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Über dieses Buch

This book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, m-polar fuzzy, Pythagorean, complex Pythagorean, and q-rung orthopair hypergraphs, as well as single-valued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. In addition, the book also sheds light on real-world applications of these hypergraphs, making it a valuable resource for students and researchers in the field of mathematics, as well as computer and social scientists.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Fuzzy Hypergraphs

Abstract
In this chapter, we present fundamental and technical concepts like fuzzy hypergraphs, fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs, fuzzy neighborhood hypergraphs, and \({\mathscr {N}}\)-hypergraphs. We describe applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niches, social networks, and business marketing. Further, we introduce complex fuzzy hypergraphs, \(\mu e^{i\theta }\)-level hypergraphs, covering constructions, 2-sections, and \(L_2\)-sections of these hypergraphs.
Muhammad Akram, Anam Luqman

Chapter 3. Hypergraphs for Interval-Valued Structures

Abstract
In this chapter, we present interval-valued fuzzy hypergraphs, \(A=[\mu ^-, \mu ^+]\)–tempered interval-valued fuzzy hypergraphs, and some of their properties. Moreover, we discuss the notions of vague hypergraphs, dual vague hypergraphs, and A-tempered vague hypergraphs. Finally, we describe interval-valued intuitionistic fuzzy hypergraphs and interval-valued intuitionistic fuzzy transversals of \(\mathscr {H}\). This chapter is due to [46, 11, 22, 25].
Muhammad Akram, Anam Luqman

Chapter 5. Extended Bipolar Fuzzy (Directed) Hypergraphs to m-Polar Information

Abstract
An m-polar fuzzy set is a useful tool to solve real-world problems that involve multi-agents, multi-attributes, multi-objects, multi-indexes, and multipolar information. In this chapter, we present the notions of regular m-polar fuzzy hypergraphs and totally regular m-polar fuzzy hypergraphs. We discuss applications of m-polar fuzzy hypergraphs in decision-making problems. Furthermore, we discuss the notion of m-polar fuzzy directed hypergraphs and depict certain operations on them. We also describe an application of m-polar fuzzy directed hypergraphs in business strategy.
Muhammad Akram, Anam Luqman

Chapter 6. (Directed) Hypergraphs: q-Rung Orthopair Fuzzy Models and Beyond

Abstract
The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. In this chapter, we present concepts including q-rung orthopair fuzzy hypergraphs, \((\alpha , \beta )\)-level hypergraphs, and transversals and minimal transversals of q-rung orthopair fuzzy hypergraphs. We implement some interesting notions of q-rung orthopair fuzzy hypergraphs into decision-making. We describe additional concepts like q-rung orthopair fuzzy directed hypergraphs, dual directed hypergraphs, line graphs, and coloring of q-rung orthopair fuzzy directed hypergraphs.
Muhammad Akram, Anam Luqman

Chapter 7. Granular Computing Based on q-Rung Picture Fuzzy Hypergraphs

Abstract
In this chapter, we present q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Moreover, we define q-rung picture fuzzy equivalence relations and its’ associated q-rung picture fuzzy hierarchical quotient space structures. We also present an arithmetic example in order to demonstrate the benefits and validity of this model. This chapter is due to [19, 24].
Muhammad Akram, Anam Luqman

Chapter 8. Granular Computing Based on m-Polar Fuzzy Hypergraphs

Abstract
An m-polar fuzzy model, as an extension of fuzzy and bipolar fuzzy models, plays a vital role in modeling of real-world problems that involve multi-attribute, multipolar information, and uncertainty. The m-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models.
Muhammad Akram, Anam Luqman

Chapter 9. Some Types of Hypergraphs for Single-Valued Neutrosophic Structures

Abstract
In this chapter, we present concepts including single-valued neutrosophic hypergraphs, dual single-valued neutrosophic hypergraphs, and transversal single-valued neutrosophic hypergraphs. Additionally, we discuss the notions of intuitionistic single-valued neutrosophic hypergraphs and dual intuitionistic single-valued neutrosophic hypergraphs. We describe an application of intuitionistic single-valued neutrosophic hypergraphs in a clustering problem.
Muhammad Akram, Anam Luqman

Chapter 10. (Directed) Hypergraphs for Bipolar Neutrosophic Structures

Abstract
In this chapter, we present bipolar neutrosophic hypergraphs and B-tempered bipolar neutrosophic hypergraphs. We describe the concepts of transversals, minimal transversals and locally minimal transversals of bipolar neutrosophic hypergraphs. Furthermore, we put forward some applications of bipolar neutrosophic hypergraphs in marketing and biology. We also introduce bipolar neutrosophic directed hypergraphs, regular bipolar neutrosophic directed hypergraphs, homomorphism, and isomorphism on bipolar neutrosophic directed hypergraphs. To conclude, we describe an efficient algorithm to solve decision-making problems. This chapter is due to [7, 10, 16].
Muhammad Akram, Anam Luqman

Backmatter

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