Intuitionistic fuzzy rule-base model for the time dependent traveling salesman problem

The Traveling Salesman Problem is a well-known combinatorial optimization problem. There are many different extensions and modifications of the original problem, such as The Time Dependent Traveling Salesman Problem, this specific extension of the original Traveling Salesman Problem towards more realistic traffic conditions assessment. In the Time Dependent Traveling Salesman Problem the “distances” (costs) between nodes vary in time, they are considered longer during the rush hour period or in the traffic jam region, e.g. the city centre. In this article we introduce an even more realistic approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem. It is an extension of the Time Dependent Traveling Salesman Problem with the additional notion of intuitionistic fuzzy sets (which is a generalization of the original fuzzy sets). Our goal is to give a useful extended, alternative model instead of the original abstract problem. By demonstrating that the addition of intuitionistic fuzzy elements to quantify the intangible jam factors creates an inference system that approximates the tour cost in a more practical way. Hence, we are one step closer to offering a more realistic solution for the generalized Traveling Salesman Problem. The results of two simple toy examples showed the general effectiveness of the model.