Comparison of fuzzy implication operators by means of fuzzy relational products used for intelligent local path-planning of AUVs

This paper describes the best choice to fuzzy implication operator and α-cut that are proper to the heuristic search technique for real-time collision avoidance of autonomous underwater vehicles (AUVs). A fuzzy implication operator is applied to the computation of fuzzy triangle product that constructs a new fuzzy relation between two fuzzy relations. An α-cut transforms a fuzzy relation into a crisp relation which is represented as a matrix. Those are the theoretical basis of heuristic search technique. In this paper, we review briefly our previous work—a heuristic search technique using fuzzy relational products for the collision avoidance system of 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 the 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 -cut generating acceptable path to the goal.

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