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<p>The composition of topological relationship matrix is always demonstrated by using the compositions table, and there exists no mathematical rule to define these relationships. On the other hand, the common operator for matrix multiply is insufficient to extract these relationships. This paper presents a new operator for matrix multiply to create the composition of two topological relationship matrixes. This novel matrix operator is based on the common matrix multiply in which the rules of the multiplication are somehow changed based on the concept of topological relationship. Unlike traditional methods, this approach provides a formal mathematical framework that eliminates the dependency on predefined composition tables. This new operation is executed on all topological relationship matrixes and the results showed that the composition of two topological relationship matrixes is obtained by using the new matrix multiply operator. This operator can be effectively applied in spatial database management, GIS applications, and topological reasoning, enhancing computational efficiency and automation.</p>

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Defining a novel matrix multiplier for the composition of topological relationship

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Saeed Behzadi,
  • Alireza Vafaeinejad,
  • Alireza Sharifi

摘要

The composition of topological relationship matrix is always demonstrated by using the compositions table, and there exists no mathematical rule to define these relationships. On the other hand, the common operator for matrix multiply is insufficient to extract these relationships. This paper presents a new operator for matrix multiply to create the composition of two topological relationship matrixes. This novel matrix operator is based on the common matrix multiply in which the rules of the multiplication are somehow changed based on the concept of topological relationship. Unlike traditional methods, this approach provides a formal mathematical framework that eliminates the dependency on predefined composition tables. This new operation is executed on all topological relationship matrixes and the results showed that the composition of two topological relationship matrixes is obtained by using the new matrix multiply operator. This operator can be effectively applied in spatial database management, GIS applications, and topological reasoning, enhancing computational efficiency and automation.