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<p>Bipolar max-product fuzzy relation equations (BMPFREs) with product negation are important in decision-making because of the consideration of both positive and negative effects. In this paper, the solvability of BMPFREs with product negation whose independent terms may take the value zero is considered. Based on the matrix representation of BMPFREs with product negation, a bipolar constraint matrix is constructed. A new necessary and sufficiency condition is proposed by exploring the structural features of bipolar constraint matrix, and all solutions are derived to solve BMPFREs. As an application of the bipolar constraint matrix method, the solvability of a special kind of bipolar max-product fuzzy relation inequalities (BMPFRIs) with product negation is further discussed.</p>

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Solvability of bipolar max-product fuzzy relation equations and inequalities with product negation

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Hongpeng Li,
  • Haitao Li

摘要

Bipolar max-product fuzzy relation equations (BMPFREs) with product negation are important in decision-making because of the consideration of both positive and negative effects. In this paper, the solvability of BMPFREs with product negation whose independent terms may take the value zero is considered. Based on the matrix representation of BMPFREs with product negation, a bipolar constraint matrix is constructed. A new necessary and sufficiency condition is proposed by exploring the structural features of bipolar constraint matrix, and all solutions are derived to solve BMPFREs. As an application of the bipolar constraint matrix method, the solvability of a special kind of bipolar max-product fuzzy relation inequalities (BMPFRIs) with product negation is further discussed.