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A Novel Approach to Decision-Making Under Uncertainty Using Spherical Linear Diophantine Fuzzy Relations

Author

Listed:
  • Muhammad Zohaib
  • Waqas Mahmood
  • Md. Ashraful Alam
  • Ghaliah Alhamzi
  • Muhammad Shoaib

Abstract

Fuzzy relations are more advanced than crisp binary relations, which are applicable in control systems in artificial intelligence. Our research study develops a fuzzy spherical linear Diophantine fuzzy SLDFu relation as a more advanced tool to handle uncertainty in decision-making. It has greater flexibility than fuzzy relations, traditional intuitionistic fuzzy IFu relations, and linear Diophantine fuzzy LDFu relations. We define union, intersection, inverse, complement, and composition in relation to SLDFu. We present reflexive, symmetric, and transitive relations in SLDFu relation. Likewise, we define the above operations with the help of numerical examples and establish that they form specific algebraic structures. In addition, we develop a score function to evaluate results and analyze the symmetry of decisions. We provide an application of the relation SLDFu in decision-making as medical dignosis.

Suggested Citation

  • Muhammad Zohaib & Waqas Mahmood & Md. Ashraful Alam & Ghaliah Alhamzi & Muhammad Shoaib, 2026. "A Novel Approach to Decision-Making Under Uncertainty Using Spherical Linear Diophantine Fuzzy Relations," Journal of Mathematics, Hindawi, vol. 2026, pages 1-22, May.
    • Handle: RePEc:hin:jjmath:5400802
    DOI: 10.1155/jom/5400802
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