Uncertain Automata And Uncertain Graph Grammar
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Uncertain Automata and Uncertain Graph Grammar
Graph theory has been widely studied, resulting in numerous applications across various felds. Among its many topics, Automata and Graph Grammar have emerged as signifcant areas of research. This paper delves into these concepts, emphasizing their adaptation to uncertain frameworks like Fuzzy, Neutrosophic, Vague, Turiyam Neutrosophic, and Plithogenic systems. By integrating uncertainty into traditional graph theoretical models, the paper aims to address ongoing research challenges and expand the scope of these models.
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
This book explores the advancement of uncertain combinatorics through innovative methods such as graphization, hyperization, and uncertainization, incorporating concepts from fuzzy, neutrosophic, soft, and rough set theory, among others. Combinatorics and set theory are fundamental mathematical disciplines that focus on counting, arrangement, and the study of collections under specified rules. While combinatorics excels at solving problems involving uncertainty, set theory has expanded to include advanced concepts like fuzzy and neutrosophic sets, which are capable of modeling complex real-world uncertainties by accounting for truth, indeterminacy, and falsehood. These developments intersect with graph theory, leading to novel forms of uncertain sets in "graphized" structures, such as hypergraphs and superhypergraphs. Innovations like Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing the boundaries of theoretical and practical advancements. This synthesis of combinatorics, set theory, and graph theory provides a strong foundation for addressing the complexities and uncertainties present in mathematical and real-world systems, paving the way for future research and application.
Neutrosophic Sets and Systems, vol. 74/2024 {Special Issue: Advances in SuperHyperStructures and Applied Neutrosophic Theories}
Author: Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2024-12-16
This volume contains the proceedings of the conference held at the University of Guayaquil on November 28 and 29, 2024, featuring contributions from researchers representing Colombia, Cuba, Ecuador, Spain, the United States, Greece, Japan, Mexico, and Peru. The conference focused on SuperHyperStructures and Applied Neutrosophic Theories, commemorating the 30th anniversary of neutrosophic theories and their extensive applications. The topic of SuperHyperStructures and Neutrosophic SuperHyperStructures explores advanced mathematical frameworks built on powersets of a set 𝐻, extending to higher orders 𝑃𝑛(𝐻). SuperHyperStructures are constructed using all non-empty subsets of 𝐻, while Neutrosophic SuperHyperStructures incorporate the empty set 𝜙, representing indeterminacy. These structures model real-world systems where elements are organized hierarchically, from sets to sub-sets and beyond, enabling the analysis of complex and indeterminate relationships.