<p>Tuberculosis (TB) remains a significant global health challenge, with patient susceptibility assessment complicated by inherent uncertainties and ambiguities. Traditional decision-making approaches often struggle to effectively manage these complexities. This study makes four key contributions to address these challenges. First, it introduces a novel fuzzy model, the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathscr {T}\)</EquationSource> </InlineEquation>-spherical <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathscr {Q}\)</EquationSource> </InlineEquation>-rung linear Diophantine fuzzy hypersoft set (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\c{t}\vphantom{Tg}\)</EquationSource> </InlineEquation>-Š<i>q</i>-RLDFHSS), designed to capture complex uncertainty in multi-attribute decision-making. Second, it develops two advanced aggregation operators, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\c{t}\vphantom{Tg}\)</EquationSource> </InlineEquation>-Š<i>q</i>-RLDFHSWA (weighted averaging) and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\c{t}\vphantom{Tg}\)</EquationSource> </InlineEquation>-Š<i>q</i>-RLDFHSWG (weighted geometric), rigorously validated for properties including idempotency, monotonicity, and boundedness, with adjustable parameters for flexible uncertainty management. Third, a comprehensive algorithm is proposed to implement the framework in multi-criteria decision-making (MCDM) scenarios. Fourth, the framework is applied to a practical medical diagnostic problem, assessing patient susceptibility to TB. Numerical simulations and comparative analyses confirm its robustness, adaptability, and superior performance, demonstrating its potential as a reliable decision-support tool for healthcare professionals in complex diagnostic contexts.</p>

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A decision-making framework for tuberculosis prognosis using \(\mathscr {T}\)-spherical \(\mathscr {Q}\)-rung linear Diophantine fuzzy hypersoft sets

  • Pairote Yiarayong

摘要

Tuberculosis (TB) remains a significant global health challenge, with patient susceptibility assessment complicated by inherent uncertainties and ambiguities. Traditional decision-making approaches often struggle to effectively manage these complexities. This study makes four key contributions to address these challenges. First, it introduces a novel fuzzy model, the \(\mathscr {T}\) -spherical \(\mathscr {Q}\) -rung linear Diophantine fuzzy hypersoft set ( \(\c{t}\vphantom{Tg}\) q-RLDFHSS), designed to capture complex uncertainty in multi-attribute decision-making. Second, it develops two advanced aggregation operators, \(\c{t}\vphantom{Tg}\) q-RLDFHSWA (weighted averaging) and \(\c{t}\vphantom{Tg}\) q-RLDFHSWG (weighted geometric), rigorously validated for properties including idempotency, monotonicity, and boundedness, with adjustable parameters for flexible uncertainty management. Third, a comprehensive algorithm is proposed to implement the framework in multi-criteria decision-making (MCDM) scenarios. Fourth, the framework is applied to a practical medical diagnostic problem, assessing patient susceptibility to TB. Numerical simulations and comparative analyses confirm its robustness, adaptability, and superior performance, demonstrating its potential as a reliable decision-support tool for healthcare professionals in complex diagnostic contexts.