Integration of spline function methods and fuzzy logic for solving complex navigation problems

This paper explores the possibility of integrating fuzzy set theory with modified piecewise approximations into a unified framework for developing advanced navigation models. The optimal combination of fuzzy logic and spline functions makes it possible to account for uncertainty and inaccuracy in navigation measurements through the application of point interpolation principles. The theoretical basis of the study relies on the fuzzy approximation theorem, which states that any system can be synthesized using fuzzy logic. A practical example is provided, demonstrating the use of fuzzy sets in spline-based trajectory modeling to ensure timely avoidance of restricted navigation areas and to determine optimal trajectory parameters under routing uncertainty. An experiment was conducted to synthesize a complex spline trajectory of a vessel using linguistic variables within fuzzy logic theory. The feasibility of combining spline function methods and fuzzy set compositions was empirically confirmed through the approximation of a smooth trajectory, which increased the speed of soft computing by 15 %. The proposed hybrid approach can serve as a mathematical foundation for adaptive fuzzy models designed to predict the trajectories of mobile objects, contributing to the development of unmanned navigation concepts. A paradigm shift is anticipated — from traditional requirements for measurement accuracy based on probabilistic and statistical methods to the fuzzy domain of information granulation. The paper also examines the alternative applicability of fuzzy logic versus probability theory when using membership functions to address non-standard navigation problems. Furthermore, the study investigates the modeling of a watch officer’s decision-making process based on fuzzy logic principles, emphasizing the influence of the human factor on navigational safety in intelligent hybrid systems. Managing uncertainty in cognitive navigation tasks is viewed as a key aspect of preventing emergencies through the application of fuzzy logic algebra.

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