A Perfectly Normal IT2 Fuzzy-Based TOPSIS Using αCuts Uncertainty Representation for MCDM Problems

This paper presents an enhanced multi-criteria decision-making (MCDM) approach that combines a Perfectly Normal Interval Type-2 (PNIT2) Fuzzy Logic with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), using α-cuts to handle uncertainty in decision-making. A perfectly normal IT2 fuzzy set enables precise uncertainty modeling by ensuring full membership in both upper and lower functions, enhancing α-cut comparisons.The α-cuts provide flexibility, giving decision-makers clearer insights into varying confidence levels. Compared to traditional TOPSIS or IT2F methods, the proposed PNIT2F-TOPSIS model with α-cuts addresses a wider range of uncertainties, leading to more reliable outcomes. The method is validated through a facility layout design case study, which evaluates key criteria such as lean service, workplace environment, and ergonomics, showing improved decision quality in uncertain environments and outperforming conventional TOPSIS models. It offers a robust, adaptable tool for managing uncertainty across different industries, avoiding the oversimplifications of heuristic methods. The proposed α-cuts PNIT2F-TOPSIS method offers a flexible solution to MCDM problems within an IT2F framework, heuristic methods rely on simplifying assumptions. While results may sometimes align, this approach better handles uncertainty. Future enhancements include refining α-cuts and using machine learning to dynamically update criteria weights.