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Journal articles on the topic 'Hyperstructure'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Novák, Michal, Štepán Křehlík, and Kyriakos Ovaliadis. "Elements of Hyperstructure Theory in UWSN Design and Data Aggregation." Symmetry 11, no. 6 (2019): 734. http://dx.doi.org/10.3390/sym11060734.

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In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying nodes or operating the network we, from the mathematical point of view, regard an operation (or a hyperoperation) and a binary relation. In this part of the paper we relate our context to already existing topics of the algebraic hyperstructure theory such as quasi-order hypergroups, E L -hyperstructures, or ordered hyperstructures. Furthermore, we make use of the theory o

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2

Rao, Yongsheng, Jietong Zhao, Aysha Khan, Maryam Akhoundi, and Saber Omidi. "An Investigation on Weak Concepts in Ordered Hyperstructures." Symmetry 13, no. 12 (2021): 2300. http://dx.doi.org/10.3390/sym13122300.

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The class of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures is a generalization of pseudoorders and interior hyperideals. In this work, we study the concept of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures and explore some results concerning the new defined concepts for ordered hyperrings and ordered Γ-semihypergroups. In this regards, we intend to concentrate our efforts on the relationship between the left weak interior hyperideal and interior hyperideal of an ordered hyperstructure. A characterization of a regular ordered hy

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Al-Tahan, M., and B. Davvaz. "N-ary hyperstructures associated to the genotypes of F2-offspring." International Journal of Biomathematics 10, no. 08 (2017): 1750118. http://dx.doi.org/10.1142/s1793524517501182.

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In this paper, we consider an application of hyperstructure theory in biological inheritance in which we deal with [Formula: see text]-ary hyperstructures associated to the genotypes of the second generation [Formula: see text] for [Formula: see text]. First, we define a hyperoperation × (mating) on [Formula: see text] and prove that it is a cyclic [Formula: see text]-semigroup under the defined hyperoperation. Then we define a ternary hyperstructure [Formula: see text] associated to the genotypes of [Formula: see text] and prove that [Formula: see text] is a ternary [Formula: see text]-semigr

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Novák, Michal, Štepán Křehlík, and Irina Cristea. "Cyclicity in EL–Hypergroups." Symmetry 10, no. 11 (2018): 611. http://dx.doi.org/10.3390/sym10110611.

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In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers the nature of generalizing this property, at least two (or rather three) approaches seem natural. Historically, all of these had been introduced and studied by 1990. However, since most of the results had originally been published in journals without proper international impact and later—without the possibility to include proper background and contex

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5

Novák, Michal. "n–ary hyperstructures constructed from binary quasi–ordered semigroups." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 3 (2014): 147–68. http://dx.doi.org/10.2478/auom-2014-0056.

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AbstractBased on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.

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6

Macodi-Ringia, Amila Pagadilan, and Gaudencio Cempron Petalcorin. "On Intuitionistic Fuzzy Hyper GR-ideals in Hyper GR-algebras." European Journal of Pure and Applied Mathematics 13, no. 2 (2020): 246–57. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3660.

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Let $P(H)$ be the power set of $H$. Consider $\ds P^*(H)=P(H)\setminus\{\phi\}$. A hyperoperation on a nonempty set $H$ is a function $\ds\circledast:H\times H\rightarrow P^*(H).$ A set $H$ endowed with a family $\Gamma$ of hyperoperations is called ahyperstructure. Hyperstructures have many applications to several sectors of both pure and applied sciences. One of the well developed hyperstructures is the hyper BCI-algebra. Recently, by following this hyperstructure, a new hyperstructure was created by Indangan et al., named as hyper GR-algebras. In this paper, fuzzy set and intuitionistic fuz

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Huwae, Elsa, Henry Willyam Michel Patty, Dorteus L. Rahakbauw, and Novita Dahoklory. "Algebra Hyperstructure Concept and Its Application on Oxidation Reduction: Actinium (Ac) and Berkelium (Bk)." Tensor: Pure and Applied Mathematics Journal 5, no. 1 (2024): 33–48. https://doi.org/10.30598/tensorvol5iss1pp33-48.

