Reducing the Risk of Wrong Choice in Group Decision Making by Optimal Weight Allocating to Decision Makers

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1. Introduction

The increasing complexity of the engineering and management environment leads to benefit from a group of experts or decision makers (DMs) to investigate all relevant aspects of decision-making problems. In the recent decade, some studies focused on Multiple Attribute Decision Making (MADM) problems to provide reliable results and take into account the analysis of the experts instead of analysis of a single expert. This makes that the Multiple Attribute Group Decision Making (MAGDM) is attracting more and more attention in management, and has received a great deal of attention from researchers (Yue, 2012a). MADM models are selector models that are used for evaluating, ranking and selecting the most appropriate alternative from among several alternatives (Alinezhad & Amini, 2011). Zavadskas, Turskis, Ustinovichius, and Shevchenko (2010) believe that, MADM methods as a response to the observed inability of people. They effectively analyze multiple streams of dissimilar information. MADM mainly consists of the following two parts (Xu, 2012); 1. Collect decision information, and 2. Aggregate the decision information through some proper approaches and then rank and select the given alternatives. A MADM problem with m alternatives and n attributes can be expressed in matrix format as follows:

(1) W= (w₁, w₂, …, w_n)where, A₁, A₂, …, A_m are feasible alternatives, U₁, U₂, …, U_n are evaluation attributes, X_ij is the performance rating of alternative A_i under attribute U_j, and W_j is the weight of attribute U_j.

MAGDM is an important part of the MADM problems. MAGDM problems may be defined as decision situations where; 1. There are two or more experts (or DMs), who are characterized by their own ideas, attitudes, motivations and knowledge, 2. There is a problem to be solved, and 3. They try to achieve a common solution. More specifically, a MAGDM problem with t (t≥1) DMs, m alternatives and n attributes can be expressed in matrices format as follows:

(2) W= (w₁^k, w₂^k, …, w_n^k), k= 1, 2 …, twhere x_k and w_k (k=1, 2, …, t), respectively, are the decision matrix and weight vector of attributes, which are provided by k_th DM (Yue, 2013a). Moreover, in the process of MADM, the DMs are usually asked to provide their preference information on attributes, and the attribute values are not precisely known but value ranges can be obtained. Therefore, it is significative that we consider MAGDM problem with interval number.

First, we let:

(3) for all kεT.

Be decision matrix of the k_th (kεT) DM, in which each of the elements is characterized by interval number (Yue, 2011b).

On the other side, the most commonly acknowledged definition of expertise is that experts show high, outstanding, and exceptional performance that is domain-specific, stable over time, and related to experience and practice. Additionally, some author regards the possession of knowledge as an essential part of expertise (Herbig & Glockner, 2009). Therefore, in general terms an expert is a person who has experience, and also possesses special skill or knowledge related to a particular task. From this definition, we can see why non-experts turn to an expert, when, looking for the best solutions to problems (Gilmour & Corner, 1998).