Evaluating the Impact of Aggregation Operators on Fuzzy Signatures for Robot Path Planning

This study investigates the impact of different aggregation operators (commonly referred to as fuzzy operators) on the application of fuzzy signatures. Fuzzy signatures are specialized multidimensional data structures that symbolically represent data. As a use case, the study focuses on robot environment representation and path planning, presenting the results obtained by applying various aggregation operators including minimum, maximum, algebraic product and arithmetic mean on the normalized values obtained from the robot sensors. The comparison highlights their effects on the computational load and path lengths of the path planning task. The findings reveal that the most efficient aggregation operator, in terms of computational load and the path length, is the algebraic product aggregation operator. Specifically, the algebraic product consistently yielded the shortest paths (as low as 22 nodes) and the lowest execution times (down to 0.0913 s), demonstrating superior efficiency compared to the maximum operator, which resulted in path lengths up to 34 nodes and execution times reaching 0.1923 s. This represents an improvement of up to 35.3% reduction in path length and 52.5% reduction in execution time when comparing the algebraic product to the maximum operator based on observed extreme values. Furthermore, this work provides the first empirical comparison of fuzzy aggregation operators specifically for fuzzy signature-based mobile robot path planning.