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The concept of algebraic hyperstructure is a generalization of the concept of algebraic structure. The algebraic hyperstructure concepts discussed in this research include hypergroups, semihypergroups, and -group and it is known that this concept has application in the field of science, one of which in the field of chemistry, namely redox reactions. The aim of this research is to discuss the concept of algebraic hyperstructures and its application in redox reactions of the elements actinium and berkelium . In this research, the redox reactions of the elements actinium and berkelium were obtain

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8

BAAS, NILS A. "HYPERSTRUCTURES AS ABSTRACT MATTER." Advances in Complex Systems 09, no. 03 (2006): 157–82. http://dx.doi.org/10.1142/s0219525906000732.

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We give a new introduction to hyperstructures and higher order structures in general. A specific implementation of a hyperstructure we call Abstract Matter, and we argue that this is a suitable model for studying and simulating various kinds of both organic and inorganic matter — even cognitive matter.

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9

Křehlík, Štěpán, and Michal Novák. "From lattices to Hv-matrices." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (2016): 209–22. http://dx.doi.org/10.1515/auom-2016-0055.

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AbstractIn this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

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10

Labrecque, Nicolas, Sylvain Ménard, Marc Oudjene, and Pierre Blanchet. "Finite Element Study of Hyperstructure Systems with Modular Light-Frame Construction in High-Rise Buildings." Buildings 12, no. 3 (2022): 330. http://dx.doi.org/10.3390/buildings12030330.

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To answer both the growth of the world’s urban population and the climate changes, new structural systems with high prefabrication levels and renewable materials need to be developed. A novel structural system that could enable the use of modular light-frame construction in high-rise buildings was modeled and analyzed. This system was achieved by having a hyperstructure carrying the loads of four-story light-frame superposed substructures. Two 20-story hyperstructures, one using glulam and another one using reinforced concrete, were designed according to the 2015 National Building Code of Cana

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11

Al Tahan, M., and B. Davvaz. "H_v -module of functions over H_v -ring of arithmetics and it’s fundamental module." Analele Universitatii "Ovidius" Constanta - Seria Matematica 32, no. 1 (2024): 5–18. https://doi.org/10.2478/auom-2024-0001.

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Abstract After introducing the definition of hypergroups by Marty, the study of hyperstructures and its connections with other fields has been of great importance. In this paper, we continue the investigation between hyperstructure theory and number theory. More precisely, we define an Hv -module of complex valued functions over the Hv -ring of arithmetics, classify its complete parts, the strongly regular relations on it and identify its fundamental module.

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Alamsyah, Alifa Raida, Edi Kurniadi, and Anita Triska. "Penentuan Hiperstruktur Aljabar dan Karakteristiknya dalam Masalah Pewarisan Biologi." Jambura Journal of Mathematics 7, no. 1 (2025): 28–33. https://doi.org/10.37905/jjom.v7i1.28270.

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This article discusses the application of mathematics in biological inheritance problems, which are closely linked to mathematical studies, particularly in algebraic hyperstructures, including hypergroupoids, hypergroups, and -semigroups. The research aims to determine types of algebraic hyperstructures arising from genetic crossing in inheritance issues, with the crossing results represented in a set where two distinct hyperoperations are applied. Findings indicate that under the first hyperoperation, the algebraic hyperstructures formed include a commutative hypergroup, a regular hypergroup,

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Yamak, S., O. Kazancı, and B. Davvaz. "Soft hyperstructure." Computers & Mathematics with Applications 62, no. 2 (2011): 797–803. http://dx.doi.org/10.1016/j.camwa.2011.06.009.

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14

Farshi, Mahdi, and Bijan Davvaz. "Generalized fuzzy hypergraphs and hypergroupoids." Filomat 30, no. 9 (2016): 2375–87. http://dx.doi.org/10.2298/fil1609375f.

