This book provides readers with an introduction to m-polar fuzzy graphs and m-polar fuzzy hypergraphs, covering both theories and applications. A special emphasis is given to m-polar fuzzy graphs at the aim of filling a gap in the literature, namely the absence of a mathematical approach to analyze multi-index, multipolar, and multi-attribute data. The book describes metrics and labeling in m-polar graphs, m-polar fuzzy matroids. It also discusses in detail important applications in decision-making problems and imaging processing. The book is expected to stimulate the curiosity of mathematics, computer scientists, and social scientists alike, and to provide both students and researchers with the necessary knowledge to understand and apply mpolar fuzzy graph theory.

Introduces the fundamentals of m-polar fuzzy sets and m-polar fuzzy graphs Describes a mathematical approach to deal with multi-index, multipolar, and multi-attribute data Describes applications to image processing and decision making

Autorentext

Muhammad Akram has received his M.Sc. degree in Mathematics and Computer Science, M.Phil. in Mathematics, and Ph.D. in Fuzzy Mathematics. He is currently serving as a Professor at the Department of Mathematics of the University of the Punjab, in Lahore, Pakistan. Muhammad Akram's research topics cover numerical solutions of parabolic partial differential equations, fuzzy graphs, fuzzy algebras, and fuzzy decision support systems. He has published about 500 research articles in international peer-reviewed journals, and 10 monographs. He has been serving as an Editorial Board Member and as a reviewer of international academic journals. Arooj Adeel is an Assistant Professor at the Department of Mathematics of the University of Education, in Lahore, Pakistan. She completed her Ph.D. degree in Mathematics at the same University. Her research covers fuzzy sets and graphs, hybrid models, and decision-making techniques. She has published more than 20 articles in international peer-reviewed journals. She is also serving as an Editorial Board Member and as a reviewer of international academic journals.

Inhalt

mPolar Fuzzy Sets and mPolar Fuzzy Graphs.- Certain Types of mPolar Fuzzy Graphs.- Certain Metrics in m Polar Fuzzy Graphs.- mPolar Fuzzy Labeling Graphs.- Certain Dominations in mPolar Fuzzy Graphs.- mpolar Fuzzy Concept Lattice.- mPolar Fuzzy Graph Structures.- mPolar Fuzzy Hypergraphs.- mPolar Fuzzy Matroids.