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<p>The fuzzy hypergraph theory is a significant framework for effectively handling the uncertain information prevailing in the multi-dimensional relationships of the real world systems. Hypersoft set theory facilitates to solve the uncertain/ imprecise information of the real-world problems where the attributes are split into sub-attributes. A number of real-world graph modeling systems are entailed with uncertainty/vagueness in their multi-dimensional relationships along with multi-level attributes. To address this, in this article, we introduce fuzzy hypersoft hypergraph (FHSHG), which incorporates the hypersoft set theory with fuzzy hypergraphs. The notions of inverse fuzzy hypersoft hypergraph (IFHSHG) and strong hypersoft hypergraph (SHSHG) are also defined. Further, the concept of duality is also introduced for FHSHG, IFHSHG and SHSHG along with suitable illustrations and theorems. Subsequently, the line graph of FHSHG, IFHSHG and SHSHG are defined and their characterizations are studied further. In addition, the centrality measures of FHSHG, IFHSHG and SHSHG are also discussed. As an application, we utilize the centrality measures of both IFHSHG and its dual to identify the most influential crop and suitable combination of intercrops in intercropping agricultural system.</p>

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A systematic study of intercropping agricultural system using fuzzy and inverse fuzzy hypersoft hypergraph

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • R. Keerthana,
  • S. Venkatesh

摘要

The fuzzy hypergraph theory is a significant framework for effectively handling the uncertain information prevailing in the multi-dimensional relationships of the real world systems. Hypersoft set theory facilitates to solve the uncertain/ imprecise information of the real-world problems where the attributes are split into sub-attributes. A number of real-world graph modeling systems are entailed with uncertainty/vagueness in their multi-dimensional relationships along with multi-level attributes. To address this, in this article, we introduce fuzzy hypersoft hypergraph (FHSHG), which incorporates the hypersoft set theory with fuzzy hypergraphs. The notions of inverse fuzzy hypersoft hypergraph (IFHSHG) and strong hypersoft hypergraph (SHSHG) are also defined. Further, the concept of duality is also introduced for FHSHG, IFHSHG and SHSHG along with suitable illustrations and theorems. Subsequently, the line graph of FHSHG, IFHSHG and SHSHG are defined and their characterizations are studied further. In addition, the centrality measures of FHSHG, IFHSHG and SHSHG are also discussed. As an application, we utilize the centrality measures of both IFHSHG and its dual to identify the most influential crop and suitable combination of intercrops in intercropping agricultural system.