Applications Of Extended Plithogenic Sets In Plithogenic Sociogram
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Applications Of Extended Plithogenic Sets In Plithogenic Sociogram
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Author : S. Sudha
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Applications Of Extended Plithogenic Sets In Plithogenic Sociogram written by S. Sudha and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches.
Introduction To Plithogenic Sociogram With Preference Representations By Plithogenic Number
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Author : Nivetha Martin
language : en
Publisher: Infinite Study
Release Date : 2020-01-01
Introduction To Plithogenic Sociogram With Preference Representations By Plithogenic Number written by Nivetha Martin and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Mathematics categories.
This paper introduces the concepts of Plithogenic Sociogram (PS) and Plithogenic Number (PN) where the former is the integration of plithogeny to the sociometric technique of sociogram and the latter is the generalization of fuzzy, intuitionistic and neutrosophic numbers that shall be used in representations of preferences in group dynamics. This research work outlines the conceptual development of these two newly proposed concepts and discusses the merits of the existing theory of similar kind with suitable substantiation.
Neutrosophic And Plithogenic Inventory Models For Applied Mathematics
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Author : Smarandache, Florentin
language : en
Publisher: IGI Global
Release Date : 2025-05-29
Neutrosophic And Plithogenic Inventory Models For Applied Mathematics 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 2025-05-29 with Mathematics categories.
As professionals navigate the evolving landscapes shaped by the advent of artificial intelligence, a critical void emerges in the optimization paradigms of applied mathematics. The dynamism of our interconnected world demands a collective research effort that transcends traditional boundaries. In response to this pressing need, Neutrosophic and Plithogenic Inventory Models for Applied Mathematics proposes a groundbreaking exploration within the frameworks of neutrosophic and plithogenic theories. This work not only seeks to address the profound impact of artificial intelligence on our lives but also aims to redefine the very foundations of optimization. Embark on a profound journey through the unexplored territories of neutrosophic and plithogenic concepts. Discover the transformative potential of neutrosophic set, logic, probability, and statistics, as well as plithogenic set, logic, probability, and statistics. Explore the synergy between artificial intelligence and responsive optimization, and navigate the intricacies of plithogenic cognitive maps. This work further explores the structural designs within neutrosophic optimization, offering an invaluable resource for scholars seeking to incorporate these advanced concepts into static, dynamic, and probabilistic inventory models and their myriad applications.
Neutrosophic Sets And Systems Vol 56 2023
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-03-20
Neutrosophic Sets And Systems Vol 56 2023 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 2024-03-20 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. 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. This theory considers every notion or idea together with its opposite or negation
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 : 2025-01-24
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 2025-01-24 with Mathematics categories.
This book is the sixth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Building upon the foundational contributions of previous volumes, this edition focuses on the exploration and development of Various New Uncertain Concepts, further enriching the study of uncertainty and complexity through innovative theoretical advancements and practical applications. The volume is meticulously organized into 15 chapters, each presenting unique perspectives and contributions to the field. From theoretical explorations to real-world applications, these chapters provide a cohesive and comprehensive overview of the state of the art in uncertain combinatorics, emphasizing the versatility and power of the newly introduced concepts and methodologies. The first chapter (SuperHypertree-depth – Structural Analysis in SuperHyperGraphs) explores the concept of SuperHypertree-depth, an extension of the classical graph parameter Tree-depth and its hypergraph counterpart Hypertree-depth. By introducing hierarchical nesting within SuperHyperGraphs, where both vertices and edges can represent recursive subsets, this study investigates the mathematical properties and structural implications of these extended parameters. The findings highlight the relationships between SuperHypertree-depth and its traditional graph-theoretic equivalents, providing a deeper understanding of their applicability to hierarchical and complex systems. The second chapter (Obstructions for Hypertree-width and SuperHypertree-width) examines the role of ultrafilters as obstructions in determining Hypertree-width and extends the concept to SuperHypertree-width. Building on hypergraph theory, which abstracts traditional graph frameworks into more complex domains, the study investigates how recursive structures within SuperHyperGraphs redefine the computational and structural properties of these parameters. Ultrafilters, with their broad mathematical significance, serve as critical tools for understanding the limitations and potentials of these advanced graph metrics. The third chapter (SuperHypertree-Length and SuperHypertree-Breadth in SuperHyperGraphs) investigates the extension of the graph-theoretic parameters Tree-length and Tree-breadth to the realms of hypergraphs and SuperHyperGraphs. By leveraging the hierarchical nesting of SuperHyperGraphs, the study explores how these parameters