{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T02:46:17Z","timestamp":1773024377881,"version":"3.50.1"},"reference-count":27,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,3,9]]},"abstract":"<jats:p>We study the lattice structure of fuzzy A-ideals in an mv-module M (fai\u00a0(M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai\u00a0(M) can be embedded into the lattice of fuzzy congruences.<\/jats:p>","DOI":"10.3233\/jifs-221552","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T10:07:58Z","timestamp":1670580478000},"page":"4509-4519","source":"Crossref","is-referenced-by-count":2,"title":["Construction of some algebras of logic by using fuzzy ideals in mv-modules"],"prefix":"10.1177","volume":"44","author":[{"given":"M.","family":"Bakhshi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Bojnord, Bojnord, Iran"}]},{"given":"S. S.","family":"Ahn","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Dongguk University, Seoul, Korea"}]},{"given":"Y. B.","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju, Korea"}]},{"given":"X. L.","family":"Xin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northwest University, Xi\u2019an, P.R. China"}]},{"given":"R. A.","family":"Borzooei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahid Beheshti University of Tehran, Tehran, Iran"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-221552_ref1","first-page":"107","article-title":"L-fuzzy A-Ideals of MV-modules","volume":"28","author":"Bakhshi","year":"2017","journal-title":"International Journal of Mathematics and Computation"},{"key":"10.3233\/JIFS-221552_ref2","doi-asserted-by":"crossref","first-page":"3305","DOI":"10.1016\/j.ins.2007.02.015","article-title":"Lattice structure on fuzzy congruence relations of a hypergroupoid","volume":"177","author":"Bakhshi","year":"2007","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-221552_ref3","doi-asserted-by":"crossref","first-page":"2050131","DOI":"10.1142\/S0219498820501315","article-title":"Saeid, MV-modules of fractions","volume":"19","author":"Banivaheb","year":"2020","journal-title":"Journal of Algebra and Its Applications"},{"key":"10.3233\/JIFS-221552_ref4","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.ijar.2003.09.003","article-title":"Elementary calculus in Riesz MV-algebras","volume":"36","author":"Bede","year":"2004","journal-title":"International Journal of Approximate Reasoning"},{"key":"10.3233\/JIFS-221552_ref5","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1017\/jsl.2014.53","article-title":"Algebraic geometry for MV-algebras","volume":"79","author":"Belluce","year":"2014","journal-title":"Journal of Symbolic Logic"},{"key":"10.3233\/JIFS-221552_ref6","unstructured":"Blyth T.S. , Lattices and ordered algebraic structures, Springer-Verlag, 2005."},{"key":"10.3233\/JIFS-221552_ref7","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.fss.2013.12.007","article-title":"State BCK algebras and state-morphism BCK-algebras","volume":"244","author":"Borzooei","year":"2014","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-221552_ref8","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","article-title":"Algebraic analysis of many valued logics","volume":"88","author":"Chang","year":"1958","journal-title":"Transactions of the American Mathematical Society"},{"key":"10.3233\/JIFS-221552_ref9","unstructured":"Cignoli R.L. , D\u2019Ottaviano I.M. and Mundici D. , Algebraic Foundations of Many-valued Reasoning, Springer Science & Business Media, 2013."