Implication operators in fuzzy relational products for a local path-planning of AUVs

This paper describes the best choice of fuzzy implication operator and α-cut that are appropriate to the heuristic search technique for real-time collision avoidance of AUVs (autonomous underwater vehicles). A fuzzy implication operator is applied to the computation of a fuzzy triangle product that constructs a new fuzzy relation between two fuzzy relations. This is the theoretical basis of the heuristic search technique. In this paper, we design a heuristic search technique using fuzzy relational products for AUVs, and propose the selection of a fuzzy implication operator and α-cut which are the most suitable for the search technique. In order to verify the optimality and efficiency of the selected fuzzy implication operator and α-cut, we simulate every case of α-cut for each fuzzy implication operator in view of the cost of path and the number of α-cuts generating an acceptable path to the goal.