Using discrete fuzzy numbers in the aggregation of incomplete qualitative information

Abstract

In this article discrete fuzzy numbers are used to model complete and incomplete qualitative information and some methods to aggregate this kind of information are proposed. When the support of discrete fuzzy numbers is a closed interval of the chain Ln={0,1,…,n}, they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms. On the other hand, when the support is not an interval of Ln, the corresponding discrete fuzzy number can be interpreted as an incomplete linguistic expert valuation. In order to aggregate this kind of information, we propose two different methods. One of them deals with the construction of aggregation functions on the set of discrete fuzzy numbers from discrete aggregation functions defined on Ln. The other one presents several procedures for estimating the missing information based on the so-called discrete associations. Finally, the proposed aggregation methods are used in a multi-expert decision making problem and a concrete example is given.