Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 186970, 15 pages

http://dx.doi.org/10.1155/2015/186970

## To Make Good Decision: A Group DSS for Multiple Criteria Alternative Rank and Selection

^{1}Graduate Institute of Information Management, National Taipei University of Technology, Taiwan^{2}Department of Management Information Systems, National Chengchi University, Taiwan

Received 26 September 2014; Accepted 7 January 2015

Academic Editor: Jianming Shi

Copyright © 2015 Chen-Shu Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Decision making is a recursive process and usually involves multiple decision criteria. However, such multiple criteria decision making may have a problem in which partial decision criteria may conflict with each other. An information technology, such as *the decision support system* (DSS) and group DSS (GDSS), emerges to assist decision maker for decision-making process. Both the DSS and GDSS should integrate with a symmetrical approach to assist decision maker to take all decision criteria into consideration simultaneously. This study proposes a GDSS architecture named hybrid decision-making support model (HDMSM) and integrated four decision approaches (Delphi, DEMATEL, ANP, and MDS) to help decision maker to rank and select appropriate alternatives. The HDMSM consists of five steps, namely, criteria identification, criteria correlation calculation, criteria evaluation, critical criteria selection, and alternative rank and comparison. Finally, to validate the proposed feasibility of the proposed model, this study also conducts a case study to find out the important indexes of corporate social responsibility (CSR) from multiple perspectives. As the case study demonstrates the proposed HDMSM enables a group of decision makers to implement the MCDM effectively and help them to analyze the relation and degree of mutual influence among different evaluation factors.

#### 1. Introduction

People are making decision all the time. Typically, decision making is a recursive process in which decision maker may repeatedly move back and forth among multiple decision steps, such as objective clarification, decision criteria identification, alternative rank, and selection. For decision maker, the primary concern is to pick up an appropriate choice from a group of candidate alternatives [1]. Such decision making process usually involves multiple decision criteria [2], so called as multiple criteria decision making (MCDM) [3]. Lots of researches are devoted to resolve sorts of MCDM problem. For example, Hung et al. provide a novel MCDM approach to solve the knowledge management (KM) adoption problem and rank the gaps of the KM aspects in control items to achieve the aspired level of performance. The findings demonstrate that the KM gaps within the service industry are higher than the gaps within the integrated circuit and banking industries [4]. Also, Hsu et al. combine DEMATEL on ANP with VIKOR to solve the recycled materials vendor selection problems of multiple dimensions and criteria that are interdependent, instead of the independent assumption of an analytic hierarchy process, for mimicking the real world [5]. Besides, Chiu et al. focus on assessing e-store strategies to reduce the gaps in the resulting customer satisfaction and combine several multicriteria decision methodologies to conduct three real cases [6]. As mentioned above, MCDM is a complicated problem but can reflect real world precisely and therefore we should pay more attention to resolve MCDM issue.

However, unfortunately, most people are much poorer at decision making than they think. For illustration, there is a misconception that the decision maker thought they do not have enough information to make good decision [7]. Contrarily, in most cases, they spend much time to collect relative (or even irrelevant) information and trap themselves in the huge amount of information. Decision making is a sophisticated art and decision makers indeed require some help.

An information technology, as known as decision support system (DSS), emerges to assist decision maker to accelerate the convergence of decision-making process. DSS is interactive computer-based information system which helps decision-makers utilize knowledge base and models to solve ill-structured problems [8]. For these decades, DSS has been widely applied among domains as follows. Koo et al. developed a DSS based on case-based reasoning approach for determining the optimal size of new expressway service areas [9]. Gottschlich and Hinz proposed a DSS design that enables investors to include the crowd’s recommendations in their investment decisions and use it to manage a portfolio [10]. Hu and Sheng also proposed a DSS for public logistics information service management and optimization for vehicle drivers and owners, logistics customers, and related logistics service providers and management institutes [11]. Then, to respond accordingly to the requirement of group decision making, DSS further evolves into group DSS (GDSS) to help group of decision makers with efficiency decision making [12–16]. A group decision support system (GDSS) is a hybrid system that uses an elaborate communications infrastructure and quantitative models to help a team of decision makers solve problems and make choices [17, 18]. However, the decision process is a classical multiple criteria problem that partial decision criteria may conflict with each other. Both the DSS and GDSS should integrate with a symmetrical approach to assist decision maker to take all decision criteria into consideration simultaneously.

