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Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation \u03b1 i 1 i 2 \u2217 on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation \u03b1 J \u2217 on the set of strong identities.<\/jats:p>","DOI":"10.3233\/jifs-210994","type":"journal-article","created":{"date-parts":[[2021,7,7]],"date-time":"2021-07-07T05:26:13Z","timestamp":1625635573000},"page":"2265-2274","source":"Crossref","is-referenced-by-count":1,"title":["Fundamental relations and identities of fuzzy hyperalgebras"],"prefix":"10.1177","volume":"41","author":[{"given":"Narjes","family":"Firouzkouhi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Golestan University, Gorgan, Iran"}]},{"given":"Abbas","family":"Amini","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Australian College of Kuwait, Mishref, Safat 13015, Kuwait and Centre for Infrastructure Engineering, Western Sydney University, Penrith 2751, NSW, Australia"}]},{"given":"Chun","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People\u2019s Republic of China"}]},{"given":"Mehdi","family":"Soleymani","sequence":"additional","affiliation":[{"name":"Department of Statistics, The University of Auckland, Auckland, New Zealand"}]},{"given":"Bijan","family":"Davvaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd, Iran"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-210994_ref1","doi-asserted-by":"crossref","unstructured":"Zadeh L.A. , Klir G.J. , Yuan B. , Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers (Vol. 6), World Scientific (1996).","DOI":"10.1142\/2895"},{"issue":"1","key":"10.3233\/JIFS-210994_ref3","first-page":"29","article-title":"On fuzzy hypergroups","volume":"8","author":"Corsini","year":"1997","journal-title":"Pure Mathematics and Applications"},{"issue":"9","key":"10.3233\/JIFS-210994_ref4","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1007\/s00500-007-0257-9","article-title":"Fuzzy hypersemigroups","volume":"12","author":"Sen","year":"2008","journal-title":"Soft Computing"},{"issue":"16","key":"10.3233\/JIFS-210994_ref5","doi-asserted-by":"crossref","first-page":"2366","DOI":"10.1016\/j.fss.2008.11.007","article-title":"Fuzzy hyperrings","volume":"160","author":"Leoreanu-Fotea","year":"2009","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"10.3233\/JIFS-210994_ref6","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.camwa.2008.11.004","article-title":"Fuzzy hypermodules","volume":"57","author":"Fotea","year":"2009","journal-title":"Computers and Mathematics with Applications"},{"issue":"2","key":"10.3233\/JIFS-210994_ref7","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.camwa.2010.08.059","article-title":"Fuzzy hyperalgebras","volume":"61","author":"Ameri","year":"2011","journal-title":"Computers and Mathematics with Applications"},{"issue":"1","key":"10.3233\/JIFS-210994_ref8","first-page":"43","article-title":"Term functions and fundamental relation of fuzzy hyperalgebras","volume":"20","author":"Ameri","year":"2010","journal-title":"Ratio Mathematica"},{"issue":"4","key":"10.3233\/JIFS-210994_ref9","doi-asserted-by":"crossref","first-page":"5179","DOI":"10.3233\/JIFS-190016","article-title":"Fuzzy soft hyperalgebras","volume":"37","author":"Nozari","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-210994_ref11","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1017\/S1446788700014671","article-title":"Multialgebras, universal algebras and identities","volume":"81","author":"Pelea","year":"2006","journal-title":"Journal of the Australian Mathematical Society"},{"key":"10.3233\/JIFS-210994_ref12","unstructured":"Pelea C. , Purdea I. , Identities in multialgebra theory, In Proceedings of the 10th International Congress on Algebraic Hyperstructures and Applications, Brno, Czech Republic (pp. 251\u2013266). 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