Bipolar Quadripartitioned Single Valued Neutrosophic Rough Set
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Bipolar Quadripartitioned Single Valued Neutrosophic Rough Set
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Author : Kalyan Sinha
language : en
Publisher: Infinite Study
Release Date : 2020-12-01
Bipolar Quadripartitioned Single Valued Neutrosophic Rough Set written by Kalyan Sinha and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
Here bipolar quadripartitioned single valued neutrosophic rough (BQSVNR) set is introduced. Some basic set theoretic terminologies like constant BQSVNR set, subsethood of two BQSVNR sets are shown. Algebraic operations like union, intersection and complement have also been defined. Different types of measure like similarity measure, quasi similarity measure and distance measures between two BQSVNR sets have been discussed with their properties. Again various measures of similarity namely distance based similarity measure, cosine similarity measure, membership function based similarity measure are introduced in this paper. A medical diagonasis problem has been solved using similarity measure at the end.
Bipolar Quadripartitioned Single Valued Neutrosophic Sets
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Author : Kalyan Sinha
language : en
Publisher: Infinite Study
Release Date :
Bipolar Quadripartitioned Single Valued Neutrosophic Sets written by Kalyan Sinha 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 notion of simple bipolar quadripartition is presented valuable neutrosophi set. Some basic theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here.
Similarity Measures Of Quadripartitioned Single Valued Bipolar Neutrosophic Sets And Its Application In Multi Criteria Decision Making Problems
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Author : Subhadip Roy
language : en
Publisher: Infinite Study
Release Date :
Similarity Measures Of Quadripartitioned Single Valued Bipolar Neutrosophic Sets And Its Application In Multi Criteria Decision Making Problems written by Subhadip Roy 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, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.
Neutrosophic Sets And Systems Vol 38 2020
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Sets And Systems Vol 38 2020 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.
“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.
Neutrosophic Sets And Systems Vol 32 2020
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Sets And Systems Vol 32 2020 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.
“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 articles in this issue: Parameter Reduction of Neutrosophic Soft Sets and Their Applications, Geometric Programming (NGP) Problems Subject to (⋁,.) Operator; the Minimum Solution, Ngpr Homeomorphism in Neutrosophic Topological Spaces, Generalized Neutrosophic Separation Axioms in Neutrosophic Soft Topological Spaces.
Neutrosophic Sets An Overview
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Author : Said Broumi
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Sets An Overview written by Said Broumi 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 study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoidal neutrosophic fuzzy number and their basic operations. Also some comparative studies between the existing neutrosophic sets and neutrosophic number are provided.
Theory And Applications Of Neutroalgebras As Generalizations Of Classical Algebras
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Author : Smarandache, Florentin
language : en
Publisher: IGI Global
Release Date : 2022-04-15
Theory And Applications Of Neutroalgebras As Generalizations Of Classical Algebras written by Smarandache, Florentin and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-15 with Mathematics categories.
Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.
Neutrosophic Sets And Systems Book Series Vol 32 2020 An International Book Series In Information Science And Engineering
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Sets And Systems Book Series Vol 32 2020 An International Book Series In Information Science And 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 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.
Analytical Decision Making And Data Envelopment Analysis
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Author : S.A Edalatpanah
language : en
Publisher: Springer Nature
Release Date : 2024-10-28
Analytical Decision Making And Data Envelopment Analysis written by S.A Edalatpanah and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-28 with Business & Economics categories.
This book explores the intersection of data envelopment analysis (DEA) and various analytical decision-making methodologies. Featuring contributions from experts in the field from across the world, each chapter delves into different aspects of DEA and its applications in real-world scenarios. The book covers a wide range of topics, including integrating DEA with machine learning techniques, performance evaluation in diverse sectors like banking and civil engineering, and using DEA in managerial decision-making. It also examines data mining during the Covid-19 pandemic and the application of blockchain and IoT in supply chain management. The book offers a deep dive into the evolution of nonparametric frontier methods and the development of new optimization algorithms, addressing the complexities of modern analytical decision-making tools. A few chapters delve into futuristic topics like fuzzy sets and their extensions in decision-making and exploring e-learning platforms for education. This book is an invaluable resource for researchers, practitioners and students interested in the latest DEA advancements and practical applications in various fields. Its multidisciplinary approach makes it a useful addition to the libraries of those seeking to understand the complexities and potentials of modern analytical decision-making tools.
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.