A study on vague-valued hesitant fuzzy graph with application

Abstract

The hesitant fuzzy graph (HFG) is one of the most powerful tools to find the strongest influential person in a network. Many problems of practical interest can be modeled and solved by using HFG algorithms. HFGs, belonging to the FG family, have good capabilities when faced with problems that cannot be expressed by FGs. The vague-valued hesitant fuzzy graph (VVHFG) is the generalization of the HFG. A VVHFG is a powerful and useful tool to find the influential person in various parts, such as meetings, conferences, and every group discussion. In this study, we introduce a new concept of the VVHFG. Our purpose is to develop a notion of the VVHFG and also to present some basic definitions, notations, remarks, and proofs related to VVHFGs. We propose a numerical method to find the most dominating person using our proposed work. Finally, an application of the VVHFG in decision-making has been introduced.

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

“…The algebraic modeling and analysis of generalized roughness in LA-Semigroups has gained significant attention in recent years. By exploring the properties, relationships, and composition of roughness sets within LA-Semigroups, researchers have deepened their understanding of this field's fundamental characteristics [6,7,26]. Additionally, the integration of data analysis and machine learning perspectives has opened up new avenues for research, enabling the development of predictive models, optimization techniques, and decision-making processes related to LA-Semigroup operations [27].…”