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<p>Interval-valued complex q-rung orthopair fuzzy sets (IVCq-rungOFSs) have been recognized as an effective framework for modeling uncertainty and imprecise information. As a generalization of interval-valued complex intuitionistic fuzzy sets (IVCIFSs) and interval-valued complex Pythagorean fuzzy sets (IVCPFSs), the proposed model extends traditional fuzzy frameworks by introducing qth parameters. These parameters independently regulate the interval-valued truth and falsity membership degrees, offering greater flexibility for handling uncertain and imprecise expert evaluations. This enhanced structure allows a more accurate representation of complex information by incorporating both amplitude and phase components within the membership functions, thereby improving the modeling capability of the system in uncertain and dynamic environments. In the proposed approach, Dombi operator-based addition and multiplication are applied within the IVCq-rungOFS framework to enhance the precision and adaptability of aggregation, enabling better representation of the interactions between amplitude and phase interval-valued membership values. This study introduces the concept of an interval-valued complex q-rung orthopair fuzzy Dombi graph structure (IVCq-rungOFDGS), which integrates graph theory with the IVCq-rungOFS framework under the Dombi operator. The proposed approach introduces a dominating Zagreb index matrix to compute the first Zagreb index energy, second Zagreb index Laplacian energy, and hyper Zagreb index signless Laplacian energy. The proposed energy measures for both upper and lower bounds are analyzed through illustrative examples. The proposed method is applied to the climatic temperature data of the United Kingdom. The results are analyzed using the scoring function based on interval-valued complex q-rung orthopair fuzzy weight average (IVCq-rungOFWA) operator to determine the optimal network structure and identify the best alternative region. An algorithm is also presented to facilitate the practical implementation of the proposed approach in real-world applications.</p>

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On Zagreb index energy of dominating interval-valued complex Q-rung orthopair fuzzy dombi graph with application

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • S. N. Suber Bathusha,
  • Ganesh Ghorai

摘要

Interval-valued complex q-rung orthopair fuzzy sets (IVCq-rungOFSs) have been recognized as an effective framework for modeling uncertainty and imprecise information. As a generalization of interval-valued complex intuitionistic fuzzy sets (IVCIFSs) and interval-valued complex Pythagorean fuzzy sets (IVCPFSs), the proposed model extends traditional fuzzy frameworks by introducing qth parameters. These parameters independently regulate the interval-valued truth and falsity membership degrees, offering greater flexibility for handling uncertain and imprecise expert evaluations. This enhanced structure allows a more accurate representation of complex information by incorporating both amplitude and phase components within the membership functions, thereby improving the modeling capability of the system in uncertain and dynamic environments. In the proposed approach, Dombi operator-based addition and multiplication are applied within the IVCq-rungOFS framework to enhance the precision and adaptability of aggregation, enabling better representation of the interactions between amplitude and phase interval-valued membership values. This study introduces the concept of an interval-valued complex q-rung orthopair fuzzy Dombi graph structure (IVCq-rungOFDGS), which integrates graph theory with the IVCq-rungOFS framework under the Dombi operator. The proposed approach introduces a dominating Zagreb index matrix to compute the first Zagreb index energy, second Zagreb index Laplacian energy, and hyper Zagreb index signless Laplacian energy. The proposed energy measures for both upper and lower bounds are analyzed through illustrative examples. The proposed method is applied to the climatic temperature data of the United Kingdom. The results are analyzed using the scoring function based on interval-valued complex q-rung orthopair fuzzy weight average (IVCq-rungOFWA) operator to determine the optimal network structure and identify the best alternative region. An algorithm is also presented to facilitate the practical implementation of the proposed approach in real-world applications.