Fuzzy averaging operators in the problem of aggregating fuzzy information

The problem of aggregating fuzzy information by constructing fuzzy averaging operators is considered. Weighted fuzzy averages of systems of fuzzy numbers are studied and a class of nonlinear fuzzy averages of systems of fuzzy numbers is introduced which is a modification to fuzzy numbers of the general class of dissipative numerical averages. The properties of the corresponding averaging operators which are “fuzzy” analogues of the characteristic properties of scalar aggregating functions, are established. This provides a justification for the use of the introduced fuzzy averaging operators in the problem of aggregation of fuzzy information. At the same time, the result of aggregation of fuzzy information given by a set of fuzzy numbers is understood as a fuzzy number that reflects the essential features of this set.