This paper presents the fuzzy induced heavy ordered weighted averaging (FIHOWA) operator. It is an aggregation operator that uses the main characteristics of three well known aggregation operators: the heavy OWA, the induced OWA and the fuzzy OWA operator. Therefore, this operator provides a parameterized family of aggregation operators that includes the OWA operator and the total operator as special cases. It uses order inducing variables in the reordering of its arguments and it deals with uncertain information represented in the form of fuzzy numbers. Some of the main properties of this operator are studied including a wide range of families of FIHOWA operators such as the fuzzy heavy weighted average and the fuzzy heavy average. An illustrative example in investment selection is also presented.