Precision and Efficiency Meet: Computing the Similarity of Interval Type-2 Trapezoidal Fuzzy Sets

The proliferation of interval type-2 fuzzy sets in domains characterized by substantial uncertainty, particularly natural language processing and intelligent decision-making systems, has highlighted the critical need for efficient and accurate similarity assessment methodologies. However, evaluating similarity between interval type-2 fuzzy sets presents considerable challenges, primarily due to the computational inefficiencies associated with traditional similarity measurement techniques. This paper addresses these challenges by proposing a computational approach aimed at enhancing the efficiency of similarity assessments between interval type-2 trapezoidal fuzzy sets. The core of proposed approach lies in leveraging the geometric properties of trapezoids to determine the closed polygon that results from the intersection of two non-normal type-1 trapezoidal fuzzy sets. The proposed method eliminates the need for complex sequential condition evaluations and intricate flowcharts traversal common in existing methods. A key contribution of this work is the novel handling of infeasible intersection points, ensuring computational efficiency without sacrificing precision. The implementation incorporates the Shoelace algorithm for polygon area computation, further enhancing computational efficiency. Numerical analysis demonstrates that the proposed approach provides a streamlined and computationally efficient solution for similarity assessment between interval type-2 trapezoidal fuzzy sets, optimizing both precision and algorithmic performance.