Novel Cosine Similarity Measures for Interval-Valued Fermatean  Neutrosophic Sets with TOPSIS-Based MCDM Applications

Saranya M; Jayanthi D

Authors

Saranya M Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, 641 043, India;
Jayanthi D Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, 641 043, India;

Keywords:

Interval-valued Fermatean neutrosophic sets, cosine similarity measures, TOPSIS method, multi criteria decision making.

Abstract

In the evolving realm of decision science, accurately measuring similarity under uncertainty is
paramount. This paper proposes three novel CSMs between IVFNS based on vector-based analysis, distance
functions, and cosine functions. Mathematical properties such as boundedness, symmetry, and identity are
proven for each proposed measure, ensuring their theoretical soundness. To improve flexibility in MCDM, we
also propose weighted extensions of these measures. The IVFNS improves traditional Fermatean neutrosophic
sets by introducing interval-valued truth, falsity, and indeterminacy. These enhancements enable more effec
tive modeling of partial ignorance and uncertainty, especially when data is vague or imprecise. Furthermore,
the study integrates the proposed CSMs into a TOPSIS-based MCDM framework under the IVFNS environ
ment. The effectiveness, accuracy, and consistency of the approach are demonstrated through three real-world
applications: pattern recognition, medical diagnosis, and international financial investment in five innovative
start-ups. A comprehensive numerical example, complemented by comparative analysis, illustrates that the
proposed approach outperforms existing methods in uncertain decision environments

DOI: 10.5281/zenodo.16903432