Muirhead Mean Operators in Quadripartitioned Single-Valued  Neutrosophic Sets for Multi-Criteria Decision-Making with  Indeterminate Information

Anitha P; Chitra Devi P; Satham Hussain; Durga Nagarajan; Said Broumi; Sankar Sahoo; Hossein  Rashmanlou

Authors

Anitha P Department of Mathematics, H.K.R.H College, Uthamapalayam- 625 533, Tamil Nadu, India.
Chitra Devi P PG & Research Centre of Mathematics, Mannar Thirumalai Naicker College, Madurai,
Satham Hussain Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai-600 127, Tamil Nadu. India;
Durga Nagarajan Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai-600 127, Tamil Nadu. India;
Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco;
Sankar Sahoo Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore– 721 102, India;
Hossein Rashmanlou School of Physics, Damghan University, Damghan, Iran

Abstract

This paper addresses the critical challenge of managing uncertainty, indeterminacy, and interde
pendencies in multi-criteria decision-making (MCDM) by introducing novel aggregation operators. Existing
methods often fall short in effectively combining diverse and conflicting information, particularly in complex
and uncertain environments. To bridge this gap, we propose the integration of the Muirhead Mean (MM) op
erator a versatile tool that generalizes arithmetic and geometric means-into the framework of Quaripartitioned
Single-Valued Neutrosophic (QSVN) set theory, which accounts for truth, contradiction, ignorance, and falsity.
The mathematical properties of the proposed operators are thoroughly analyzed, demonstrating their robust
ness and flexibility. A new decision-making process is developed to tackle uncertainty and interdependencies,
supported by illustrative examples that highlight the practical significance of this approach. This work offers
a substantial advancement in the design of dependable and adaptable decision-making frameworks for complex
real-world scenarios.

DOI: 10.5281/zenodo.15399562