Boosting Fuzzy System Performance: Efficient Algorithms for Discrete Fuzzy Numbers
By Arnau Mir, Alejandro Mus, Juan Vicente Riera
Published on November 24, 2025| Vol. 1, Issue No. 1
Content Source
This is a curated briefing. The original article was published on cs.LG updates on arXiv.org.
Summary
This research introduces new, efficient algorithms for precisely computing the pos function and its inverse for discrete fuzzy numbers. These fuzzy numbers, particularly those defined over a finite chain, are fundamental for representing linguistic information within fuzzy systems. By exploiting the combinatorial structure of total orders, the proposed approach achieves a computational complexity of O(n^2 m log n), where the linear dependency on the number of membership levels (m) is the dominant factor. This significant reduction in computational cost substantially enhances scalability and enables more efficient implementation of fundamental algebraic operations, such as aggregation and implication, within the framework of discrete fuzzy numbers.
Why It Matters
For AI professionals, this work represents a crucial advancement in the practical application of fuzzy logic, a vital paradigm for handling uncertainty and linguistic information in AI systems. The ability to compute operations on discrete fuzzy numbers with significantly reduced computational cost directly translates into more scalable and efficient fuzzy systems. This efficiency is critical for deploying fuzzy logic in real-world applications such as decision support systems, intelligent control, expert systems, and natural language processing, where processing linguistic variables quickly and accurately is paramount.
In an era where AI models are becoming increasingly complex and resource-intensive, foundational improvements in computational frameworks for specific AI components like fuzzy numbers are invaluable. Faster processing means that fuzzy systems can be applied to larger datasets, respond in real-time environments, or be deployed on resource-constrained edge devices more effectively. Ultimately, this research strengthens the utility and accessibility of fuzzy logic within the broader AI landscape, allowing professionals to build more robust, responsive, and resource-friendly intelligent systems that can effectively interpret and act upon imprecise human language. It ensures that fuzzy logic remains a powerful and practical tool in the AI developer's toolkit for tackling problems that require nuanced understanding beyond crisp, binary logic, thereby broadening its applicability in diverse AI challenges.