Triangular intuitionistic fuzzy numbers (TIFNs) are effective and flexible to characterize the fuzziness and uncertainty in real-world problems. The theories of TIFNs have been used in multi-attribute decision making but are rarely applied in a two-sided matching decision. Therefore, it is important and necessary to investigate the two-sided matching problem with TIFNs. This paper develops a decision method for two-sided matching with triangular intuitionistic fuzzy numbers and applies it to smart environmental protection. First, a similarity measure between generalized triangular fuzzy numbers (TFNs) is presented. Then, a novel similarity measure between TIFNs is extended, where the maximum membership degrees and minimum non-membership degrees, areas, and perimeters are considered. With respect to the two-sided matching problem with TIFNs, the two-sided matching model with TIFNs is established. Using similarity measures between TIFNs, the similarity matrices of triangular intuitionistic fuzzy preference matrices are constructed by using the positive idea vectors. Then, the two-sided matching model with similarity measures is obtained. Using the arithmetic mean, normalization formulas and linear weighting, the two-sided matching model with similarity measures is transformed into a mono-objective model. The optimum matching scheme is obtained by solving the model. Thus, a similarity measure-based two-sided matching decision method for TIFNs is proposed. Finally, a matching example in smart environmental protection is provided to illustrate the advantages of the proposed method.INDEX TERMS Two-sided matching, smart environmental protection, triangular intuitionistic fuzzy number, similarity measure, model.

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