A Novel Rough Set Model In Generalized Single Valued Neutrosophic Approximation Spaces And Its Application
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A Novel Rough Set Model In Generalized Single Valued Neutrosophic Approximation Spaces And Its Application
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Author : Zhi-Lian Guo
language : en
Publisher: Infinite Study
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A Novel Rough Set Model In Generalized Single Valued Neutrosophic Approximation Spaces And Its Application written by Zhi-Lian Guo 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 extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment.
A New Type Of Single Valued Neutrosophic Covering Rough Set Model
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Author : Jingqian Wang
language : en
Publisher: Infinite Study
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A New Type Of Single Valued Neutrosophic Covering Rough Set Model written by Jingqian Wang 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.
Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation.
On Single Valued Neutrosophic Re Ned Rough Set Model And Its Application
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Author : Yan-Ling Bao
language : en
Publisher: Infinite Study
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On Single Valued Neutrosophic Re Ned Rough Set Model And Its Application written by Yan-Ling Bao 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) theory was originally established by Smarandache for handling indeterminate and inconsistent information.
Symmetry Vol 9 Issue 10 2007 Special Issue Neutrosophic Theories Applied In Engineering
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
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Symmetry Vol 9 Issue 10 2007 Special Issue Neutrosophic Theories Applied In Engineering 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.
This Special Issue presents original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.
Two Types Of Single Valued Neutrosophic Covering Rough Sets And An Application To Decision Making
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Author : Jingqian Wang
language : en
Publisher: Infinite Study
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Two Types Of Single Valued Neutrosophic Covering Rough Sets And An Application To Decision Making written by Jingqian Wang 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.
In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented.
Medical Diagnosis Based On Single Valued Neutrosophic Probabilistic Rough Multisets Over Two Universes
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Author : Chao Zhang
language : en
Publisher: Infinite Study
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Medical Diagnosis Based On Single Valued Neutrosophic Probabilistic Rough Multisets Over Two Universes written by Chao Zhang 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 real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information.
Neutrosophic Sets And Systems Vol 62 2023 Neutrosophic Advancements And Their Impact On Research In Latin America
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2023-12-15
Neutrosophic Sets And Systems Vol 62 2023 Neutrosophic Advancements And Their Impact On Research In Latin America 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 2023-12-15 with Mathematics categories.
In the ever-evolving landscape of contemporary research, the utilization of neutrosophic methods has burgeoned into an innovative and multidisciplinary approach, offering profound insights and solutions to intricate issues spanning education, law, and healthcare. This expanded preface not only introduces a unique collection of articles authored by experts from Mexico, Peru, Cuba, Spain, Chile, Brazil, República Dominicana, Colombia, Estados Unidos, Uruguay, Panamá, Canada, Paraguay and Ecuador but also underscores the transformative impact of neutrosophic research on the fabric of Latin American society. The growth of research in neutrosophy has been particularly pronounced, manifesting its influence across diverse domains. In the realm of education, researchers are exploring novel ways to integrate neutrosophic principles into pedagogical strategies, fostering a nuanced understanding of complex subjects and encouraging critical thinking among students. Neutrosophy has thus become a cornerstone in shaping the educational landscape, challenging traditional paradigms and encouraging a more comprehensive approach to learning. Furthermore, the legal arena has witnessed a paradigm shift with the incorporation of neutrosophic decisionmaking. The nuanced and balanced perspectives offered by neutrosophy have proven instrumental in addressing legal complexities, contributing to a more equitable and just legal system. The articles in this collection delve into the application of neutrosophic models in legal frameworks, highlighting their potential to revolutionize the practice of law in the region. In the healthcare sector, the adoption of neutrosophic modeling for resource allocation signifies a departure from conventional approaches. By incorporating the inherent uncertainty and indeterminacy of healthcare decision-making, researchers are paving the way for more adaptive and responsive healthcare systems. This collection explores the potential of neutrosophic methods to optimize healthcare resource allocation, thereby enhancing the quality of care provided to diverse communities. A noteworthy development accompanying this surge in neutrosophic research is the establishment and growth of the Latin American Association of Neutrosophic Clinics. This association serves as a nexus for collaboration, fostering interdisciplinary exchanges and providing a platform for researchers and practitioners to share their advancements and challenges. The association’s commitment to promoting neutrosophic research across Latin America is exemplified by its flagship publication, the "Neutrosophic Computing and Machine Learning" journal. Undoubtedly, the pioneering efforts of Dr. Florentin Smarandache and Dr. Mohamed Abdel-Baset have played a pivotal role in nurturing the growth of neutrosophy in the region. Their unwavering support, both in terms of advocacy and research contributions, has catalyzed the expansion of neutrosophic studies in Latin America. This collection, in many ways, stands as a testament to their enduring commitment and the collaborative spirit that propels the field forward. This collection of articles represents not only a snapshot of the current state of neutrosophic research in Latin America but also a testament to its transformative potential. As readers delve into these contributions, they are invited to witness the ongoing evolution of neutrosophy and its profound implications for education, law, healthcare, and beyond.
