Rough Neutrosophic Relation On Two Universal Sets

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Rough Neutrosophic Relation On Two Universal Sets

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Author : I. AROCKIARANI
language : en
Publisher: Infinite Study
Release Date :

Rough Neutrosophic Relation On Two Universal Sets written by I. AROCKIARANI and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

In this paper, we define the rough neutrosophic relation of two universe sets and study the algebraic properties of two rough neutrosophic relations that are interesting in the theory of rough sets. Finally, we present the similarity rough neutrosophic relation with an example.

Rough Neutrosophic Multisets Relation With Application In Marketing Strategy

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Author : Suriana Alias
language : en
Publisher: Infinite Study
Release Date :

Rough Neutrosophic Multisets Relation With Application In Marketing Strategy written by Suriana Alias and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. Therefore, the objective of this paper is to define the definition of rough neutrosophic multisets relation of Cartesian product over a universal set. Some of the relation properties of rough neutrosophic multisets such as max, min, the composition of two rough neutrosophic multisets relation, inverse rough neutrosophic multisets relation, and reflexive, symmetric and transitive rough neutrosophic multisets relation over the universe are defined. Subsequently, their properties are successfully proven. Finally, the application of rough neutrosophic multisets relation for decision making in marketing strategy is presented.

Neutrosophic Sets And Systems

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
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Neutrosophic Sets And Systems written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Some Relation Properties Of Rough Neutrosophic Multisets

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Author : Suriana Alias
language : en
Publisher: Infinite Study
Release Date :

Some Relation Properties Of Rough Neutrosophic Multisets written by Suriana Alias and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Rough neutrosophic multisets are an improved model of generalization pf neutrosophic multisets represented within the Pawlak’s boundary set of information: lower and upper approximation. The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. This paper establishes an axiomatic definition of rough neutrosophic multisets relation of Cartesian product over a universal set.

Neutrosophic Sets And Systems An International Book Series In Information Science And Engineering Vol 21 2018

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2018

Neutrosophic Sets And Systems An International Book Series In Information Science And Engineering Vol 21 2018 written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Handbook Of Research On Advances And Applications Of Fuzzy Sets And Logic

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Author : Broumi, Said
language : en
Publisher: IGI Global
Release Date : 2022-03-04

Handbook Of Research On Advances And Applications Of Fuzzy Sets And Logic written by Broumi, Said and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-04 with Mathematics categories.

Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. The Handbook of Research on Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.

The Encyclopedia Of Neutrosophic Researchers 2nd Volume

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
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The Encyclopedia Of Neutrosophic Researchers 2nd Volume written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This is the second volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to my invitation. The introduction contains a short history of neutrosophics, together with links to the main papers and books.

Neutrosophic Multi Criteria Decision Making

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Author : Florentin Smarandache
language : en
Publisher: MDPI
Release Date : 2018-10-12

Neutrosophic Multi Criteria Decision Making written by Florentin Smarandache and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.

This book is a printed edition of the Special Issue "Neutrosophic Multi-Criteria Decision Making" that was published in Axioms

Generalized Interval Neutrosophic Rough Sets And Its Application In Multi Attribute Decision Making

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Author : Hai-Long Yang
language : en
Publisher: Infinite Study
Release Date :

Generalized Interval Neutrosophic Rough Sets And Its Application In Multi Attribute Decision Making written by Hai-Long Yang and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information.

Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-20

Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-20 with Mathematics categories.

