Trust-Number : Trust-Based Modeling to Handle Decision-Making Problems

Fuzzy sets play an effective role in dealing with the uncertainty and ambiguity of the 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 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. Besides, it introduces new operations on T-numbers to develop a decision model based on this theory. The performance of this model has been analyzed by its implementation in two case studies and by comparing the Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS) and its T-numbers extension (T-TOPSIS). According to the obtained results, it can be concluded that T-numbers can be applied to classical fuzzy numbers facing uncertain and distrust information available