A compromise decision-support technique with an augmented scoring function within circular intuitionistic fuzzy settings

The VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method provides a valuable means of evaluating options based on assessment criteria, intending to generate the finest compromise options through multiple-criteria optimization. However, decision-making often involves uncertainty, where decision-makers may lack complete information or struggle to predict outcomes accurately. Circular intuitionistic fuzzy (C-IF) sets offer a versatile way to represent uncertainty and indecision, adding circularity to intuitionistic fuzzy sets' membership and non-membership. C-IF sets bring sophistication by incorporating circular functions to address complicated ambiguity, alongside assigning membership and non-membership components. This research aims to create a C-IF VIKOR decision-support method to handle multiple-criteria compromise solutions with C-IF uncertainties. The study focuses on enhancing the augmented scoring function and Chebyshev distance metric in C-IF surroundings. The augmented scoring function exhibits unique characteristics, including a direct relationship between membership and function value, an inverse correlation with nonmembership, and reflection of information reliability. The enhanced C-IF Chebyshev distance measure combines radial and membership/nonmembership distances, considering their special features. The proposed C-IF VIKOR technique utilizes these concepts to identify superior and inferior options and determine the finest compromise solution using an identification mechanism and VIKOR indices. The method is demonstrated in the context of healthcare waste disposal and will undergo sensitivity analyses and comparative studies to showcase its advantages, adaptability, and robustness.