In this research, we proposed a hybrid GDSS architecture, named HDMSM, integrated four decision approaches (Delphi, DEMATEL, ANP, and MDS) to help decision maker with alternative rank and selection issue. HDMSM consists of four steps. In Step 1, HDMSM adopts Delphi to collect the decision criteria from domain experts. After that, in Step 2, domain experts use DEMATEL approach to evaluate the relevant among the selected criteria (in Step 1) and then generate a correlation matrix of these decision criteria. Then, in Step 3, HDMSM adopts ANP to calculate the correlation and important weight for each decision criteria in Step 4. Finally, in Step 5, the MDS can rank all available alternatives according to these important weights and visualize the similarity (or difference) of all available alternatives.

The priorities of decision criteria imply the preference of domain expert and therefore, to make better decision, and decision maker can make their choice according to the alternative rank via HDMSM. Also, the visual abilities of HDMSM enable decision maker to compare all available alternative form perspective and then improve decision making quality. Finally, we provide a system demonstration section to illustrate that how HDMSM aggregated the opinion from a group of domain experts. How to appropriately integrate a variety of MCDM approaches is an important issue in decision science [19]. HDMSM provides a valuable recommendation for decision maker to optimize multiple criteria decision making.

The remainder of this paper is organized as follows. Section 2 briefly reviews four decision analysis methodologies adopted in this study. Section 3 presents the proposed hybrid decision-making support model (HDMSM) and details the operational process of HDMSM. To validate the feasibility of HDMSM, according to five steps of HDMSM, a case study in Section 4 illustrates how decision makers appropriately select multiple decision criteria for corporate social responsibility (CSR) implementation step by step. Finally, Section 5 concludes some interest finding and proposes possible future research opportunities.

#### 2. Literature Review

The HDMSM proposed in this study integrates four decision approaches, namely, Delphi, DEMATEL, ANP, and MDS, to help decision maker with criteria selection and alternative ranking when facing a decision problem. Four methodologies are briefly introduced below.

##### 2.1. Delphi Method

Delphi method relies mainly on a panel of experts’ experiences, intuition, and value judgment. The experts participate in multiple rounds of questionnaire interviews and are given ways to understand one another’s viewpoints on the same question. The experts are encouraged to revise their previous opinions, so that the experts as a group can finally reach a consensus on the goal of decision making [19]. To perform the Delphi method, the following procedures are included.

###### 2.1.1. Choose a Panel of Decision-Making Experts and Select the Criteria for Decision Making

Determine the goal of decision making and list relevant evaluation criteria for the decision making, choose experts in the related field to form an expert group, and invite the experts to answer in a Delphi expert questionnaire interview for multiple rounds. The experts must judge the importance and suitableness for each evaluation criteria and give each criterion a score between 0 and 100.

###### 2.1.2. Test the Expert Group Consensus

To enable expert group to gradually reach a general agreement of opinion, a consensus deviation index (CDI) for each evaluation criteria is calculated as a round of the Delphi expert questionnaire finished. A smaller CDI indicates a higher consensus among the experts. In general, a CDI threshold is set to 0.05. That is, when the last round of Delphi expert questionnaire is completed and the CDI for all of the evaluation criteria is smaller than 0.05, this indicates a consensus of experts has been reached [20]. Herein, the score of the th criterion rated by the th expert in the th round of Delphi questionnaire is defined as , and the CDI is calculated by the formula:where is the mean of the scores of the th criterion rated by all the experts in the th round of Delphi expert questionnaire, and is the standard deviation of the scores of the th evaluation criterion rated by all the experts in the th round of Delphi expert questionnaire.

###### 2.1.3. Normalize the CDI and Choose the Evaluation Criteria

The CDI calculated based on the last round of Delphi expert questionnaire has to be normalized to derive the relative weight of each of the evaluation criteria. A small weight indicates the criterion does not have sufficient influence on the decision problem. In other words, when the weight of a particular criterion is less than a threshold set by the decision maker, the criterion is deleted from the candidate decision criteria, wherein is calculated by the following formula:

The evaluation criteria involved in decision making problem can be identified via Delphi. Then, DEMATEL is adopted to analyze the direct/indirect effects among these evaluation criteria detailed below.