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This article first generalizes the ordinary fuzzy hypergraphs to generalized fuzzy hypergraphs and it makes a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. We construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Moreover, we construct higher order fuzzy hypergroupoids and study their properties. Finally, by considering a regular equivalence relation on a (g-f)p-hypergroupoid, we define a quotient (g-f)phypergroupoid and we investigate some relationships between diagonal product of hypergroupoids

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15

Oguz, Gulay, and Bijan Davvaz. "Soft topological hyperstructure." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 8755–64. http://dx.doi.org/10.3233/jifs-200242.

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Molodtsov proposed the theory of soft sets which can be considered as a recent mathematical tool to deal with uncertainties. The main purpose of this paper is to give the definition of soft topological hypergrupoid by examining the concept of hypergrupoid which is one of the hyperystructures with soft set theory from the topological point of view. Also, the relation between soft topological hypergroupoids and soft hypergroupoids is examined and some theoretical results are obtained. By introducing the concept of soft good topological homomorphism, the category of soft topological hypergrupoids

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16

CRIADO, R., M. ROMANCE, and M. VELA-PÉREZ. "HYPERSTRUCTURES, A NEW APPROACH TO COMPLEX SYSTEMS." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 877–83. http://dx.doi.org/10.1142/s0218127410026162.

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We define a new concept, a hyperstructure, which is related to networks and hypernetworks and allows us to represent real problems. We also define the efficiency of this hyperstructure and we apply it to an example.

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17

Kohiyama, Masamichi, John Herrick, and Vic Norris. "Open Questions about the Roles of DnaA, Related Proteins, and Hyperstructure Dynamics in the Cell Cycle." Life 13, no. 9 (2023): 1890. http://dx.doi.org/10.3390/life13091890.

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The DnaA protein has long been considered to play the key role in the initiation of chromosome replication in modern bacteria. Many questions about this role, however, remain unanswered. Here, we raise these questions within a framework based on the dynamics of hyperstructures, alias large assemblies of molecules and macromolecules that perform a function. In these dynamics, hyperstructures can (1) emit and receive signals or (2) fuse and separate from one another. We ask whether the DnaA-based initiation hyperstructure acts as a logic gate receiving information from the membrane, the chromoso

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18

Hila, Kostaq, and Jani Dine. "On Hyperideals in Left Almost Semihypergroups." ISRN Algebra 2011 (September 14, 2011): 1–8. http://dx.doi.org/10.5402/2011/953124.

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This paper deals with a class of algebraic hyperstructures called left almost semihypergroups (LA-semihypergroups), which are a generalization of LA-semigroups and semihypergroups. We introduce the notion of LA-semihypergroup, the related notions of hyperideal, bi-hyperideal, and some properties of them are investigated. It is a useful nonassociative algebraic hyperstructure, midway between a hypergroupoid and a commutative hypersemigroup, with wide applications in the theory of flocks, and so forth. We define the topological space and study the topological structure of LA-semihypergroups usin

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19

Al Tahan, M., and B. Davvaz. "The cyclic hypergroup associated with Sn, its automorphism group and its fuzzy grade." Discrete Mathematics, Algorithms and Applications 10, no. 05 (2018): 1850070. http://dx.doi.org/10.1142/s1793830918500702.

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Hyperstructure is the generalized concept of algebraic structure. The study of it and its applications is extremely interesting, offering interesting results to one who is willing to look for structure. This paper deals with hyperstructures associated to the symmetric group [Formula: see text]. First, we define a new hyperoperation [Formula: see text] on [Formula: see text] and study its properties. Next, we prove that [Formula: see text] is a single-power cyclic hypergroup with finite period. Then, we determine the set of all automorphisms of [Formula: see text] and prove that it is a finite

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20

Norris, Vic, Tanneke den Blaauwen, Roy H. Doi, et al. "Toward a Hyperstructure Taxonomy." Annual Review of Microbiology 61, no. 1 (2007): 309–29. http://dx.doi.org/10.1146/annurev.micro.61.081606.103348.

