Enhancing Decision Making with Interval - Valued  Refined Neutrosophic Hesitant Fuzzy Sets

Iswariya S; Sahaya Sudha A

Authors

Iswariya S PG & Research Department of Mathematics, Nirmala College for Women, Coimbatore, India ;
Sahaya Sudha A PG & Research Department of Mathematics, Nirmala College for Women, Coimbatore, India;

Keywords:

Interval Valued Refined Neutrosophic Hesitant Fuzzy Set (IVRNHFS), Hesitant Fuzzy (HF), Neutrosophic Set, Score Function

Abstract

The Interval-Valued Refined Neutrosophic Hesitant Fuzzy Set (IVRNHFS) is a
sophisticated mathematical set that is capable of capturing and handling complicated uncertainty,
hesitancy, and vagueness in decision-making problems. In this paper, the formal definition of
IVRNHFS is proposed by combining the refined aspects of truth, indeterminacy, and falsity with
interval-valued hesitant information, thus providing a richer and more flexible representation of
imprecise data. To facilitate practical use, new score and accuracy functions are constructed to
facilitate useful comparison and ranking of alternatives. Moreover, fundamental operations like
union, intersection, complement, and aggregation are redefined in the IVRNHFS context to
maintain the natural interval-based refinement and hesitation. The proposed framework is
demonstrated with examples and compared with existing models to show its expressiveness,
computational depth, and decision correctness advantage.

DOI: 10.5281/zenodo.17096050