A novel family of fractional integral based Archimedean T-norm with application to circular intuitionistic fuzzy multi-criteria decision making problem

This paper introduces a novel family of t-norm and t-conorm based on the Riemann Liouville fractional integral. These t-norm and t-conorm offer a generalized algebraic foundation that enhances the capacity of analyzing uncertain data. Leveraging the proposed family of t-norm and t-conorm, a set of advanced aggregation operators is developed for circular intuitionistic fuzzy sets (CIFSs). The proposed operators for CIFSs include the Heronian mean operator, the weighted average operator and the geometric mean operator. Each operator is specifically designed to preserve the structural properties of CIFSs while accurately capturing the uncertainty represented by hesitancy radius, membership and non-membership components. The applicability of the proposed approach is demonstrated through Multi-Criteria Decision Making (MCDM) under circular intuitionistic fuzzy environment. Numerical examples are presented to illustrate its effectiveness. The example focuses on the selection of a dominant farming strategy for small-scale farmers, highlighting the practical relevance of CIFSs. Comparative analyses shows that the method is more adaptable, efficient and effective than existing approaches. In addition, a higher-dimensional MCDM example is included to demonstrate the applicability of the method to complex decision problems.