adapt to increasingly complex and multi-level structures. Comparative analyses between these extended parameters and their classical counterparts reveal new insights into their relevance and utility in advanced graph and hypergraph theory. Plithogenic Sets, which generalize Fuzzy and Neutrosophic Sets, are extended in the fourth chapter (Extended HyperPlithogenic Sets and Generalized Plithogenic Graphs) to Extended Plithogenic Sets, HyperPlithogenic Sets, and SuperHyperPlithogenic Sets. This study further investigates their application to graph theory through the concepts of Extended Plithogenic Graphs and Generalized Extended Plithogenic Graphs. The chapter provides a concise exploration of these frameworks, offering insights into their potential for addressing uncertainty and complexity in graph structures. Soft Sets provide an effective framework for decision-making by mapping parameters to subsets of a universal set, addressing uncertainty and vagueness. The fifth chapter (Double-Framed Superhypersoft Set and Double-Framed Treesoft Set) introduces the Double-Framed SuperHypersoft Set and the Double-Framed Treesoft Set as extensions of traditional and advanced soft set frameworks, such as Hypersoft and SuperHypersoft Sets. The chapter explores their relationships with existing concepts, offering new tools to handle complex decision-making scenarios with enhanced structural flexibility. The sixth paper (HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set) introduces the concepts of the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set, which extend the Plithogenic Cubic Set by integrating both interval-valued and single-valued fuzzy memberships. These sets leverage multi-attribute aggregation techniques inherent to plithogenic structures, allowing for nuanced representations of uncertainty. Additionally, related constructs such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set are explored, further enriching the theoretical and practical applications of this framework. The seventh chapter (L-Neutrosophic Sets and Nonstationary Neutrosophic Sets) extends the foundational concepts of fuzzy sets by integrating Neutrosophic and Plithogenic frameworks. By introducing L-Neutrosophic Sets and Nonstationary Neutrosophic Sets, the study enhances the representation of uncertainty through independent membership components: truth, indeterminacy, and falsity. These advanced constructs also incorporate multi-dimensional and contradictory attributes, providing a robust means of modeling complex decision-making and uncertain data. Plithogenic and Rough Sets, known for generalizing uncertainty modeling and classification, are extended in the eight chapter (Forest HyperPlithogenic and Forest HyperRough Sets) to Forest HyperPlithogenic Sets, Forest SuperHyperPlithogenic Sets, Forest HyperRough Sets, and Forest SuperHyperRough Sets. These frameworks incorporate hierarchical and recursive structures to advance existing set-theoretic paradigms. The chapter explores their applications in multi-level data analysis and uncertainty classification, demonstrating their adaptability to complex systems. Building on Fuzzy, Neutrosophic, and Plithogenic Sets, the tenth chapter (Symbolic HyperPlithogenic Sets) introduces Symbolic HyperPlithogenic Sets and Symbolic n-SuperHyperPlithogenic Sets. These sets incorporate symbolic components and algebraic coefficients, enabling flexible operations within a defined prevalence order. By extending symbolic representation into hyperplithogenic and superhyperplithogenic domains, the chapter opens new pathways for addressing uncertainty and hierarchical complexity in mathematical modeling. Soft Sets, designed to manage uncertainty and imprecision, have evolved through various extensions like Hypersoft Sets and SuperHypersoft Sets. The eleventh chapter (N-SuperHypersoft and Bijective SuperHypersoft Sets) introduces N-SuperHypersoft Sets, N-Treesoft Sets, Bijective SuperHypersoft Sets, and Bijective Treesoft Sets. These new constructs enhance decision-making frameworks by incorporating advanced hierarchical and bijective relationships, building on existing theories and expanding their applications. Plithogenic Sets, known for integrating multi-valued attributes and contradictions, and Rough Sets, which partition data into definable approximations, are combined in the twelfth chapter (Plithogenic Rough Sets) to form Plithogenic Rough Sets. This fusion provides a powerful framework for addressing uncertainty in dynamic and complex decision-making scenarios, offering a novel approach to uncertainty modeling. Expanding on Neutrosophic Sets, which represent truth, indeterminacy, and falsehood, this chapter introduces Plithogenic Duplets and Plithogenic Triplets. These constructs leverage the Plithogenic framework to incorporate attributes, values, and contradiction measures. The thirteenth chapter (Plithogenic Duplets and Triplets) examines their relationships with Neutrosophic Duplets and Triplets, offering new tools for multi-dimensional data representation and decision-making. Building on foundational concepts like Rough Sets and Vague Sets, the fourteenth chapter (SuperRough and SuperVague Sets) introduces SuperRough Sets and SuperVague Sets. These generalized frameworks extend uncertainty modeling by incorporating hierarchical structures. The study also demonstrates that SuperRough Sets can evolve into SuperHyperRough Sets, providing further generalizations for advanced data classification and analysis. The fifteenth chapter (Neutrosophic TreeSoft Expert and ForestSoft Sets) revisits the Neutrosophic TreeSoft Set, which combines the hierarchical structure of TreeSoft Sets with the Neutrosophic framework for uncertainty representation. Additionally, it introduces the Neutrosophic TreeSoft Expert Set, incorporating expert knowledge into the model. The chapter also explores the ForestSoft Set and its extension, the Neutrosophic ForestSoft Set, to provide multi-level, tree-structured approaches for complex data representation and analysis.
Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches
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Author : Sikkanan Sudha
language : en
Publisher: Infinite Study
Release Date :
Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches written by Sikkanan Sudha 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.
Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with normal and combined plithogenic hypersoft sets. The sensitivity analysis performed exhibits the efficacy of combined plithogenic hypersoft sets in representing the realistic data. This integrated decision framework contributes to Plithogenic applications of handling complex decision systems.
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set 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 2025-01-01 with Mathematics categories.
The Plithogenic Set is renowned for generalizing concepts such as Fuzzy Sets and Neutrosophic Sets. The Extended Plithogenic Set represents an advanced concept of the Plithogenic Set, as recently defined in [62]. A hypersoft set is a mathematical structure that maps distinct attributes with non-overlapping values to subsets of a universal set, facilitating multi-criteria decision analysis. Recent studies have explored the combination of Plithogenic Sets and Hypersoft Sets, leading to the development of the Plithogenic Hypersoft Set. This paper further extends these concepts to introduce and examine the Plithogenic SuperHypersoft Set and the Extended Plithogenic SuperHypersoft Set.
Uncertain Labeling Graphs And Uncertain Graph Classes With Survey For Various Uncertain Sets
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date :
Uncertain Labeling Graphs And Uncertain Graph Classes With Survey For Various Uncertain Sets 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 with Mathematics categories.
Graph theory, a branch of mathematics, studies the relationships between entities using vertices and edges. Uncertain Graph Theory has emerged within this field to model the uncertainties present in real-world networks. Graph labeling involves assigning labels, typically integers, to the vertices or edges of a graph according to specific rules or constraints. This paper introduces the concept of the Turiyam Neutrosophic Labeling Graph, which extends the traditional graph framework by incorporating four membership values—truth, indeterminacy, falsity, and a liberal state—at each vertex and edge. This approach enables a more nuanced representation of complex relationships. Additionally, we discuss the Single-Valued Pentapartitioned Neutrosophic Labeling Graph.The paper also examines the relationships between these novel graph concepts and other established types of graphs. In the Future Directions section, we propose several new classes of Uncertain Graphs and Labeling Graphs. And the appendix of this paper details the findings from an investigation into set concepts within Uncertain Theory. These set concepts have inspired numerous proposals and studies by various researchers, driven by their applications, mathematical properties, and research interests.
Applications Of Fuzzy Logic In Decision Making And Management Science
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Author : Subrata Jana
language : en
Publisher: Springer Nature
Release Date : 2025-05-19
Applications Of Fuzzy Logic In Decision Making And Management Science written by Subrata Jana and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-19 with Computers categories.
The fuzzy logic theory is a branch of mathematics dealing with uncertainty in measurement of any quantity or any estimation. The concept of fuzzy logic uses membership functions. The range of values from various functions or operations determines their construction. A defined rules set can create an application process and membership controls. Fuzzy applications include control system engineering, image processing, power engineering, industrial automation, robotics, consumer electronics and AI. Artificial intelligence, machine learning and expert systems have various applications that address complicated issues. The fuzzy logic inference rules have solved many problems in manufacturing and other industries. Auto engines by Honda, lift control by Mitsubishi Electric, palmtop computers by Hitachi, dishwashers by Matsushita and anti-lock brakes by Nissan are examples of corporations using machine-learning techniques with fuzzy principles. Fuzzy approaches and rule sets interpret computer vision, machine learning and evolution. Fuzzy sets can govern decision rules. Several areas use fuzzy systems in different ways. Computer vision, image processing and meta heuristic evolutionary computing are typical face research applications. Fuzzy theories can optimise and fine-tune the classifier model. Fuzzy theory is used in management, stock market analysis, information retrieval, linguistics, and behavioural science with good results. Fuzzy applications are seen in data mining and stock market prediction. The fuzzy machine learning model in the ensemble pattern accurately classifies and predicts all kinds of tasks. Fuzzy theories help maintain high accuracy. For categorisation and prediction, the ensemble pattern uses fuzzy concepts. The constant growth of fuzzy domain leads to several categorisation and prediction methods. Fuzzy type 2 and intuitionistic fuzzy logic exhibit promise accuracy and versatility. Such fuzzy logic variations can readily overcome the drawbacks of the simple fuzzy model. The book has been developed keeping in view about readers of different categories starting from the students to the professionals and researchers as well. The development of the book and its content layout will be done so meticulously proving the enough insights of the subjects to the readers so that the readers can easily pursue their research concept from the book. Overall the book serve as the purpose of repository of good amount of information and their technical presentations.
Neutrosophic Sets And Systems Vol 74 2024 Special Issue Advances In Superhyperstructures And Applied Neutrosophic Theories
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-12-16
Neutrosophic Sets And Systems Vol 74 2024 Special Issue Advances In Superhyperstructures And Applied Neutrosophic Theories 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 2024-12-16 with Mathematics categories.
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.