فایل ورد کامل قالب TOPSIS برای تعیین وزن تصمیم گیرنده در مشکلات تصمیم گیری گروهی با اطلاعات نامشخص

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تعداد صفحات این فایل: ۲۴ صفحه

بخشی از مقاله انگلیسیعنوان انگلیسی:Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information~~en~~

Abstract

In traditional TOPSIS method, the ideal solutions for alternatives are expressed in vectors. An important step in the process of group decision making is to determine the relative importance of each decision maker. In this paper, the weights of decision makers derived from individual decision are determined by using an extended TOPSIS method with interval numbers. The ideal decisions for all individual decisions are expressed in matrices. The positive ideal decision is the intersection of all individual decisions; the negative ideal decision is the union of all individual decisions. Comparisons with other methods are also made. A numerical example is examined to show the potential applications of the proposed method.

۱ Introduction

Decision making is the process of finding the best option from all of the feasible alternatives. The increasing complexity of the socio-economic environment makes it less and less possible for a single decision maker (DM) to consider all relevant aspects of a problem (Kim & Ahn, 1999). As a result, many decision making processes, in the real world, take place in group settings.

To determine the weights of every DMs is a very important step in multiple attribute group decision making (MAGDM) (Yue, Jia, & Ye, 2009; Yue, 2011b, c). There are many applications, which necessitate different weights (Ramanathan & Ganesh, 1994) because a DM cannot be expected to have sufficient expertise to comment on all aspects of the problem but on a part of the problem for which he/she is competent (Weiss & Rao, 1987). In this paper, we suppose that the weights of DMs are different and unknown. How to measure the weights of DMs Up to now, many methods have been developed. French Jr (1956) proposed a method to determine the relative importance of the group’s members by using the influence relations, which may exist between the members. Theil (1963) proposed a method based on the correlation concepts when the member’s inefficacy is measurable. Keeney and Kirkwood (1975) and Keeney (1976) suggested the use of the interpersonal comparison to determine the scales constant values in an additive and weighted social choice function. Bodily (1979) and Mirkin and Fishburn (1979) proposed two approaches which use the eigenvectors method to determine the relative importance of the group’s members. Brock (1980) used a Nash bargaining based approach to estimate the weights of group members intrinsically. Ramanathan and Ganesh (1994) proposed a simple and intuitively appealing eigenvector based method to intrinsically determine the weights of group members using their own subjective opinions. Van den Honert (2001) used the REMBRANDT system (multiplicative AHP and associated SMART model) to quantify the decisional power vested in each member of a group, based on subjective assessments by other group members. Jabeur and Martel (2002) proposed a procedure which exploits the idea of Zeleny (1982) to determine the relative importance coefficient of each member. Jabeur, Martel, and Khelifa (2004) proposed a distance-based collective preorder integrating the relative importance of the group’s members. By using the deviation measures between additive linguistic preference relations, Xu (2008b) gave some straightforward formulas to determine the weights of DMs. Chen and Fan (2006, 2007) studied a method for the ranking of experts according to their levels in group decision. Recently, Yue (2011a) presented an approach for group decision making based on determining weights of DMs using TOPSIS (technique for order preference by similarity to an ideal solution) (Hwang & Yoon, 1981). And please refer to Yue (2011d,e,f) for some related research method.

The above methods have numerous advantages, however, most of the performance rating is quantified as crisp values. Under many circumstances, crisp data are inadequate to model real-life situations. Since human judgments including preferences are often uncertain, it is difficult to rate them as exact numerical values. In addition, in case of conflicting situations or attribute, a DM must also consider imprecise or uncertain data, which is very usual in this type of decision problems. A more realistic approach may be to use interval data instead of crisp values, that is, to suppose that the ratings of the attributes in the problem are assessed by means of interval data. In this paper, we will present a new TOPSIS method with interval data for MAGDM problems.

The remaining paper is organized as follows. In Section 2, the concepts of interval number are presented and discussed, including the operations of interval numbers. Based on the concepts in Section 2, the proposed approach for determining the weights of DMs using an extended TOPSIS is shown in Section 3. Section 4 compares the proposed method with other methods. Then, an illustrative example is used to demonstrate the feasibility and practicability of the proposed method in Section 5. Finally, Section 6 concludes this paper.

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