Complex fuzzy sets have been successfully applied to many domains. In some applications, complex fuzzy operators play an vital role, especially those results depend on the particular choice of the conjunction, disjunction and complement operators. This paper introduces an equivalence relation on complex fuzzy sets, called parallelity. Then we provide a criterion that operators should satisfy the property of parallelity preserving, for the choices of complex fuzzy operators. Finally, several parallelity preserving inference methods are discussed for complex fuzzy reasoning.
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