Intuitionistic fuzzy threshold hypergraphs

A hypergraph is a graph that allows any number of vertices to be connected by an edge. A threshold hypergraph is a hypergraph H for which there exists a function w : U(H) → N ∪ {0} and a non-negative integer s such that for all V ⊆ U(H), V is independent if and only if (Formula presented). We introduce Intuitionistic Fuzzy Threshold Hypergraph(IFTHG) along with some of the multiple forms of them such as core, simple, elementary, sectionally elementary IFTHGs and (µ, ν)- tempered IFTHGs, with few of its properties. It is further proven that if an IFTHG HG is elementary, support simple and simply ordered, then HG is a (µ, ν)-tempered IFTHG. Further, we discuss how this method can be used to recognize water wastage using IFTHG and identify regions where it can be reduced, demonstrating that it is more effective for controlling water management systems compared to other methodologies. © 2024 Forum-Editrice Universitaria Udinese SRL. All rights reserved.