Application of Complex Neutrosophic Sets to Real-World Decision Making Problems

Abstract

This paper presents a comprehensive study on the application of Com
plex Neutrosophic Sets (CNS) to real-world decision-making problems characterized by
 uncertainty, imprecision, and conflicting information. CNS extends classical neutro
sophic sets by introducing complex-valued membership functions for truth, indetermi
nacy, and falsity, allowing for the modeling of information with both magnitude and
 phase components. We establish the mathematical structure of CNS, including set
theoretic operations, properties, and comparisons with existing fuzzy, intuitionistic, and
 neutrosophic frameworks. The novelty of the CNS model lies in its capacity to handle
 multidimensional ambiguity more effectively than real-valued models. To demonstrate
 the practicality and robustness of the proposed framework, we apply it to a multi-criteria
 decision-making (MCDM) problem under uncertain conditions. One example illustrates
 it: it describes how complex-valued membership grades provide better sensitivity in
 ranking alternatives and identifying optimal choices. Comparative analysis with other
 methods verifies the improved performance and interpretability of CNS in representing
 dynamic decision environments. The findings are validated for the applicability of the  model to areas like engineering design, medical diagnosis, and financial analysis. Over all, this piece of work contributes a novel mathematical tool to decision support systems
 by incorporating complex uncertainties in an organized and analytically valid way.

DOI: 10.5281/zenodo.16754463