© 2021 Elsevier LtdDecision-making techniques are among important topics applied in operations research. Multi-Criteria Decision-Making (MCDM) is one of the very commonly used subjects of this issue. Technique for Order Preference by Similarity to Ideal Solutions (TOPSIS) is among the most utilized MCDM approaches in terms of both convenience and efficiency. To provide the reality and ease of application of these methods as much as possible Interval Type-2 Fuzzy Numbers (IT2FN)s, a special kind of type-2 fuzzy sets (T2FS)s, are frequently used together with MCDM methods. However, before the final stage of the solution to the problem, defuzzification techniques are applied for obtaining the optimum solution. Switching to crisp numbers before the last step of the procedure reduces the effectiveness of using the IT2FNs. The aim of this paper is to contribute to the literature with a new idea of fuzzy metric function whose result is again a fuzzy number. The result of this study will be a serious contribution to the literature with its metric function structure that is a fuzzy number. A metric function whose result will be a fuzzy set can also be made for different fuzzy structures. Also, a new partial order relation will be given for IT2FNs to define this fuzzy metric function. Moreover, this new fuzzy metric will be adapted to the TOPSIS method. Hence, it will be assured that the defuzzification operations are used only in the final sorting stage and the advantage of using fuzzy numbers will be able to continue in further steps. The advanced TOPSIS with a new fuzzy metric will be applied to a video chat program selection problem as an example.