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21

Brown, Robert D., Geoffrey M. Downs, Peter Willett, and A. P. F. Cook. "Hyperstructure model for chemical structure handling: generation and atom-by-atom searching of hyperstructures." Journal of Chemical Information and Modeling 32, no. 5 (1992): 522–31. http://dx.doi.org/10.1021/ci00009a020.

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22

Cristea, Irina, Juš Kocijan, and Michal Novák. "Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures." Mathematics 7, no. 10 (2019): 885. http://dx.doi.org/10.3390/math7100885.

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The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are H v -groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, t

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23

Kazancı, Osman, Sarka Hoskova-Mayerova, and Bijan Davvaz. "Application Multi-Fuzzy Soft Sets in Hypermodules." Mathematics 9, no. 18 (2021): 2182. http://dx.doi.org/10.3390/math9182182.

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The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy soft hyperstructure. We investigate the notion of multi-fuzzy soft hypermodules and some of their structural properties are discussed. We discuss the behavior image and inverse image of a multi-fuzzy soft set under the multi-fuzzy soft function. According to Zadeh’s extension principle, we prove that the image and inverse image of a multi-fuzzy soft hypermodules are further multi-fuzzy soft hypermodule.

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24

Trinei, Mirella, Jean-Pierre Vannier, Marie Beurton-Aimar, and Vic Norris. "A hyperstructure approach to mitochondria." Molecular Microbiology 53, no. 1 (2004): 41–53. http://dx.doi.org/10.1111/j.1365-2958.2004.04141.x.

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25

Lei, Xiaofei, Peng Chen, Heping Hou, Shanhui Liu, and Peng Liu. "Longitudinal vibration wave in the composite elastic metamaterials containing Bragg structure and local resonator." International Journal of Modern Physics B 34, no. 26 (2020): 2050232. http://dx.doi.org/10.1142/s021797922050232x.

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In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the establi

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26

Brailsford, David F. "Separable hyperstructure and delayed link binding." ACM Computing Surveys 31, no. 4es (1999): 30. http://dx.doi.org/10.1145/345966.346029.

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27

Muhiuddin, Ghulam, Nabilah Abughazalah, Ahsan Mahboob, and Abdullah G. Alotaibi. "Hyperstructure Theory Applied to BF-Algebras." Symmetry 15, no. 5 (2023): 1106. http://dx.doi.org/10.3390/sym15051106.

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This study applies the hyperstructure theory to BF-algebra, which is an algebraic structure. In fact, we define hyper-BF-algebras and hyper-BF ideals and investigate several of their related characteristics. BF-algebra and hyper-BF ideal characteristics are taken into account, and supported examples are built. Here, we also develop new concepts known as hyper-B-algebra, hyper-BG-algebra, and hyper-BH algebra as generalizations of other classes of hyper-BCK-/BCI-algebras. Additionally, we demonstrate that each hyper-BF is a weak hyper-BF in hyper-BF-algebra, but the opposite is not true. It is

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28

BROWN, R. D., G. M. DOWNS, P. WILLETT, and A. P. F. COOK. "ChemInform Abstract: A Hyperstructure Model for Chemical Structure Handling: Generation and Atom-by-Atom Searching of Hyperstructures." ChemInform 24, no. 4 (2010): no. http://dx.doi.org/10.1002/chin.199304286.

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29

MACALOON, JOHN J. "Hyperstructure, hierarchy and humanitas in Olympic ritual." Anthropology Today 35, no. 3 (2019): 7–10. http://dx.doi.org/10.1111/1467-8322.12504.

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30

Fujita, Takaaki, and Florentin Smarandache. "Examples of Fuzzy Sets, Hyperfuzzy Sets, and SuperHyperfuzzy Sets in Climate Change and the Proposal of Several New Concepts." Climate Change Reports 2 (February 7, 2025): 1–18. https://doi.org/10.61356/j.ccr.2025.2485.