This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of Various SuperHyperConcepts, building on the foundational advancements introduced in previous volumes. The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties. At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity. In this fifth volume, the exploration of Various SuperHyperConcepts provides an innovative lens to address uncertainty, complexity, and hierarchical relationships. It synthesizes key methodologies introduced in earlier volumes, such as hyperization and neutrosophic extensions, while advancing new theories and applications. From pioneering hyperstructures to applications in advanced decision-making, language modeling, and neural networks, this book represents a significant leap forward in uncertain combinatorics and its practical implications across disciplines. The book is structured into 17 chapters, each contributing unique perspectives and advancements in the realm of Various SuperHyperConcepts and their related frameworks: Chapter 1 introduces the concept of Body-Mind-Soul-Spirit Fluidity within psychology and phenomenology, while examining established social science frameworks like PDCA and DMAIC. It extends these frameworks using Neutrosophic Sets, a flexible extension of Fuzzy Sets, to improve their adaptability for mathematical and programming applications. The chapter emphasizes the potential of Neutrosophic theory to address multi-dimensional challenges in social sciences. Chapter 2 delves into the theoretical foundation of Hyperfunctions and their generalizations, such as Hyperrandomness and Hyperdecision-Making. It explores higher-order frameworks like Weak Hyperstructures, Hypergraphs, and Cognitive Hypermaps, aiming to establish their versatility in addressing multi-layered problems and setting a foundation for further studies. Chapter 3 extends traditional decision-making methodologies into HyperDecision-Making and n-SuperHyperDecision-Making. By building on approaches like MCDM and TOPSIS, this chapter develops frameworks capable of addressing complex decision-making scenarios, emphasizing their applicability in dynamic, multi-objective contexts. Chapter 4 explores integrating uncertainty frameworks, including Fuzzy, Neutrosophic, and Plithogenic Sets, into Large Language Models (LLMs). It proposes innovative models like Large Uncertain Language Models and Natural Uncertain Language Processing, integrating hierarchical and generalized structures to advance the handling of uncertainty in linguistic representation and processing. Chapter 5 introduces the Natural n-Superhyper Plithogenic Language by synthesizing natural language, plithogenic frameworks, and superhyperstructures. This innovative construct seeks to address challenges in advanced linguistic and structural modeling, blending attributes of uncertainty, complexity, and hierarchical abstraction. Chapter 6 defines mathematical extensions such as NeutroHyperstructures and AntiHyperstructures using the Neutrosophic Triplet framework. It formalizes structures like neutro-superhyperstructures, advancing classical frameworks into higher-dimensional realms. Chapter 7 explores the extension of Binary Code, Gray Code, and Floorplans through hyperstructures and superhyperstructures. It highlights their iterative and hierarchical applications, demonstrating their adaptability for complex data encoding and geometric arrangement challenges. Chapter 8 investigates the Neutrosophic TwoFold SuperhyperAlgebra, combining classical algebraic operations with neutrosophic components. This chapter expands upon existing algebraic structures like Hyperalgebra and AntiAlgebra, exploring hybrid frameworks for advanced mathematical modeling. Chapter 9 introduces Hyper Z-Numbers and SuperHyper Z-Numbers by extending the traditional Z-Number framework with hyperstructures. These extensions aim to represent uncertain information in more complex and multidimensional contexts. Chapter 10 revisits category theory through the lens of hypercategories and superhypercategories. By incorporating hierarchical and iterative abstractions, this chapter extends the foundational principles of category theory to more complex and layered structures. Chapter 11 formalizes the concept of n-SuperHyperBranch-width and its theoretical properties. By extending hypergraphs into superhypergraphs, the chapter explores recursive structures and their potential for representing intricate hierarchical relationships. Chapter 12 examines superhyperstructures of partitions, integrals, and spaces, proposing a framework for advancing mathematical abstraction. It highlights the potential applications of these generalizations in addressing hierarchical and multi-layered problems. Chapter 13 revisits Rough, HyperRough, and SuperHyperRough Sets, introducing new concepts like Tree-HyperRough Sets. The chapter connects these frameworks to advanced approaches for modeling uncertainty and complex relationships. Chapter 14 explores Plithogenic SuperHyperStructures and their applications in decision-making, control, and neuro systems. By integrating these advanced frameworks, the chapter proposes innovative directions for extending existing systems to handle multi-attribute and contradictory properties. Chapter 15 focuses on superhypergraphs, expanding hypergraph concepts to model complex structural types like arboreal and molecular superhypergraphs. It introduces Generalized n-th Powersets as a unifying framework for broader mathematical applications, while also touching on hyperlanguage processing. Chapter 16 defines NeutroHypergeometry and AntiHypergeometry as extensions of classical geometric structures. Using the Geometric Neutrosophic Triplet, the chapter demonstrates the flexibility of these frameworks in representing multi-dimensional and uncertain relationships. Chapter 17 establishes the theoretical groundwork for SuperHyperGraph Neural Networks and Plithogenic Graph Neural Networks. By integrating advanced graph structures, this chapter opens pathways for applying neural networks to more intricate and uncertain data representations.