<p>This study proposes a hybrid decision-support methodology that integrates Fuzzy Cognitive Maps (FCMs) and Linear Programming (LP) to support the design of strategy maps within the Balanced Scorecard framework. FCMs are employed to formalize experts’ cognitive representations of strategic objectives and to infer causal intensities through similarity-based measures, thereby capturing perceived strategic interdependencies while limiting expert input to objective-level importance assessments. The resulting causal structure is then used as input to an LP model that selects a strategically coherent subset of objectives and relationships by minimizing map complexity subject to structural, perspective-based, and importance-related constraints. The proposed approach generates actionable strategic insights by identifying the objectives and causal paths that are most critical for conveying an organization’s strategic logic under different design preferences, while explicitly revealing trade-offs between map simplicity, strategic coverage, and emphasis. Strategy map quality is evaluated using quantitative indicators related to relationship density, objective inclusion, similarity across parameter configurations, and expert-based assessments of interpretability and strategic coherence. The methodology is illustrated through a case study in a metalworking company and benchmarked against a Fuzzy DEMATEL-based approach, demonstrating a substantial reduction in expert judgment requirements while producing strategy maps with comparable structural consistency. The results show that the proposed method supports a structured exploration of alternative strategic configurations and enhances transparency in strategy map design. The approach is subject to limitations related to expert judgment bias, parameter sensitivity, and the illustrative nature of the empirical application.</p>