Representing uncertainty about fuzzy membership grade

A novel uncertainty representation framework is introduced based on the inter-linkage between the inherent fuzziness and the agent’s confusion in its representation. The measure of fuzziness and this confusion is considered to be directly related to the lack of distinction between membership and non-membership grades. We term the proposed structure as confidence fuzzy set (CFS). It is further generalized as generalized CFS, quasi CFS and interval-valued CFS to take into consideration the DM’s individualistic bias in the representation of the underlying fuzziness. The operations on CFSs are investigated. The usefulness of CFS in multi-criteria decision making is discussed, and a real application in supplier selection is included.