SuperHyperTopologies and SuperHyperStructures with their Applications

This volume presents some original research on SuperHyperStructures and SuperHyperTopologies, new branches of mathematics with applications in applied sciences. These frameworks extend classical notions of sets, graphs and topologies by incorporating uncertainty, indeterminacy and multivalued membership, rooted in neutrosophic and Plithogenic logic. They provide non-rigorous methods for the analysis of complex systems in which ambiguity and dynamic interactions are fundamental. The n-th powersets that are the bases o the SuperHyperStructure, together with their particular cases such as: SuperHyperAlgebra (endowed with SuperHyperOperations and SuperHyperAxioms), SuperHyperGraph (including SuperHyperTree), SuperHyperSoft Set, SuperHyperFunction, SuperHyperTopology (all built on the powersets of P(H), or Pn(H), for n ≥ 1) and SuperHyperTopology were all founded by Smarandache and developed between 2016 - 2024. The book is largely deals with 3 main subject-matters. The first one introduces mathematical foundations, including SuperHyperTopologies, Neutrosophic and Plithogenic extensions, fuzzy and soft set frameworks, and links with Łukasiewicz algebras. The second one develops structural perspectives through SuperHyperGraphs, weighted hyperedges, fuzzy neural networks, and neutrosophic automata. The third subject-matter illustrates interdisciplinary applications in medicine, finance, agriculture, tourism, economics, and data science. An important feature of the volume is its inter-disciplinary orientation. Mathematical theories are linked to practical problems, showing how SuperHyper concepts can support decision-making, optimize resources and model uncertainty in different fields. By combining fuzzy, neutrosophic and plithogenic logics within hyperstructural frameworks, the book highlights innovative approaches to indeterminate and multilayered phenomena. The subject-matters and content of this volume is aimed not only at researchers but also graduate students and professionals in mathematics, computer science and related disciplines. It offers a comprehensive reference and several practical research avenues, paving the way for further interdisciplinary research and applications.