Scholarlink

<p>This paper investigates the use of fuzzy set theory in approximating solutions to differential equations under uncertainty. By defining lower and upper bounds, a robust framework is developed for modeling transitions between function extrema, extending classical methods to fuzzy initial value problems. The study demonstrates universal approximation properties and proposes numerical techniques that ensure stability and convergence. Applications highlight the practical utility of this approach in engineering and computational mathematics, solidifying fuzzy set theory as a powerful tool for addressing uncertainty in mathematical modeling.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Lower and Upper Approximations of Real-Valued Functions and Their Applications to Differential Equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月23日

查看全文
  • Zahra Alijani,
  • Martina Daňková

摘要

This paper investigates the use of fuzzy set theory in approximating solutions to differential equations under uncertainty. By defining lower and upper bounds, a robust framework is developed for modeling transitions between function extrema, extending classical methods to fuzzy initial value problems. The study demonstrates universal approximation properties and proposes numerical techniques that ensure stability and convergence. Applications highlight the practical utility of this approach in engineering and computational mathematics, solidifying fuzzy set theory as a powerful tool for addressing uncertainty in mathematical modeling.