Spline synthesis of navigational data integrated with fuzzy set methods

The paper examines the possibility of two-dimensional spline approximation in terms of the potential of fuzzy set theory for synthesizing any field of navigational data. The assumption is analyzed that, in reality, intuitive decision-making by the officer of the watch is based not on classical binary logic, but on fuzzy associative rules. The adaptive fuzzy model optimally Imitates intellectual reasoning in assessing the cognitive states of a skipper as a human accident risk factor. The “incompatibility principle” is investigated in detail as a compromise between the accuracy of calculated values and the approximate nature of meaning in terms of fuzzy logic. The “accuracy paradox” is interpreted as achieving a balance between accuracy and complexity for the effective modeling of a navigational isosurface. A hypothesis is proposed that the axiomatics of intuitionistic sets is ideally suited for synthesizing navigational processes over time when their future performance assessment under conditions of ambiguity lacks sufficient probabilistic grounds. Within a set-theoretic approach, a variable representation of the reachable set is considered as a validated set of navigational parameters of the modeled mathematical object. Using the synthesis of a hypothetical navigational database as an example, a computational experiment based on fuzzy rules empirically demonstrated a 4% increase in computational speed through the use of “soft computing”. It was found that the experimental performance of the three-dimensional approximant is almost four times lower than the improved result obtained for the planar problem, while calculation speed increased by 15% according to the results of the author’s computational study. It is assumed that assessment of the effectiveness of three-dimensional modeling should take into account the mathematical complexity of constructing spatial isolines. A visualized representation of the geometric interpretation of the navigational isosurface on an onboard monitoring display is intended to support correct decision-making by the navigator in real time. Based on the study, it is predicted that effective management of uncertainty in the cognitive problems faced by the officer of the watch is a crucial factor in ensuring navigational safety, since seafarers rely heavily on navigational data that may sometimes be inaccurate and on measurements that may be incomplete.