| Title of paper:
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Degrees and regularity of intuitionistic fuzzy semihypergraphs
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| Author(s):
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 1, pages 111–126
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.1.111-126
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| Download:
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 PDF (375 Kb, File info)
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| Abstract:
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This research work takes a new paradigm on the hypergraph concept which is a combination of a hypergraph and a semigraph. A semihypergraph is a connected hypergraph in which each hyperedge must have at least three vertices and any two hyperedges have at least one vertex in common. In a semihypergraph, vertices are classified as end, middle or middle-end vertices. This distinction, combined with membership and non-membership values, enables a more granular examination of vertices and their degrees in Intuitionistic Fuzzy Semihypergraphs (IFSHGs).
This paper proposes four types of degrees: degree, end vertex degree, adjacent degree and consecutive adjacent degree on an IFSHG. Each degree reflects specific patterns within the intuitioistic fuzzy semihypergraphs. Additionally, three types of sizes are also defined: size, crisp size and pseudo size of IFSHGs. Concepts such as regular and totally regular IFSHGs with their properties are also defined.
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| Keywords:
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Intuitionistic fuzzy semihypergraphs (IFSHGs), Degree, End vertex degree, Adjacent degree, Consecutive adjacent degree, Size, Regular, Totally regular.
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| AMS Classification:
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05C65, 05C72.
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| References:
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