{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:28Z","timestamp":1777704328579,"version":"3.51.4"},"reference-count":34,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10]]},"abstract":"<jats:p>\n                    The aim of this paper is to develop the spectral theory of prime\n                    <jats:italic>L<\/jats:italic>\n                    -ideals in ordered semigroups. Firstly the concepts of an\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy ideal and that of an\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy prime ideal are given and discussed. And then a topological space, called the\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy prime spectrum of an ordered semigroup, has been gained. This topological space is\n                    <jats:italic>T<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    and sober. Furthermore some homeomorphic spaces of this topological space are investigated. Finally, a contravariant functor from the category of commutative ordered semigroups into the category of sober topological spaces is obtained.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18743","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T11:25:27Z","timestamp":1534505127000},"page":"3847-3857","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["<i>L<\/i>\n                    -fuzzy prime spectra of ordered semigroups"],"prefix":"10.1177","volume":"35","author":[{"given":"Huanrong","family":"Wu","sequence":"first","affiliation":[{"name":"College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China"}]},{"given":"Bin","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"issue":"4","key":"e_1_3_2_2_2","first-page":"61","article-title":"Spectrum of prime fuzzy hyperideals","volume":"6","author":"Ameri R.","year":"2009","unstructured":"AmeriR. and MahjoobR., Spectrum of prime fuzzy hyperideals, Iranian Journal of Fuzzy Systems 6(4) (2009), 61\u201372.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90038-R"},{"issue":"3","key":"e_1_3_2_4_2","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s00233-015-9773-6","article-title":"Weak inverses modulo Green\u0105\u0155s relation H on E-inversive and group-closed semigroups","volume":"92","author":"Fan X.","year":"2016","unstructured":"FanX., ChenQ. and KongX., Weak inverses modulo Green\u0105\u0155s relation H on E-inversive and group-closed semigroups, Semigroup Forum 92(3) (2016), 691\u2013711.","journal-title":"Semigroup Forum"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788715000373"},{"key":"e_1_3_2_6_2","article-title":"Springer Science and Business Media","author":"Gr\u00e4tzer G.","year":"2002","unstructured":"Gr\u00e4tzerG., Springer Science and Business Media, General lattice theory 2002.","journal-title":"General lattice theory"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.03.012"},{"key":"e_1_3_2_8_2","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1090\/S0002-9947-1965-0194880-9","article-title":"The space of minimal prime ideals of a commutative ring","volume":"115","author":"Henriksen M.","year":"1965","unstructured":"HenriksenM. and JerisonM., The space of minimal prime ideals of a commutative ring, Transactions of the American Mathematical Society 115 (1965), 110\u2013130.","journal-title":"Transactions of the American Mathematical Society"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-152042"},{"key":"e_1_3_2_10_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.fss.2017.10.003","article-title":"The L-ordered igroups based on L-partial orders semigroup","volume":"339","author":"Huang X.K.","year":"2018","unstructured":"HuangX.K., LiQ.G. and XiaoQ.M., The L-ordered igroups based on L-partial orders semigroup, Fuzzy Sets and Systems 339 (2018), 31\u201350.","journal-title":"Fuzzy Sets and Systems"},{"key":"e_1_3_2_11_2","article-title":"Connectedness for lattice-valued subsets in lattice-valued convergence spaces","author":"Jin Q.","year":"2018","unstructured":"JinQ., LiL., LvY., ZhaoF. and ZouJ., Connectedness for lattice-valued subsets in lattice-valued convergence spaces, Quaestiones Mathematicae (2018). doi: 10.2989\/16073606.2018.1441920.","journal-title":"Quaestiones Mathematicae"},{"issue":"1","key":"e_1_3_2_12_2","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF02574353","article-title":"On prime, weakly prime ideals in ordered semigroup","volume":"44","author":"Kehayopulu N.","year":"1992","unstructured":"KehayopuluN., On prime, weakly prime ideals in ordered semigroup, Semigroup Forum 44(1) (1992), 341\u2013346.","journal-title":"Semigroup Forum"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002330010079"},{"issue":"1","key":"e_1_3_2_14_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1112\/plms\/s3-13.1.31","article-title":"Minimal prime ideals in commutative semigroup","volume":"3","author":"Kist J.","year":"1963","unstructured":"KistJ., Minimal prime ideals in commutative semigroup, Proceedings of the London Mathematical Society 3(1) (1963), 31\u201350.","journal-title":"Proceedings of the London Mathematical Society"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90202-S"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-011-9309-7"},{"issue":"2","key":"e_1_3_2_17_2","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1007\/s00233-014-9576-1","article-title":"The