Traffic and Emergency Network Optimisation Using Domination in Picture Fuzzy Directed Graphs

J. Shivangi Mishra, A. Meenakshi, Antonios Kalampakas, Leo Mršić, Tofigh Allahviranloo and Sovan Samanta

Journal of Mathematics, 2026, vol. 2026, 1-16

Abstract: In this paper, the picture fuzzy digraphs PFDGs are analysed in depth concerning their domination number (DN) and connectedness, offering new insights into structural properties and decision-making approaches for handling uncertainty. Picture fuzzy sets (PFS) are a generalisation of traditional intuitionistic fuzzy sets, which provide a mathematical tool for dealing with complicated and real-life problems where solutions could show grades of yes, no, abstain or refusal. This enhanced representational capability renders PFDGs as an optimal choice whenever classical fuzzy models may fail to deliver reliable outcomes. This paper presents structural features such as domination and its related concepts, which are fundamental in determining the effectiveness and control in random networks. The effects of such traits on models employed for making decisions during circumstances of uncertainty are also explored in this paper. Also, in this study, graph product operations are introduced in PFDGs to obtain the optimal network based on the DN in PFDGs. This computational approach offers a solution by identifying effective and resilient network structures, which enhances the flexibility of PFDGs in modelling various systems such as communication networks, transportation and strategic planning.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6069384

DOI: 10.1155/jom/6069384

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