Trust number: Trust-based modeling for handling decision-making problems

Fuzzy sets play an effective role in dealing with the uncertainty and ambiguity of input data in real-world decision-making problems. Nevertheless, the effectiveness of fuzzy sets becomes unreliable and even more uncertain when the input data come from untrustworthy sources. Therefore, a new measurement could be considered based on the data's degree of trust to reduce the deviation of unreliable information in fuzzy decision-making problems. The main aim of this study is to introduce a new information modeling called trust numbers (T-numbers), which models variations and deviations associated with triangular fuzzy numbers and their application to decision-making. In addition, it introduces new operations on T-numbers to develop a decision model based on this theory. The performance of this model was analyzed through its implementation in two case studies and by comparing the fuzzy technique for order of Preference by similarity to the ideal solution (F-TOPSIS) and its T-number extension(T-TOPSIS). Results indicate that T-numbers can be applied to classical fuzzy numbers when the available information is uncertain and a degree of distrust exists.