Complex fuzzy aggregation operation (CFAO) is a formalized definition of combining several complex fuzzy sets into a single complex fuzzy set. It extends classical fuzzy aggregation operation (FAO) to the complex-valued domain retaining classical real-valued weight. CFAO was initially defined with complex weight by Ramot et al. However, there has been virtually no progress in developing CFAO with complex weight. In this paper, we study the CFAOs with complex weight. We first discuss how to define complex weights meeting the restriction that the sum of weights is equal to 1. We give a new natural type of complex weight which is different from Ramot et al.’s complex weight. Then we study various properties which include idempotency, homogeneity, rotational invariance and shift invariance for CFAOs with both types of complex weights.
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