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

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

Mohammad Azadfallah (Saipayadak, Tehran, Iran)
Copyright: © 2018 |Pages: 23
DOI: 10.4018/IJRCM.2018040101

Abstract

How to determine a weight for decision makers (DMs) is one of the key issues in Multiple Attribute Group Decision Making (MAGDM). While, some experts (or DMs) clearly wiser and more powerful in such matters than others, it has often seen that experts play their roles with same weights of importance. Meanwhile, it will lead to the wrong choice (or decision risk) and loss of values. Since, in the absence of any other standards about how to reduce this potential risk for bias, in this article, based on judgment matrices and error analysis, the author presents two new algorithm taken from crisp (the correlation-based approach) and interval (the ideal-based approach) TOPSIS method, respectively. Finally, two numerical examples are given to demonstrate the feasibility of the developed method.
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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, …, wn)where, A1, A2, …, Am are feasible alternatives, U1, U2, …, Un are evaluation attributes, Xij is the performance rating of alternative Ai under attribute Uj, and Wj is the weight of attribute Uj.

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= (w1k, w2k, …, wnk), k= 1, 2 …, twhere xk and wk (k=1, 2, …, t), respectively, are the decision matrix and weight vector of attributes, which are provided by kth 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 kth (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).

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