Route intelligent recommendation model and algorithm under the Pythagorean hesitant fuzzy linguistic environment

The development of tourism and society has made people's travel routes under complex and uncertain information an important issue. In this paper, we introduce a novel Pythagorean hesitant fuzzy linguistic term set (PHFLTS) to describe the information in more detail and unify the Pythagorean fuzzy linguistic term set (PFLTS) and hesitant fuzzy linguistic term set (HFLTS) to make the calculation more convenient. To help travelers consider time, distance, economic cost, and other factors, the Pythagorean hesitant fuzzy linguistic (PHFL) aggregation operators are proposed. Based on this, the PHFL route recommendation dynamic programming model is established to find the optimal route considering multiple factors, and the PHFL Dijkstra's algorithm is studied to find the shortest directed route. Different travelers value different factors when choosing a route, so the weights of each factor are uncertain. By combining the PHFL aggregation operator and the PHFL Dijkstra's algorithm, a route intelligent recommendation algorithm (RIRA) is proposed to help travelers choose the most suitable route according to their intentions. Finally, a numerical example is given to illustrate the effectiveness and practicality of the dynamic programming model and algorithm.