Dealing with the "Don't Know" Answer in Risk Assessment

Decision making often deals with incomplete and uncertain information. Uncertainty concerns the level of confidence associated with the value of a piece of information, while incompleteness derives from the unavailability of data. Fuzzy numbers capture the uncertainty of information, but they are not able to explicitly represent incompleteness. In this paper we discuss an extension of fuzzy numbers, called fuzzy numbers with indeterminateness, and show how they can be used to model decision process involving incomplete information. In particular, the paper focuses on the “Don’t Know” answer to questionnaires and develops an aggregation model that accounts for these type of answers. The main contribution lies in the formalization of the interrelationships between the risk of a decision and the incompleteness of the information on which it is made.

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