A sensitivity analysis approach to introducing weight factors into decision functions in fuzzy multicriteria decision making

In fuzzy multicriteria decision making, the evaluations for criteria are aggregated using a suitable decision function. Many of the aggregation operators from fuzzy set theory that can be used as decision functions assume that the criteria have equal importance. This paper considers the extension of these functions when the criteria are not equally weighted. The criteria weights are interpreted as factors influencing the sensitivity of the decision function to the corresponding criteria. A set of conditions is specified which a weighted decision function should satisfy. This leads to a systematic way of introducing the weight factors into the decision functions. The proposed analysis is applied to a class of operators in which the parameter may be interpreted as the decision maker's characteristic optimism index. In this context, it is shown that the well-known method of multiplication of weight factors with membership values is suitable for optimistic decision makers, while Yager's power raising method is suitable for pessimistic decision makers only. A geometric interpretation of the decision making process is also given. (C) 1998 Elsevier Science B.V. All rights reserved.