{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:15Z","timestamp":1760234055779,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures\u2019 operations and\/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as NeutroHv-Semigroups and study their properties by providing several illustrative examples.<\/jats:p>","DOI":"10.3390\/sym13040535","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T21:09:45Z","timestamp":1616706585000},"page":"535","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["On Some NeutroHyperstructures"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4243-7935","authenticated-orcid":false,"given":"Madeleine","family":"Al-Tahan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lebanese International University, Bekaa 1803, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1941-5372","authenticated-orcid":false,"given":"Bijan","family":"Davvaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd 89139, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Mathematics and Science Division, Gallup Campus, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osman","family":"Anis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lebanese International University, Akkar 35111, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"ref_1","first-page":"8","article-title":"NeutroAlgebra is a Generalization of Partial Algebra","volume":"2","author":"Smarandache","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_2","unstructured":"Smarandache, F. (2019). Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures. Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House. Available online: http:\/\/fs.unm.edu\/AdvancesOfStandardAndNonstandard.pdf."},{"key":"ref_3","first-page":"1","article-title":"Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)","volume":"31","author":"Smarandache","year":"2020","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_4","first-page":"41","article-title":"Introduction to NeutroGroups","volume":"6","author":"Agboola","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_5","first-page":"62","article-title":"Introduction to NeutroRings","volume":"7","author":"Agboola","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_6","first-page":"133","article-title":"NeutroOrderedAlgebra: Applications to Semigroups","volume":"39","author":"Smarandache","year":"2021","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_7","unstructured":"Al-Tahan, M., Davvaz, B., Smarandache, F., and Osman, O. (2021). On Some Properties of Productional NeutroOrderedSemigroups, submitted."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"110","DOI":"10.54216\/IJNS.080204","article-title":"Neutro-BCK-Algebra","volume":"8","author":"Hamidi","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_9","first-page":"8","article-title":"On Neutro-BE-algebras and Anti-BE-algebras","volume":"4","author":"Rezaei","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_10","first-page":"8","article-title":"A New Trend to Extensions of CI-algebras","volume":"5","author":"Smarandache","year":"2020","journal-title":"Int. J. Neutrosophic Sci. IJNS"},{"key":"ref_11","unstructured":"Marty, F. (1934, January 14\u201318). Sur une generalization de la notion de groupe. Proceedings of the 8th Congress on Mathmatics, Scandinaves, Stockholm, Sweden."},{"key":"ref_12","first-page":"9","article-title":"Chemical Hyperstructures for Astatine, Tellurium and for Bismuth","volume":"7","author":"Davvaz","year":"2019","journal-title":"Bull. Comput. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.jnt.2016.10.017","article-title":"On the Existence of Hyperrings Associated to Arithmetic Functions","volume":"174","author":"Davvaz","year":"2017","journal-title":"J. Number Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.mbs.2017.01.002","article-title":"Algebraic Hyperstructures Associated to Biological Inheritance","volume":"285","author":"Davvaz","year":"2017","journal-title":"Math. Biosci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Davvaz, B., and Al-Tahan, M. (2020). Calculus of Meet Plus Hyperalgebra (Tropical Semihyperrings). Commun. Algebra, 48.","DOI":"10.1080\/00927872.2019.1710178"},{"key":"ref_16","unstructured":"Corsini, P. (1993). Prolegomena of Hypergroup Theory, Udine Aviani Editore."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Davvaz, B. (2013). Polygroup Theory and Related Systems, World Scientific Publishing Co., Pte. Ltd.","DOI":"10.1142\/8593"},{"key":"ref_18","unstructured":"Davvaz, B., and Leoreanu-Fotea, V. (2008). Hyperring Theory and Applications, International Academic Press."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Vougiouklis, T. (1991). The Fundamental Relation in Hyperrings. The General Hyperfield. Proceedings of the Fourth International Congress on Algebraic Hyperstructures and Applications (AHA 1990), World Scientific.","DOI":"10.1142\/9789814539555"},{"key":"ref_20","unstructured":"Vougiouklis, T. (1994). Hyperstructures and Their Representations, Hadronic Press, Inc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0012-365X(94)00390-5","article-title":"Hv-groups Defined on the Same Set","volume":"155","author":"Vougiouklis","year":"1996","journal-title":"Discret. Math."},{"key":"ref_22","first-page":"90","article-title":"Weak Hyperstructures on Small Sets","volume":"12","author":"Vougiouklis","year":"1997","journal-title":"Ratio Math."},{"key":"ref_23","first-page":"15","article-title":"Introduction to NeutroHyperGroups","volume":"38","author":"Ibrahim","year":"2020","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_24","first-page":"290","article-title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-\/Neutro-\/Anti-)HyperAlgebra","volume":"33","author":"Smarandache","year":"2020","journal-title":"Neutrosophic Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/535\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:40:51Z","timestamp":1760161251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/535"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,25]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["sym13040535"],"URL":"https:\/\/doi.org\/10.3390\/sym13040535","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,3,25]]}}}