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A fuzzy set generalizes classical set theory by assigning each element a membership value within [0, 1], allowing for the representation of partial or uncertain membership. It is well established that fuzzy sets can be further extended to Hyperfuzzy sets and SuperHyperfuzzy sets. However, as these concepts have been introduced only recently, their practical applications remain largely unexplored. In this paper, we investigate potential applications of Fuzzy sets, Hyperfuzzy sets, and SuperHyperfuzzy sets in the context of climate change and environmental factors. Additionally, we introduce the

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31

Harijani, Kh, and S. Anvariyeh. "A hypervaluation of a hyperfield onto a totally ordered canonical hypergroup." Studia Scientiarum Mathematicarum Hungarica 52, no. 1 (2015): 87–101. http://dx.doi.org/10.1556/sscmath.52.2015.1.1303.

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This paper attempts an exposition of the connection between valuation theory and hyperstructure theory. In this regards, by considering the notion of totally ordered canonical hypergroup we define a hypervaluation of a hyperfield onto a totally ordered canonical hypergroup and obtain some related basic results.

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Imran, Muhammad, Huaping Wang, Yuyu Jiang, Zhiwei Xu, and Lian Shen. "Harnessing graphene-hBN hyperstructure for single-photon sources." Optics Express 27, no. 12 (2019): 16461. http://dx.doi.org/10.1364/oe.27.016461.

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33

Baas, Nils A. "Extended Memory Evolutive Systems in a Hyperstructure Context." Axiomathes 19, no. 2 (2009): 215–21. http://dx.doi.org/10.1007/s10516-009-9066-3.

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Cheng, Min, Ping Fu, and Shengyu Chen. "Tunable Dyakonov surface waves in graphene-hBN hyperstructure." Optics Communications 482 (March 2021): 126630. http://dx.doi.org/10.1016/j.optcom.2020.126630.

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35

Singh, N. B., David House, and Bradley Arnold. "Hyperstructure and Meta Morphology Formation in Heavy Metal Chalcogenides." International Journal of Advanced Materials Manufacturing and Characterization 3, no. 1 (2013): 15–19. http://dx.doi.org/10.11127/ijammc.2013.02.004.

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36

Maturo, Antonio. "Finitely additive conditional probabilities with values on a hyperstructure." Journal of Information and Optimization Sciences 22, no. 2 (2001): 227–40. http://dx.doi.org/10.1080/02522667.2001.10699486.

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37

Kazancı, Osman, Sarka Hoskova-Mayerova, and Bijan Davvaz. "Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups." Mathematics 10, no. 13 (2022): 2178. http://dx.doi.org/10.3390/math10132178.

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The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. I

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38

Zhang, Xiaohong, Florentin Smarandache, and Yingcang Ma. "Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups." Symmetry 11, no. 10 (2019): 1217. http://dx.doi.org/10.3390/sym11101217.

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The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture th

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39

Downs, G. M., G. S. Gill, P. Willett, and P. Walsh. "Automated Descriptor Selection and Hyperstructure Generation to Assist SAR Studies." SAR and QSAR in Environmental Research 3, no. 4 (1995): 253–64. http://dx.doi.org/10.1080/10629369508050152.

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Brown, Robert D., Geoffrey M. Downs, Gareth Jones, and Peter Willett. "Hyperstructure model for chemical structure handling: Techniques for substructure searching." Journal of Chemical Information and Modeling 34, no. 1 (1994): 47–53. http://dx.doi.org/10.1021/ci00017a006.

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41

Maurer, H., N. Scherbakov, K. Andrews, and P. Srinivasan. "Object-oriented modelling of hyperstructure: overcoming the static link deficiency." Information and Software Technology 36, no. 6 (1994): 315–22. http://dx.doi.org/10.1016/0950-5849(94)90031-0.

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42

Davvaz, Bijan, A. Dehghan Nezhad, and S. M. Moosavi Nejad. "Algebraic Hyperstructure of Observable Elementary Particles Including the Higgs Boson." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 90, no. 1 (2018): 169–76. http://dx.doi.org/10.1007/s40010-018-0553-z.

