University of New Mexico
The College of Wooster
CUNY Queensborough Community College
Linfield College
Lynchburg College
University of North Dakota
Washington University in St. Louis
Boise State University
(R2139) Italian Domination Number For Some Classes Of Trees,
2026
Vellore Institute of Technology, India
(R2139) Italian Domination Number For Some Classes Of Trees, Amritha Prakash, Ragukumar Pandurangan
Applications and Applied Mathematics: An International Journal (AAM)
For a graph G with vertex set V , an Italian dominating function is a function f from V to {0, 1, 2} which has the property that for every vertex which is assigned 0, it must either adjacent to a vertex assigned 2 under f or adjacent to at least two vertices assigned 1 under f. The weight of an Italian dominating function is the sum of all weights assigned to the vertices. The minimum weight of an Italian dominating function f is the Italian domination number. Finding a graph’s Italian domination number is a well-known NP-Complete problem. Even …
Toward Completeness Theorem For Guarded Kleene Algebra With Tests,
2026
Bucknell University
Toward Completeness Theorem For Guarded Kleene Algebra With Tests, Hung Pham
Honors Theses
Code refactoring is a fundamental practice in software engineering, in which a program is restructured without changing the actions it performs and the results it produces. To carry out refactoring with confidence, one requires a formal method for verifying that two programs are equivalent. Guarded Kleene Algebra with Tests (GKAT) provides such a framework, an algebraic system designed to reason about a natural class of programs, namely those in which every branch and loop is governed by a Boolean condition, such as if–else and while statements. Central to GKAT is a finite set of algebraic axioms for deriving program equivalences. …
Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3),
2025
Embry-Riddle Aeronautical University
Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal
Doctoral Dissertations and Master's Theses
Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …
New View Of Some Propositions On Hesitant Fuzzy Set And Its Application In Selecting The Best Person In Any Job,
2025
Tanta University - Faculty of Engineering
New View Of Some Propositions On Hesitant Fuzzy Set And Its Application In Selecting The Best Person In Any Job, Manar Mohamed Omran Dr., Arafa A. Nasef A.Dr, Reham Abd El-Aziz Abo Khadra Dr., Mahmoud Arafa Nasef Dr.
Journal of Engineering Research
An essential part of uncertainty is played by the hesitant fuzzy set (HFS). So, it can be utilized when making decisions. The suggested use of HFS to choose the best candidate for any post is thoroughly discussed and introduces new HFS concepts
Belonging,
2025
The University of Texas at El Paso
Orientable Quadrilateral Embeddings Of Cartesian Products Of Graphs,
2025
Belmont University
Orientable Quadrilateral Embeddings Of Cartesian Products Of Graphs, Matthew Farnsworth, Max Goskie, Adrian Volpe, Jackson Sayre
SPARK Symposium Presentations
In the spirit of Pisanski (1989) we consider orientable quadrilateral embeddings of Cartesian products of cycles on surfaces. We offer a constructive example of such an embedding of three low-order cycles. Then we show more generally that such embeddings exist for the product of a 2-cycle, and even cycle, and an arbitrary third cycle. We represent our graphs using rotation schemes to show this existence. Use of rotation schemes led to the ultimate characterization of our findings visually, providing conjectures for generalizations of products of three cycles.
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set,
2025
University of New Mexico
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I),
2025
University of New Mexico
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
This work investigates the evolution of traditional set theory to address complex and ambiguous real-world phenomena. It introduces hierarchical hyperstructures and superhyperstructures, where superhyperstructures are formed by iteratively applying power sets to create nested abstractions. The focus is placed on three foundational set-based frameworks—Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets and their extensions into Hyperfuzzy Sets, HyperNeutrosophic Sets, and Hyperplithogenic Sets. These extensions are applied to various domains, including Statistics, TOPSIS, K-means Clustering, Evolutionary Theory, Topological Spaces, Decision Making, Probability, and Language Theory. By exploring these generalized forms, this paper seeks to guide and inspire further research and development in …
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined,
2025
University of New Mexico
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations,
2025
University of New Mexico
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as …
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set,
2025
University of New Mexico
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds on the foundational advancements introduced in [22, 29–32]. The Neutrosophic Set pro-vides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others,
2025
University of New Mexico
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic …
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii),
2025
University of New Mexico
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper delves into the advancements of classical set theory to address the complexities and uncertainties inherent in real-world phenomena. It highlights three major extensions of traditional set theory - Fuzzy Sets [288], Neutrosophic Sets [237], and Plithogenic Sets [243] - and examines their further generalizations into Hyperfuzzy [106], HyperNeutrosophic [90], and Hyperplithogenic Sets [90]. Building on previous research [83], this study explores the potential applications of HyperNeutrosophic Sets and SuperHyperNeutrosophic Sets across various domains. Specifically, it extends f undamental c oncepts such as Neutrosophic Logic, Cognitive Maps, Graph Neural Networks, Classifiers, and Triplet Groups through these advanced set structures …
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set,
2025
University of New Mexico
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [30, 72], Neutrosophic Sets [53, 55], Rough Sets [37], and Plithogenic Sets [59] have been extensively studied to address uncertainty, with diverse applications across various fields. Recently, TreeFuzzy, TreeNeutrosophic, TreePlithogenic, and TreeRough Sets have been defined [15]. This work examines their extensions: ForestFuzzy, ForestNeutrosophic, ForestPlithogenic, and ForestRough Sets.
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set,
2025
University of New Mexico
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [23, 47], Neutrosophic Sets [32, 33], and Plithogenic Sets [35] have been extensively studied for addressing uncertainty, with diverse applications across numerous fields. Building on the Plithogenic Set, the HyperPlithogenic Set and SuperHyperPlithogenic Set have also gained recognition [15]. A Plithogenic Cubic Set integrates interval-valued and single-valued fuzzy memberships, augmented by multiattribute aggregation using plithogenic structures. This paper defines the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set and explores related concepts such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set.
Neutrosophic Treesoft Expert Set And Forestsoft Set,
2025
University of New Mexico
Neutrosophic Treesoft Expert Set And Forestsoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [28,57],Neutrosophic Sets [42,44], and Plithogenic Sets [48] have been extensively studied to address uncertainty, finding diverse applications across various fields. The Soft Set provides a framework that associates each parameter with subsets of a universal set, enabling flexible approximations [31]. The TreeSoft Set extends the Soft Set by introducing hierarchical, tree-structured parameters, allowing for multi-level data representation [53]. In this paper, we revisit the concept of the Neutrosophic TreeSoft Set, which has been discussed in other studies [8, 34]. Additionally, we propose and examine the Neutrosophic TreeSoft Expert Set by incorporating the framework of the …
Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing,
2025
University of New Mexico
Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing, Muhammad Saeed, Neha Andaleeb Khalid, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper proposes a modified structure for the neutrosophic set called the Quantified Neutrosophic Set (QtNS) with a parameterized setting. Unlike conventional approaches, the QtNS provides a quantified environment for the indeterminacy by its dependence on truthness and falsity components. This innovative approach quantifies the uncertainty and improves the assessment process via expert-guided opinions, customising it according to the specific situations in real-world decision-making scenarios. Some QtNS operations along with useful characteristics are addressed. Furthermore, two algorithms, QtNSUI and QtNSAO, are developed for the proposed operations of union, intersection, AND, and OR based on QtNS. In the world of sustainable …
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set,
2025
University of New Mexico
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic,
2025
University of New Mexico
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in …
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra,
2025
University of New Mexico
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.
