Issue:Degrees and regularity of intuitionistic fuzzy semihypergraphs

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Title of paper: Degrees and regularity of intuitionistic fuzzy semihypergraphs Author(s): K. K. Myithili     0000-0001-6756-0131 Department of Mathematics (CA), Vellalar College for Women, Erode-638012, Tamilnadu, India mathsmyth@gmail.com P. Nithyadevi     0000-0002-9060-4945 Department of Mathematics (CA), Vellalar College for Women, Erode-638012, Tamilnadu, India nithyadevi@vcw.ac.in Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 1, pages 111–126 DOI: https://doi.org/10.7546/nifs.2025.31.1.111-126 Download:  PDF (375  Kb, File info) Abstract: 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. Keywords: Intuitionistic fuzzy semihypergraphs (IFSHGs), Degree, End vertex degree, Adjacent degree, Consecutive adjacent degree, Size, Regular, Totally regular. AMS Classification: 05C65, 05C72. References: Archana, S., & Kuttipulackal, P. (2024). Analysis of various degrees and sizes in a fuzzy semigraph. IAENG International Journal of Applied Mathematics, 54(5), 975–983. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Berlin. Berge, C. (1976). Graphs and Hypergraphs. North-Holland, New York. Jagadeesan, S., Myithili, K. K., Thilagavathi, S., & Gayathri, L. (2024). A new paradigm on semihypergraph. Journal of Computational Analysis and Applications, 33(2), 514–522. Mordeson, J. N., & Nair, P. S. (2000). Fuzzy Graphs and Fuzzy Hypergraphs. Physica-Verlag, New York. Myithili, K. K., & Keerthika, R. (2023). Regularity and duality of intuitionistic fuzzy k-partite hypergraphs. Notes on Intuitionistic Fuzzy Sets, 29(4), 401–410. Myithili, K. K., & Nithyadevi. P. (2024). Intuitionistic fuzzy semihypergraphs. International Journal of Communication Networks and Information Security, 16(4), 466–481. Nagoor Gani, A., & Radha, K. (2008). On regular fuzzy graphs. Journal of Physical Sciences, 12, 33–40. Parvathi, R., & Karunambigai, M. G.(2006). Intuitionistic fuzzy graphs. Proceedings of 9th Fuzzy Days International Conference on Computational Intelligence, Advances in Soft Computing: Computational Intelligence, Theory and Applications, Springer-Verlag, 38, 139–150. Parvathi, R., Thilagavathi, S., & Karunambigai, M. G. (2009). Intuitionistic fuzzy hypergraphs, Cybernetics and Information Technologies, 9(2), 46–53. Pradeepa, I., & Vimala, S. (2016). Properties of irregular intuitionistic fuzzy hypergraphs. International Journal of Recent Scientific Research, 7(6), 11971–11975. Pradeepa, I., & Vimala, S. (2016). Regular and totally regular intuitionistic fuzzy hypergraph. International Journal of Mathematics and Its Applications, 4(1-c), 137–142. Radha, K., & Renganathan, P. (2020). On fuzzy semigraphs. Our Heritage, 68(4), 397–404. Sampathkumar, E. (1990). Semigraphs and their applications. Technical Report [DST/MS/022/94], Department of Science & Technology, Govt. of India. Shannon, A., & Atanassov, K. (1994). A first step to a theory of the intuitionistic fuzzy graphs. In: Lakov, D. (ed.). Proceedings of the First Workshop on Fuzzy Based Expert Systems, 28-30 September 1994, Sofia, Bulgaria, 59–61. Shetty, J., Sudhakara, G., & Arathi Bhat, K. (2022). Regularity in semigraphs. Engineering Letters, 30(4), 1299–1305. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.