This research evaluates how students’ perceptions of artificial intelligence (AI)-based learning tools affect calculus education by examining the middle factors between cognitive and emotional student responses. Research built upon cognitive load theory and social cognitive theory evaluates how students perceive AI adaptability, feedback accuracy, trust, and pedagogical value because these perceptions alter their learning processes as well as their academic outcomes. University professors from nine Rajamangala Universities of Technology in Thailand provided data through structured questionnaires to the research study. The researchers used partial least squares structural equation modeling (PLS-SEM) to evaluate their proposed theoretical connections. Results show that student perceptions regarding AI-based learning directly affect cognitive-emotional responses, and these responses powerfully determine academic achievements. The predictive model detects 75.7% of learning outcome variance in student performance (R² = 0.757), which demonstrates robust model specification and documentation. Research revealed that emotional and cognitive outcomes serve to bridge AI-based learning perceptions and educational outcomes, thereby demonstrating their importance in the learning achievement process. The research emphasizes the need to build AI learning platforms that enhance students’ engagement alongside their resilience and confidence because these elements drive academic achievement in calculus and STEM subjects.

We propose a reformulated notion of Levitin–Polyak (abbreviated as LP) well posedness for fuzzy optimization problems formulated in the fuzzy order-preserving (FOP) setting, where minimizing sequences are governed by a total ordering defined on fuzzy intervals. Under this formulation, we present verifiable sufficient conditions that guarantee LP well-posed behavior. These conditions are derived using ranking mechanisms that maintain interval order relations and ensure solution comparability. One central contribution is an equivalence-based theoretical characterization of LP well posedness obtained through an examination of the topological properties of the approximate solution mapping, particularly its closed-graph structure and upper semicontinuity. In addition, convergence of approximating solution sequences is investigated under the upper Hausdorff metric, leading to stability results for the associated solution sets. The established criteria provide a comprehensive framework for analyzing the convergence performance of algorithms designed for fuzzy optimization environments.