},{"key":"10.3233\/JIFS-221552_ref10","first-page":"193","article-title":"Product MV-algebras","volume":"6","author":"Di Nola nd","year":"2001","journal-title":"Multiple-Valued Logic"},{"key":"10.3233\/JIFS-221552_ref11","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0021-8693(03)00332-6","article-title":"MV-modules","volume":"276","author":"Di Nola","year":"2003","journal-title":"Journal of Algebra"},{"key":"10.3233\/JIFS-221552_ref12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.29252\/hatef.jahla.1.2.1","article-title":"On the free S 1 w - free algebras","volume":"1","author":"Di Nola","year":"2020","journal-title":"Journal of Algebraic Hyperstructures and Logical Algebras"},{"key":"10.3233\/JIFS-221552_ref13","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF01057937","article-title":"Perfect MV-algebras are categorically equivalent to abelian \u2018-groups","volume":"53","author":"Di Nola","year":"1994","journal-title":"Studia Logica"},{"key":"10.3233\/JIFS-221552_ref14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.52547\/HATEF.JAHLA.3.1.4","article-title":", A short note on categorical equivalences of proper weak EMV-algebras","volume":"3","author":"Dvurecenskij","year":"2022","journal-title":"Journal of Algebraic Hyperstructures and Logical Algebras"},{"key":"10.3233\/JIFS-221552_ref15","first-page":"477","article-title":"Fuzzy A-ideals in MV-modules","volume":"10","author":"Forouzesh","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"10.3233\/JIFS-221552_ref17","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0165-0114(94)90099-X","article-title":"Fuzzy implicative and Boolean ideals of MValgebras","volume":"66","author":"Hoo","year":"1994","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-221552_ref18","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0165-0114(94)90078-7","article-title":"Fuzzy ideals of BCI and MV-algebras","volume":"62","author":"Hoo","year":"1994","journal-title":"Fuzzy Sets and Systems"},{"issue":"2","key":"10.3233\/JIFS-221552_ref19","doi-asserted-by":"crossref","first-page":"45","DOI":"10.29252\/hatef.jahla.1.2.5","article-title":"Hyper equality ideals: Basic properties","volume":"1","author":"Paad","year":"2020","journal-title":"Journal of Algebraic Hyperstructures and Logical Algebras"},{"key":"10.3233\/JIFS-221552_ref20","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1023\/A:1022801907138","article-title":"DRL-semigroups and MV-algebras","volume":"48","author":"Rach\u016fnek","year":"1998","journal-title":"Czechoslovak Mathematical Journal"},{"key":"10.3233\/JIFS-221552_ref21","first-page":"1981","article-title":"A Course in Universal Algebra","volume":"78","author":"Sankappanavar","journal-title":"Graduate Text in Mathematics"},{"key":"10.3233\/JIFS-221552_ref22","first-page":"283","article-title":"On Injective MVModules","volume":"47","author":"Saidi Goraghani","year":"2018","journal-title":"Bulletin of the Section of Logic"},{"key":"10.3233\/JIFS-221552_ref23","first-page":"1","article-title":"Most results on Aideals in MV-modules","volume":"5","author":"Saidi Goraghani","year":"2017","journal-title":"Journal of Algebraic Systems"},{"key":"10.3233\/JIFS-221552_ref24","doi-asserted-by":"crossref","first-page":"794","DOI":"10.2991\/ijcis.d.200602.001","article-title":"New kind of MV-modules","volume":"13","author":"Saidi Goraghani","year":"2020","journal-title":"International Journal of Computational Intelligence Systems"},{"key":"10.3233\/JIFS-221552_ref25","doi-asserted-by":"crossref","first-page":"269","DOI":"10.18778\/0138-0680.2020.17","article-title":"Module structure on effect algebras","volume":"49","author":"Saidi Goraghani","year":"2020","journal-title":"Bulletin of the Section of Logic"},{"key":"10.3233\/JIFS-221552_ref26","first-page":"183","article-title":"Results on prime ideals in PMV-algebras and MV-modules","volume":"37","author":"Saidi Goraghani","year":"2017","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"10.3233\/JIFS-221552_ref27","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Information and Control"},{"key":"10.3233\/JIFS-221552_ref28","doi-asserted-by":"crossref","first-page":"573","DOI":"10.3390\/sym10110573","article-title":"Q-filters of quantum B-algebras and basic implication algebras,ID:","volume":"10","author":"Zhang","year":"2018","journal-title":"Symmetry"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-221552","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T07:52:49Z","timestamp":1769673169000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-221552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":27,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-221552","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,9]]}}}