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 : 2025-01-15
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 2025-01-15 with Mathematics categories.
This book represents the fourth volume in the series 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 the HyperUncertain Set, 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 fourth volume, the integration of set theory with graph theory takes center stage, culminating in "graphized" structures such as hypergraphs and superhypergraphs. These structures, paired with innovations like Neutrosophic Oversets, Undersets, Offsets, and the Nonstandard Real Set, extend the boundaries of mathematical abstraction. This fusion of combinatorics, graph theory, and uncertain set theory creates a rich foundation for addressing the multidimensional and hierarchical uncertainties prevalent in both theoretical and applied domains. The book is structured into thirteen chapters, each contributing unique perspectives and advancements in the realm of HyperUncertain Sets and their related frameworks. The first chapter (Advancing Traditional Set Theory with Hyperfuzzy, Hyperneutrosophic, and Hyperplithogenic Sets) explores the evolution of classical set theory to better address the complexity and ambiguity of real-world phenomena. By introducing hierarchical structures like hyperstructures and superhyperstructures—created through iterative applications of power sets—it lays the groundwork for more abstract and adaptable mathematical tools. The focus is on extending three foundational frameworks: Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets into their hyperforms: Hyperfuzzy Sets, Hyperneutrosophic Sets, and Hyperplithogenic Sets. These advanced concepts are applied across diverse fields such as statistics, clustering, evolutionary theory, topology, decision-making, probability, and language theory. The goal is to provide a robust platform for future research in this expanding area of study. The second chapter (Applications and Mathematical Properties of Hyperneutrosophic and SuperHyperneutrosophic Sets) extends the work on Hyperfuzzy, Hyperneutrosophic, and Hyperplithogenic Sets by delving into their advanced applications and mathematical foundations. Building on prior research, it specifically examines Hyperneutrosophic and SuperHyperneutrosophic Sets, exploring their integration into: Neutrosophic Logic, Cognitive Maps,Graph Neural Networks, Classifiers, and Triplet Groups. The chapter also investigates their mathematical properties and applicability in addressing uncertainties and complexities inherent in various domains. These insights aim to inspire innovative uses of hypergeneralized sets in modern theoretical and applied research. The third chapter (New Extensions of Hyperneutrosophic Sets – Bipolar, Pythagorean, Double-Valued, and Interval-Valued Sets) studies advanced variations of Neutrosophic Sets, a mathematical framework defined by three membership functions: truth (T), indeterminacy (I), and falsity (F). By leveraging the concepts of Hyperneutrosophic and SuperHyperneutrosophic Sets, the study extends: Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets. These extensions address increasingly complex scenarios, and a brief analysis is provided to explore their potential applications and mathematical underpinnings. Building on prior research, the fourth chapter (Hyperneutrosophic Extensions of Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets) expands on Neutrosophic Set theory by incorporating recent advancements in Hyperneutrosophic and SuperHyperneutrosophic Sets. The study focuses on extending: Complex Neutrosophic Sets, Single-Valued Triangular Neutrosophic Sets, Fermatean Neutrosophic Sets, and Linguistic Neutrosophic Sets. The analysis highlights the mathematical structures of these hyperextensions and explores their connections with existing set-theoretic concepts, offering new insights into managing uncertainty in multidimensional challenges. The fifth chapter (Advanced Extensions of Hyperneutrosophic Sets – Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, and m-Polar) delves deeper into the evolution of Neutrosophic Sets by exploring advanced frameworks designed for even more intricate applications. New extensions include: Dynamic Neutrosophic Sets, Quadripartitioned Neutrosophic Sets, Pentapartitioned Neutrosophic Sets, Heptapartitioned Neutrosophic Sets, and m-Polar Neutrosophic Sets. These developments build upon foundational research and aim to provide robust tools for addressing multidimensional and highly nuanced problems. The sixth chapter (Advanced Extensions of Hyperneutrosophic Sets – Cubic, Trapezoidal, q-Rung Orthopair, Overset, Underset, and Offset) builds upon the Neutrosophic framework, which employs truth (T), indeterminacy (I), and falsity (F) to address uncertainty. Leveraging