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<p>This paper centers around novel solutions of interval-valued linear systems within the context of CIA and SCIA operations, specifically encompassing upper solutions, lower solutions, proper solutions, and oscillatory solutions. To begin with, the conditions facilitating the existence of least upper solutions, greatest lower solutions, and proper solutions for two fundamental interval-valued algebraic equations are comprehensively examined under the MIA, CIA, and SCIA operations, respectively. Subsequently, the conditions guaranteeing the existence of (least) upper, (greatest) lower, and oscillatory solutions for interval-valued linear systems with a crisp coefficient matrix are thoroughly established in the sense of CIA and SCIA operations. Finally, several conditions ensuring the presence of upper, lower, or proper solutions for interval-valued linear systems with interval coefficient matrices are suitably formulated within the framework of CIA and SCIA operations. Ample examples are furnished to validate and elucidate the practicability of the methodology proposed herein.</p>

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New solutions of interval-valued linear systems based on the CIA and SCIA arithmetic operations

  • 期刊论文

  • 发表日期：

    2025年4月24日

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  • Yonghong Shen,
  • Dong Qiu,
  • Linxia Hu

摘要

This paper centers around novel solutions of interval-valued linear systems within the context of CIA and SCIA operations, specifically encompassing upper solutions, lower solutions, proper solutions, and oscillatory solutions. To begin with, the conditions facilitating the existence of least upper solutions, greatest lower solutions, and proper solutions for two fundamental interval-valued algebraic equations are comprehensively examined under the MIA, CIA, and SCIA operations, respectively. Subsequently, the conditions guaranteeing the existence of (least) upper, (greatest) lower, and oscillatory solutions for interval-valued linear systems with a crisp coefficient matrix are thoroughly established in the sense of CIA and SCIA operations. Finally, several conditions ensuring the presence of upper, lower, or proper solutions for interval-valued linear systems with interval coefficient matrices are suitably formulated within the framework of CIA and SCIA operations. Ample examples are furnished to validate and elucidate the practicability of the methodology proposed herein.