Group MCDM Based on the Fuzzy AHP Approach

Group MCDM Based on the Fuzzy AHP Approach

Quang Hung Do (Feng Chia University, Taiwan, ROC) and Jeng-Fung Chen (Feng Chia University, Taiwan, ROC)
Copyright: © 2014 |Pages: 7
DOI: 10.4018/978-1-4666-5202-6.ch100
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Introduction

Multiple criteria decision making (MCDM) is one of the most important fields of management science. It is related to several different goals or criteria that are to a certain extent in conflict with each other. The purpose of the decision making is to find the best or the most desirable alternatives. The complexity of the decision-making problem makes it impossible for a single decision maker to consider all aspects of a problem. As a consequence, many decision-making processes take place in a group setting.

Analytic hierarchy process (AHP) (Saaty, 1980) is a powerful management science tool that successfully solves many multiple criteria decision problems. The main steps in the application of AHP are:

  • 1.

    Structuring a decision problem in a hierarchy with different levels,

  • 2.

    Determining the local priorities at each level of the hierarchy, and

  • 3.

    Calculating the global priorities of the decision alternatives.

In the pure AHP, the relative importance of decision elements is evaluated from comparison judgments which are represented as crisp values. However, in many cases, the human preference is uncertain and decision makers usually feel more confident utilizing linguistic variables rather than expressing their judgments in the form of numeric values. In order to deal with more decision making problems in real situations, the fuzzy set theory (Zadeh, 1965) was incorporated into AHP. Being an extension of AHP, fuzzy AHP is able to solve the hierarchical fuzzy decision-making problems. Since its appearance, the fuzzy AHP method has been widely used by many researchers to solve different decision making problems in various areas, such as selection, evaluation, resource allocation, planning and development.

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Background

Group multiple criteria decision making is an overlapping field of group decision making and multiple criteria decision making. Decision making is the study of identifying and choosing alternatives based on the judgments of the decision makers. It has been proved that a decision made by a group tends to be more objective and effective than a decision made by an individual. Therefore, group decision making is an aggregate decision making process in which individuals’ decisions are grouped together to solve a particular problem. A major part of decision making involves the analysis of a set of alternatives described in terms of some evaluative criteria. In order to find the most suitable alternative or determine the relative priority of each alternative, it requires to rank these alternatives. Solving such problems is the focus of Multiple Criteria Decision Making (MCDM) in decision and information sciences. MCDM is supported by a set of techniques, some of the main techniques are the analytic hierarchy process (AHP), technique for order preference by similarity to ideal solution (TOPSIS), preference ranking organization method for enrichment evaluation (PROMETHEE), and elimination and choice translating reality (ELECTRE) (Triantaphyllou, 2000). Among these, the AHP approach has appeared to be a very popular method and has been widely applied to deal with various complex decision making problems (Vaidya & Kumar, 2004). In the AHP, each alternative is compared with every other alternative in terms of the relative importance of its contribution to the criterion under consideration. The pairwise comparisons are represented in the form of crisp values. The comparison is repeated for each criterion and the pairwise comparison matrix is then formed. The weight vector can be obtained from the pairwise comparison matrix. The pure AHP method tends to be less effective when dealing with the uncertainty in the decision making process. This led to the development of fuzzy AHP methods.

Key Terms in this Chapter

Weight: Assessment of relative importance or preference of the criteria or alternatives.

Alternatives: Objects or options to be assessed or evaluated in a decision making process.

Criteria/Attributes: Features of an alternative on which a decision or judgment can be based.

Linguistic Variable: A linguistic variable is a variable whose values are words or sentences in a natural or artificial language.

Defuzzification: The process of interpreting the membership degrees of the fuzzy sets into a specific decision or real value.

Consistency Ratio: The ratio between the consistency of a given evaluation matrix and the consistency of a random matrix.

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