Properties of fuzzy complementary preference relation have been studied. Based on the transformation between fuzzy complementary preference relation and reciprocal fuzzy preference relation, this paper proposes definitions of additive consistency for fuzzy complementary preference relation, gives the concepts of restricted max-min transitivity, restricted max-max transitivity and weak monotonicity for fuzzy complementary preference relation. Using the comparative method of triangular fuzzy number, the inherent relationships between the consistent fuzzy complementary preference relation and their properties are studied. It is also given an aggregation method for fuzzy complementary preference relation based on OWA operation. At the same time, this paper also proposes an algorithm that can judge whether a fuzzy complementary preference relation has the property of satisfied transitivity. Finally, it is illustrated by a numerical example that this method is feasible and effective.
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