##### 2.2. Decision-Making Trial and Evaluation Laboratory

Decision making trial and evaluation laboratory (DEMATEL) was originated from the Geneva of the Battelle Memorial Institute in 1973. It effectively observes the level of mutual influence among different factors and understands the complicated cause-and-effect relationship in the decision problem [21]. The analytic processes are listed below.

###### 2.2.1. Define the Correlation among Evaluation Factors

List the factors that may affect the decision-making problem through literature review or brainstorming and interview with the domain experts to determine the correlation between any two factors.

###### 2.2.2. Establish Direct Relation Matrix

As the decision problem has evaluated factors, an direct relation matrix showing the scores of influencing degree is established, which is presented as* Z-matrix in formula (3)*. Element represents the degree by which the factor affects factor :

###### 2.2.3. Establish Direct/Indirect Relation Matrix

In order to understand whether two evaluation criteria relate to each other indirectly, formula (4) produces a direct/indirect relation matrix , where is the identity matrix:

###### 2.2.4. Calculate the Prominence Score

If is an element of matrix , where , the sum of the column and the row are denoted by and , respectively. Among them, represents the sum of the criterion influencing other criteria, represents the sum of the criterion being affected by other criteria, and represents the prominence degree of each criterion in the decision-making problem. A prominence score can reveal both the importance and mutual effects among these criteria. In other words, DEMATEL analyzes the direct and indirect effect of these evaluation criteria on decision problem. The analysis results can be further plotted as a network structure via ANP approach.

##### 2.3. Analytic Network Process

ANP is a decision-making analytical method that uses network and nonlinear structure to represent a decision problem. ANP is developed in response to the fact that many decision problems in the realistic environment could not be presented with the structured hierarchy. The main objective of ANP is to correct the traditional AHP, with which the problems of dependence and feedback might occur between the criteria or the layers [22].

ANP can decompose a decision problem into multiple types of dimensions, and each dimension can include multiple criteria. The dimensions and the criteria are correlated with one another to form a network structure of the evaluation framework, and arrows are used to indicate their mutual influence.

Through the pairwise comparison of among each two criteria, ANP is calculated to acquire the eigenvectors of criteria and to form a Supermatrix, as shown in

Through normalization of the Supermatrix and complex matrix multiplication, a limit supermatrix containing the weights of the evaluation criteria can be obtained. According to these weights, the decision maker can figure out the priority of evaluation criterion for decision problem solving.

##### 2.4. Multidimensional Scaling

Multidimensional scaling (MDS) is a data reduction method, which uses the distance or similarity between data points to locate the spatial coordinates and the relative positions of several given data in the low-dimensional space [23].

MDS computes the Euclidean distance between each two factors and shows all factors in perceptual map which has two dimensions. If the similarity between two factors is more stronger, the configuration of two factors would be more close in the map. As a result, through the illustration of perceptual map, the spatial relation among factors can be visualized more clearly. The classification results of factors can be achieved via spatial difference analysis that helps decision maker to easily grasp the concept of factors.

To obtain the perceptual map, the Euclidean distance () between each two factors should be computed first. Further, the Euclidean distance matrix of the factors is generated. The Euclidean distance equation is shown aswhere denotes the perceived value of factor and denotes the coordinate of factor .

For decision making, decision maker must locate important decision criteria and evaluate the fitness of all possible alternatives. To increase decision process, decision maker needs to compare these alternatives as soon as possible. Via MDS, the visualization of candidate alternative enables decision maker to quickly grasp the similarities and dissimilarities among the alternatives.

#### 3. Hybrid Decision-Making Support Model (HDMSM)

This study proposes a GDSS architecture named hybrid decision-making support model (HDMSM) as shown in Figure 1. According to the decision-making procedures, HDMSM consists of five steps, namely, criteria identification, criteria correlation calculation, criteria evaluation, critical criteria selection, and alternative rank and comparison, which are detailed below.