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Hesitant neutrosophic sets can accomodate more uncertainty compare to hesitant fuzzy sets and hesitant intuitionistic sets. On the other hand, triangular neutrosophic numbers are often used by the decision makers to evaluate their opinion in multi-attribute group decision making problems. Based on the combination of triangular neutrosophic numbers and hesitant neutrosophic sets, in this paper, we propose hesitant triangular neutrosophic numbers. Also, we discuss various types of operations between them including some properties. Then, we propose various types of hesitant triangular neutrosophic weighted aggregation operators to aggregate the hesitant triangular neutrosophic information. Furthermore, we introduce score of hesitant triangular neutrosophic numbers to ranking the hesitant triangular neutrosophic numbers. Based on the hesitant triangular neutrosophic weighted aggregation operators and score of hesitant triangular neutrosophic numbers, we develop a multi attribute decision making (MADM) approach, in which the evaluation values of alternatives on the attribute are represented in terms of hesitant triangular neutrosophic numbers and the alternatives are ranked according to the values of the score of hesitant triangular neutrosophic numbers to select the most desirable one. Finally, we give a practical example, including a comparision study with the other existing method, for enterprise resource planning system selection to verify the application and effectiveness of the proposed method.