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<p>This paper investigates fuzzy <i>q</i>-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of <i>q</i>-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular <i>q</i>-symmetric differentiability, we derive necessary optimality conditions for fuzzy <i>q</i>-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of <i>q</i>-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.</p>

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Generalized transversality conditions for fuzzy quantum-symmetric variational problems via granular approach

  • 期刊论文

  • 发表日期：

    2025年6月15日

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  • Martin Bohner,
  • Ewa Girejko,
  • Agnieszka B. Malinowska,
  • Linh Nguyen,
  • Baruch Schneider,
  • Tri Truong

摘要

This paper investigates fuzzy q-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of q-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular q-symmetric differentiability, we derive necessary optimality conditions for fuzzy q-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of q-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.