advancements in Hyperneutrosophic and SuperHyperneutrosophic Sets, the study extends: Cubic Neutrosophic Sets, Trapezoidal Neutrosophic Sets, q-Rung Orthopair Neutrosophic Sets, Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets. The chapter provides a brief analysis of these new set types, exploring their properties and potential applications in solving multidimensional problems. The seventh chapter (Specialized Classes of Hyperneutrosophic Sets – Support, Paraconsistent, and Faillibilist Sets) delves into unique classes of Neutrosophic Sets extended through Hyperneutrosophic and SuperHyperneutrosophic frameworks to tackle advanced theoretical challenges. The study introduces and extends: Support Neutrosophic Sets, Neutrosophic Intuitionistic Sets, Neutrosophic Paraconsistent Sets, Neutrosophic Faillibilist Sets, Neutrosophic Paradoxist and Pseudo-Paradoxist Sets, Neutrosophic Tautological and Nihilist Sets, Neutrosophic Dialetheist Sets, and Neutrosophic Trivialist Sets. These extensions address highly nuanced aspects of uncertainty, further advancing the theoretical foundation of Neutrosophic mathematics. The eight chapter (MultiNeutrosophic Sets and Refined Neutrosophic Sets) focuses on two advanced Neutrosophic frameworks: MultiNeutrosophic Sets, and Refined Neutrosophic Sets. Using Hyperneutrosophic and nn-SuperHyperneutrosophic Sets, these extensions are analyzed in detail, highlighting their adaptability to multidimensional and complex scenarios. Examples and mathematical properties are provided to showcase their practical relevance and theoretical depth. The ninth chapter (Advanced Hyperneutrosophic Set Types – Type-m, Nonstationary, Subset-Valued, and Complex Refined) explores extensions of the Neutrosophic framework, focusing on: Type-m Neutrosophic Sets, Nonstationary Neutrosophic Sets, Subset-Valued Neutrosophic Sets, and Complex Refined Neutrosophic Sets. These extensions utilize the Hyperneutrosophic and SuperHyperneutrosophic frameworks to address advanced challenges in uncertainty management, expanding their mathematical scope and practical applications. The tenth chapter (Hyperfuzzy Hypersoft Sets and Hyperneutrosophic Hypersoft Sets) integrates the principles of Fuzzy, Neutrosophic, and Soft Sets with hyperstructures to introduce: Hyperfuzzy Hypersoft Sets, and Hyperneutrosophic Hypersoft Sets. These frameworks are designed to manage complex uncertainty through hierarchical structures based on power sets, with detailed analysis of their properties and theoretical potential. The eleventh chapter (A Review of SuperFuzzy, SuperNeutrosophic, and SuperPlithogenic Sets) revisits and extends the study of advanced set concepts such as: SuperFuzzy Sets, Super-Intuitionistic Fuzzy Sets,Super-Neutrosophic Sets, and SuperPlithogenic Sets, including their specialized variants like quadripartitioned, pentapartitioned, and heptapartitioned forms. The work serves as a consolidation of existing studies while highlighting potential directions for future research in hierarchical uncertainty modeling. Focusing on decision-making under uncertainty, the tweve chapter (Advanced SuperHypersoft and TreeSoft Sets) introduces six novel concepts: SuperHypersoft Rough Sets,SuperHypersoft Expert Sets, Bipolar SuperHypersoft Sets, TreeSoft Rough Sets, TreeSoft Expert Sets, and Bipolar TreeSoft Sets. Definitions, properties, and potential applications of these frameworks are explored to enhance the flexibility of soft set-based models. The final chapter (Hierarchical Uncertainty in Fuzzy, Neutrosophic, and Plithogenic Sets) provides a comprehensive survey of hierarchical uncertainty frameworks, with a focus on Plithogenic Sets and their advanced extensions: Hyperplithogenic Sets, SuperHyperplithogenic Sets. It examines relationships with other major concepts such as Intuitionistic Fuzzy Sets, Vague Sets, Picture Fuzzy Sets, Hesitant Fuzzy Sets, and multi-partitioned Neutrosophic Sets, consolidating their theoretical interconnections for modeling complex systems. This volume not only reflects the dynamic interplay between theoretical rigor and practical application but also serves as a beacon for future research in uncertainty modeling, offering advanced tools to tackle the intricacies of modern challenges.
Multigranulation Single Valued Neutrosophic Covering Based Rough Sets And Their Applications To Multi Criteria Group Decision Making
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Author : J. Q. Wang
language : en
Publisher: Infinite Study
Release Date :
Multigranulation Single Valued Neutrosophic Covering Based Rough Sets And Their Applications To Multi Criteria Group Decision Making written by J. Q. Wang 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.
In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).
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.