📄 中文摘要
自然语言规划中常涉及模糊谓词（例如，“合适的替代品”、“足够稳定”），这些谓词的满足度本质上是分级的。现有的范畴理论规划器虽然提供了组合结构和基于回拉（pullback）的硬约束验证能力，但它们将适用性视为明确的、非此即彼的，这导致在处理模糊概念时不得不进行阈值化。这种阈值化操作会抹平有意义的区分度，并且无法在多步规划中追踪质量的渐进退化。针对这一局限性，提出了一种模糊范畴理论规划方法。该方法将模糊逻辑与范畴理论的严格数学框架相结合，旨在实现对分级语义约束的自主目标满足。通过引入模糊集合和模糊关系，能够表示和处理谓词的渐进满足度，从而避免了硬性阈值带来的信息损失。
📄 English Summary
Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints
Natural language planning frequently encounters vague predicates (e.g., 'suitable substitute,' 'stable enough') whose satisfaction is inherently graded. While existing category-theoretic planners offer compositional structure and pullback-based hard-constraint verification, they treat applicability as crisp, necessitating thresholding. This thresholding operation collapses meaningful distinctions and fails to track quality degradation across multi-step plans. To address this limitation, a Fuzzy Category-theoretic planning approach is proposed. This method integrates fuzzy logic with the rigorous mathematical framework of category theory to achieve autonomous goal satisfaction under graded semantic constraints. By introducing fuzzy sets and fuzzy relations, the approach can represent and process the gradual degree of predicate satisfaction, thereby avoiding the information loss associated with sharp thresholds. During the planning process, this method quantifies and propagates the degree of fuzziness, allowing uncertainty and vagueness to be considered in every decision step. This capability enables the planning system to generate more robust and intuitively aligned action sequences when faced with complex, imprecise natural language instructions. Furthermore, by embedding fuzziness into the morphisms and objects of category theory, categorical structures can be constructed that reflect the fuzzy nature of system states and behaviors. This not only enhances the planner's ability to handle fuzzy information but also offers a new perspective for understanding and modeling uncertainty in complex intelligent systems. The proposed method is particularly well-suited for applications that require processing the inherent vagueness and subjectivity of human language, such as human-robot collaboration, intelligent decision support systems, and highly adaptive autonomous systems.