A sensitivity-based analysis of weighted fuzzy aggregation

Weighted aggregation of information in fuzzy set theory is considered The weighted aggregation plays an important role, especially in fuzzy decision making, where the decision criteria can have different degrees of importance. The weight factors, however, can not he used with most aggregation operators such as t-norms and t-conorms that are used in fuzzy set theory. This paper introduces a general framework based on sensitivity analysis for extending fuzzy set aggregation operators to their weighted counterparts. As an example, the framework is applied to the extension oft-norms to their weighted counterparts. It is shown that some of the methods that have Been suggested in literature for weighted aggregation with t-norms apply only in particular situations. Conditions are given under which the previously proposed methods are valid.