Acquisition of Fuzzy Measures in Multicriteria Decision Making Using Similarity-based Reasoning

Abstract

Continuous development has been occurring in the area of decision support systems. Modern systems focus on applying decision models that can provide intelligent support to the decision maker. These systems focus on modelling the human reasoning process in situations requiring decision. This task may be achieved by using an appropriate decision model. Multicriteria decision making (MCDM) is a common decision making approach. This research investigates and seeks a way to resolve various issues associated with the application of this model. MCDM is a formal and systematic decision making approach that evaluates a given set of alternatives against a given set of criteria. The global evaluation of alternatives is determined through the process of aggregation. It is well established that the aggregation process should consider the importance of criteria while determining the overall worth of an alternative. The importance of individual criteria and of sub-sets of the criteria affects the global evaluation. The aggregation also needs to consider the importance of the sub-set of criteria. Most decision problems involve dependent criteria and the interaction between the criteria needs to be modelled. Traditional aggregation approaches, such as weighted average, do not model the interaction between the criteria. Non-additive measures such as fuzzy measures model the interaction between the criteria. However, determination of non-additive measures in a practical application is problematic. Various approaches have been proposed to resolve the difficulty in acquisition of fuzzy measures. These approaches mainly propose use of past precedents. This research extends this notion and proposes an approach based on similarity-based reasoning. Solutions to the past problems can be used to solve the new decision problems. This is the central idea behind the proposed methodology. The methodology itself applies the theory of reasoning by analogy for solving MCDM problems. This methodology uses a repository of cases of past decision problems. This case base is used to determine the fuzzy measures for the new decision problem. This work also analyses various similarity measures. The illustration of the proposed methodology in a case-based decision support system shows that interactive models are suitable tools for determining fuzzy measures in a given decision problem. This research makes an important contribution by proposing a similarity-based approach for acquisition of fuzzy measures.