basic generalization of two results for orthodox semigroups","volume":"89","author":"Kong X.","year":"2014","unstructured":"KongX. and MengF., The basic generalization of two results for orthodox semigroups, Semigroup Forum 89(2) (2014), 394\u2013402.","journal-title":"Semigroup Forum"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90276-A"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90077-9"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00339-8"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.10.006"},{"issue":"5","key":"e_1_3_2_22_2","first-page":"397","article-title":"On iprime and prime Q-fuzzy ideals in ordered semigroups","volume":"6","author":"Lekkoksung S.","year":"2012","unstructured":"LekkoksungS., On iprime and prime Q-fuzzy ideals in ordered semigroups, International Journal of Mathematical Analysis 6(5) (2012), 397\u2013404.","journal-title":"International Journal of Mathematical Analysis"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-016-9534-2"},{"key":"e_1_3_2_24_2","first-page":"465","article-title":"On weakly prime L-ideals","volume":"36","author":"Mahjoob R.","year":"2016","unstructured":"MahjoobR., On weakly prime L-ideals, Italian Journal of Pure and Applied Mathematics 36 (2016), 465\u2013472.","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"e_1_3_2_25_2","doi-asserted-by":"crossref","DOI":"10.1142\/3929","article-title":"World Scientific","author":"Mordeson J.N.","year":"1998","unstructured":"MordesonJ.N. and MalikD.S., World Scientific, Fuzzy commutative algebra 1998.","journal-title":"Fuzzy commutative algebra"},{"key":"e_1_3_2_26_2","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1007\/s00500-016-2105-2","article-title":"The hull-kernel topology on prime ideals in posets","volume":"21","author":"Mundlik N.","year":"2016","unstructured":"MundlikN., JoshiV. and Hala\u0161R., The hull-kernel topology on prime ideals in posets, Soft Computing 21 (2016), 1653\u20131665.","journal-title":"Soft Computing"},{"issue":"8","key":"e_1_3_2_27_2","first-page":"167","article-title":"Intuitionistic fuzzy prime spectrum of a ring","volume":"9","author":"Sharma P.K.","year":"2017","unstructured":"SharmaP.K. and KaurG., Intuitionistic fuzzy prime spectrum of a ring, International Journal of Fuzzy Systems 9(8) (2017), 167\u2013175.","journal-title":"International Journal of Fuzzy Systems"},{"issue":"1","key":"e_1_3_2_28_2","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1017\/S144678870001911X","article-title":"Spaces of ideals of distributive lattices II. minimal prime ideals","volume":"18","author":"Speed T.P.","year":"1974","unstructured":"SpeedT.P., Spaces of ideals of distributive lattices II. minimal prime ideals, Journal of the Australian Mathematical Society 18(1) (1974), 54\u201372.","journal-title":"Journal of the Australian Mathematical Society"},{"key":"e_1_3_2_29_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21136\/CPMF.1938.124080","article-title":"Topological representations of distributive lattices and brouwerian logics","volume":"67","author":"Stone M.H.","year":"1937","unstructured":"StoneM.H., Topological representations of distributive lattices and brouwerian logics, \u010casopis Pro P\u011bstov\u00e1n\u00ed Matematiky a Fysiky 67 (1937), 1\u201325.","journal-title":"\u010casopis Pro P\u011bstov\u00e1n\u00ed Matematiky a Fysiky"},{"key":"e_1_3_2_30_2","article-title":"Preprint","author":"Wu H.","year":"2018","unstructured":"WuH., LiQ. and YuB., Preprint, The hull-kernel topology on prime ideals in ordered semigroups 2018.","journal-title":"The hull-kernel topology on prime ideals in ordered semigroups"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.07.006"},{"key":"e_1_3_2_32_2","article-title":"A novel type of soft rough covering and its application to multicriteria group decision making","author":"Zhan J.","year":"2018","unstructured":"ZhanJ. and AlcantudJ.C.R., A novel type of soft rough covering and its application to multicriteria group decision making, Artificial Intelligence Review (2018). doi: 10.1007\/s10462-018-9617-3.","journal-title":"Artificial Intelligence Review"},{"key":"e_1_3_2_33_2","article-title":"A survey of parameter reduction of soft sets and corresponding algorithms","author":"Zhan J.","year":"2018","unstructured":"ZhanJ. and AlcantudJ.C.R., A survey of parameter reduction of soft sets and corresponding algorithms, Artificial Intelligence Review (2018). doi: 10.1007\/s10462-017-9592-0.","journal-title":"Artificial Intelligence Review"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.03.038"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.09.012"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18743","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18743","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18743","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:58Z","timestamp":1777455658000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18743"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,17]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["10.3233\/JIFS-18743"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18743","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,17]]}}}