This monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar informationpositive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.
Chapter 1: Bipolar Fuzzy Sets and Bipolar Fuzzy Graphs.
Chapter 2:
Distance Measures in Bipolar Fuzzy Graphs.
Chapter 3: Special Types of
Bipolar Fuzzy Graphs.
Chapter 4: Bipolar Fuzzy Competition Graphs.-
Chapter 5: Bipolar Fuzzy Planar Graphs.
Chapter 6: Domination in Bipolar
Fuzzy Graphs.
Chapter 7: Bipolar Fuzzy Circuits.
Chapter 8: Energy in
Bipolar Fuzzy Graphs.
Chapter 9: Bipolar Neutrosophic Competition Graphs.-
Chapter 10: Bipolar Neutrosophic Graph Structures.
MUHAMMAD AKRAM is Professor at the Department of Mathematics, University of the Punjab, Lahore, Pakistan. He previously served at Punjab University College of Information Technology as Assistant Professor and Associate Professor. He earned his Ph.D. in Fuzzy Mathematics from Government College University, Lahore, Pakistan. His research interests include numerical algorithms, fuzzy graphs, fuzzy algebras, and fuzzy decision support systems. He has published 09 books and over 365 research articles in peer-reviewed international journals and supervised 12 Ph.D. students.
MUSAVARAH SARWAR is Assistant Professor at Government College Women University, Sialkot, Pakistan. A gold medalist in academic excellence, Dr Sarwar received her Ph.D. in Mathematics from the University of the Punjab, Lahore, Pakistan. Her research interests include graph theory, fuzzy graphs and fuzzy decision support systems/decision-making models. She has published 18 research articles in international peer-reviewed journals.
WIESLAW ALEKSANDER DUDEK is Professor at the Department of Pure and Applied Mathematics, Wrocaw University of Science and Technology, Wrocaw, Poland. He completed his Ph.D. in Mathematics at the Department of Higher Algebra, State University of Chisinau, Republic of Moldova, under the supervision of Prof. V.D. Belousov. He received his Degree of Habilitated Doctor from the Warsaw University of Technology. The main areas of his scientific interests include polyadic groups, quasigroups, fuzzy algebras, fuzzy graphs and their applications. Professor Dudek has authored 2 monographs, 4 textbooks, and published 200 research articles in international peer-reviewed journals. He is Editor-in-Chief of the journal Quasigroups and Related Systems and on the editorial board of several international journals. He has promoted 4 doctors of mathematics.
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