project for oil-fields development. Sloane, Liberatore, Nydick, Luo, and Chung (2003) used the AHP as a clinical engineering tool to facilitate an iterative and microeconomic health technology assessment. Liu and Shih (2005) integrated AHP and data mining for product recommendation based on customer lifetime value. Ngai (2003) used the AHP to select the web sites for online advertising. Yang and Kuo (2003) proposed a hierarchical AHP/DEA methodology for the facilities layout design problem. Theoretically, the methodology is valuable when the decision making framework has a unidirectional hierarchical relationship among decision levels. Another favorable technique for solving MCDM problems is the Dempster–Shafer theory of evidence (DST) (Dempster, 1968 and Shafer, 1976). Yang, Wang, Xu, and Chin (2006) proposed the evidential reasoning approach for MCDM under both probabilistic and fuzzy uncertainties. Yang and Xu (2002) presented the evidential reasoning algorithm for MCDM under uncertainty. Guo, Yang, Chin, and Wang (2007) introduced evidential reasoning based preference programming for MCDM under uncertainty. Chin, Wang, Poon, and Yang (2009) proposed failure mode and effects analysis using a group-based evidential reasoning approach. Wang, Yang, and Xu (2006) used the evidential reasoning approach to assess the environmental impact. The merit of ER approach is to handle MCDM problems having both quantitative and qualitative information with uncertainties and subjectivity. The DS/AHP method was proposed by Beynon, Curry, and Morgan (2000), which incorporates Dempster–Shafer theory with AHP, shows potential on dealing with MCDM problems with incomplete information. The DS/AHP method is useful in that it could be an initial study of all the alternatives available, the results of which could lower the number of alternatives that fit the limited number of opinions given so far, with only a few opinions stated (Hua, Gong, & Xu, 2008). Hinted by the DS/AHP method, Hua et al. (2008) introduced the DS–AHP method for the MCDM problem with incomplete decision matrix. The DS–AHP method is useful in that it could identify all possible focal elements from the incomplete decision matrix. The framework of DS–AHP makes it possible to deal with various decision matrixes, either complete or incomplete, crisp or fuzzy, certain or uncertain, using the belief structure, which allows decision makers to describe their evaluations on decision alternatives (DAs) in a flexible, natural and reliable manner. In addition, the DS–AHP method has advantages over AHP on the number of comparisons and consistency checks. In this paper, a method of incorporating DS/AHP with extended TOPSIS is proposed, and it has been applied to evaluate emergency alternative selection problem (EASP). The rest of the paper is organized as follows. The Dempster–Shafer theory and TOPSIS method are briefly introduced in Section 2. The method of incorporating DS/AHP with extended TOPSIS is described in Section 3. An emergency alternative evaluation selection problem is used as an example to illustrate the method of aggregating DS/AHP with extended TOPSIS in Section 4. A conclusion remark is presented in Section 5.

A new method to solve group multi-criteria decision making problems with incomplete information based on the Dempster–Shafer theory and extended TOPSIS method has been proposed in this paper. The proposed method involves three steps: (1) Identify the focal elements of different decision maker under each criterion according to the group decision matrix using linguistic terms. (2) Construct the group weighted normalized belief interval decision matrix using Dempster’s rule of combination. (3) Propose the extended TOPSIS approach for group interval data to rank the emergency alternatives. The characteristic of the proposed method is to consider the distance of a decision alternative from the positive ideal solution (the maximum plausibility of all emergency alternatives under each criterion), as well as the distance from the negative ideal solution (the minimum belief of all emergency alternatives under each criterion). This paper also has taken an illustrative example to demonstrate the feasibility and practicability of the proposed methods for group decision making in emergency alternative evaluation selection problem under incomplete information. Results show that the method for group decision making can effectively deal with the emergency alternative evaluation selection problem. Further considerations involve the comparison of the proposed method with other available approaches such as VIKOR (the compromise ranking method) and AHP. This method for group decision making can not only be applied into solving the emergency alternative evaluation selection problem, but also be utilized in other areas with incomplete information.