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OSTADHADI-DEHKORDI, S. "Chain Condition and Fundamental Relation on (∆;G)-Sets Derived from Gamma-Semihypergroups." Kragujevac Journal of Mathematics 45, no. 01 (2021): 21–37. http://dx.doi.org/10.46793/kgjmat2101.021o.

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The aim of this research work is to deﬁne a new class of hyperstructure as a generalization of semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, we deﬁne fundamental relation on (Δ,G)-sets and prove some results in this respect. Then, we introduce the notions of quotient (Δ,G)-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) (Δ,G)-sets.

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Lei, X. F., H. P. Hou, P. Liu, Z. F. Xu, S. H. Liu, and B. B. Hu. "Flexural vibration band gaps in Bragg acoustical hyperstructure beam with local-resonance system." Modern Physics Letters B 33, no. 23 (2019): 1950278. http://dx.doi.org/10.1142/s0217984919502786.

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Bragg acoustical hyperstructure can scatter elastic wave, local resonance system can fight against vibration by the reaction force with reversed phase in low-frequency range, for improving the scattering performance of Bragg hyperstructure, a novel composite beam of Bragg beam with local resonator is investigated theoretically. Its dispersion relations and bang gaps are calculated by the established theoretical model. In order to confirm the veritable existence of band gaps, the transmission spectrum of flexural vibration waves are also studied by finite-element method, and comparing the relat

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45

Norris, Vic. "Division in bacteria is determined by hyperstructure dynamics and membrane domains." Journal of Biological Physics and Chemistry 01, no. 01 (2001): 29–37. http://dx.doi.org/10.4024/06no01a.01.01.

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MAUS, C., F. FONTAINE, G. VAN DEN BOSSCHE, R. SOBRY, and R. JÉRÔME. "SAXS analysis of hyperstructure in carboxylato-telechelic poly(tert.butyl acrylate)'s." Le Journal de Physique IV 03, no. C8 (1993): C8–67—C8–70. http://dx.doi.org/10.1051/jp4:1993814.

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Cabin-Flaman, Armelle, Camille Ripoll, Milton H. Saier Jr., and Vic Norris. "Hypothesis: Chemotaxis in Escherichia coli Results from Hyperstructure Dynamics." Journal of Molecular Microbiology and Biotechnology 10, no. 1 (2005): 1–14. http://dx.doi.org/10.1159/000090343.

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48

Al-Odhari, Adel. "A Brief Comparative Study on HyperStructure, SuperHyperStructure, and n- Super SuperHyperStructure." Neutrosophic Knowledge 6 (March 30, 2025): 38–49. https://doi.org/10.5281/zenodo.15107294.

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Abstract:  This article compares Hyperfunction, Extra Hyperfunction, Super Hyperfunction, and Extra Super  Hyperfunction depending on the nth-PowerSet. The nth-PowerSet reflects many real-world  problems because any ontological object, like a system, organization, country, or entity, can be  represented by systems and subsystems by the nth-PowerSet. This article will review the concepts  and investigate some theorems and examples.    Keywords: nth-PowerSet, HyperFunction, Extra HyperFunction, SuperHyperFunction, and Extra  SuperHyperFunction.

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Wang, Yingxu, and Jun Peng. "Big Data Analytics." International Journal of Cognitive Informatics and Natural Intelligence 11, no. 2 (2017): 41–56. http://dx.doi.org/10.4018/ijcini.2017040103.

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Big data are pervasively generated by human cognitive processes, formal inferences, and system quantifications. This paper presents the cognitive foundations of big data systems towards big data science. The key perceptual model of big data systems is the recursively typed hyperstructure (RTHS). The RTHS model reveals the inherited complexities and unprecedented difficulty in big data engineering. This finding leads to a set of mathematical and computational models for efficiently processing big data systems. The cognitive relationship between data, information, knowledge, and intelligence is

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Qiu, Dong, and Weiquan Zhang. "Convexity Invariance of Fuzzy Sets under the Extension Principles." Journal of Function Spaces and Applications 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/849104.

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We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.

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