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Certain Operations on Complex Spherical Fuzzy Graphs with Application in Decision Making
Abrar Ahmad, M. Khalid Mahmood and Daud Ahmad
The complex spherical fuzzy set (CSFS) generalizes the spherical fuzzy set (SFS) by extending its degrees to the complex plane, confined within a unit disc across three dimensions. This extension serves as a powerful tool for handling uncertainty and fuzziness in complex decision-making scenarios. The complex spherical fuzzy graph (CSFG), based on a CSFS, plays a crucial role in networking and decision-making applications. This article introduces and investigates various operations on CSFGs, including maximal product, symmetric difference, residue product, and rejection. Through these operations, certain properties and results are obtained. Additionally, illustrative examples are provided to highlight the novelty of the findings. Furthermore, we demonstrate the practical application of the proposed approach by solving a real-world problem, with analysis that validates the theoretical outcomes. This study advances the research on fuzzy systems and their use in solving complex decision-making problems.
Keywords: Complex spherical fuzzy graph, maximal product, symmetric difference, rejection, residue product