Parallels and Meridians in the Intuitionistic Fuzzy Triangle: A Confidence-Aware Framework for Decision Making

The paper proposes a completely new geometric interpretation of intuitionistic fuzzy sets for confidence-aware decision making. Instead of directly using ordered pairs of membership and non-membership degrees, we reinterpret the intuitionistic fuzzy triangle as a structured coordinate framework that simultaneously represents the evaluation outcomes and the evaluators’ expertise in the following manner: experts’ confidence levels are modelled with line segments parallel to the hypotenuse, while evaluation scores are represented by line segments radiating from the origin of the coordinate system toward the hypotenuse. Their intersections form a finite lattice of points whose total number depends on the chosen confidence and assessment scales. The proposed construction preserves the semantic foundations of intuitionistic fuzziness: points closer to the origin reflect higher uncertainty in the evaluator’s confidence, while points onto the hypotenuse represent determinate judgments (with varying degrees of positivity or negativity) based on the complete evaluator’s confidence. The geometric distances between intersections provide a formal explanation of varying discriminative power: assessments from highly confident reviewers are more distinguishable than those from less confident ones. In addition, a colour-based visualization further supports the intuitive interpretation of confidence-weighted evaluations. The proposed framework offers an alternative yet fully consistent way to model expertise-dependent decision processes within the intuitionistic fuzzy setting, bridging geometric insight and practical evaluation scenarios via a structured system of parallels and meridians.