{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:53:12Z","timestamp":1777704792781,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T00:00:00Z","timestamp":1535500800000},"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: Applications in Engineering and Technology"],"published-print":{"date-parts":[[2019,2,16]]},"abstract":"<jats:p>\n                    In this paper, we study the idea of rough approximations in LA-polygroups, and present some examples in this respect. In particular, we study some properties of rough LA-subpolygroup which is an extension of LA-subpolygroup. We prove that the lower (upper) approximation of an LA-subpolygroup is an LA-subpolygroup. We consider the factor LA-polygroup\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    \/\n                    <jats:italic toggle=\"yes\">H<\/jats:italic>\n                    and interpret the lower and upper approximations as subsets of the factor LA-polygroup\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    \/\n                    <jats:italic toggle=\"yes\">H<\/jats:italic>\n                    . Then, we introduce the concept of factor rough LA-subpolygroups. Also, we provided some results on homomorphisms of rough LA-subpolygroups.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18776","type":"journal-article","created":{"date-parts":[[2018,8,31]],"date-time":"2018-08-31T12:03:55Z","timestamp":1535717035000},"page":"517-526","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Approximations in left almost polygroups"],"prefix":"10.1177","volume":"36","author":[{"given":"Naveed","family":"Yaqoob","sequence":"first","affiliation":[{"name":"Majmaah University","place":["Suadi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,8,29]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"251","article-title":"Rough groups and rough subgroups","volume":"42","author":"Biswas R.","year":"1994","unstructured":"BiswasR. and NandaS., Rough groups and rough subgroups, Bull Polish Acad Sci Math 42 (1994), 251\u2013254.","journal-title":"Bull Polish Acad Sci Math"},{"key":"e_1_3_2_3_2","doi-asserted-by":"crossref","unstructured":"BonikowaskiZ. Algebraic structures of rough sets Rough sets Fuzzy sets and Knowledge Discovery Springer-Verlag Berlin (1995) pp. 242\u2013247.","DOI":"10.1007\/978-1-4471-3238-7_29"},{"key":"e_1_3_2_4_2","doi-asserted-by":"crossref","unstructured":"ComerS. Extension of polygroups by polygroups and their representations using colour schemes Lecture notes in Meth 1004 Universal Algebra and Lattice Theory (1982) 91\u2013103.","DOI":"10.1007\/BFb0063431"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(84)90225-4"},{"key":"e_1_3_2_6_2","unstructured":"CorsiniP. Prolegomena of hypergroup theory second edition ain editor 1993."},{"issue":"3","key":"e_1_3_2_7_2","first-page":"721","article-title":"Cat1-polygroup and pullback cat1-polygroup","volume":"40","author":"Davvaz B.","year":"2014","unstructured":"DavvazB. and AlpM., Cat1-polygroup and pullback cat1-polygroup, Bull Iranian Math Soc 40(3) (2014), 721\u2013735.","journal-title":"Bull Iranian Math Soc"},{"key":"e_1_3_2_8_2","doi-asserted-by":"crossref","unstructured":"DavvazB. World Scientific Polygroup theory and related systems 2013.","DOI":"10.1142\/8593"},{"key":"e_1_3_2_9_2","first-page":"91","article-title":"Rough polygroups","volume":"12","author":"Davvaz B.","year":"2002","unstructured":"DavvazB., Rough polygroups, Italian J Pure Appl Math 12 (2002), 91\u201396.","journal-title":"Italian J Pure Appl Math"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2006-00324"},{"key":"e_1_3_2_11_2","first-page":"45","article-title":"Rough set theory applied to BCI-algebras","volume":"9","author":"Dudek W.A.","year":"2002","unstructured":"DudekW.A., JunY.B. and KimH.S., Rough set theory applied to BCI-algebras, Quasigroups and Relat Syst 9 (2002), 45\u201354.","journal-title":"Quasigroups and Relat Syst"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/IJMMS.2005.437"},{"key":"e_1_3_2_13_2","first-page":"303","article-title":"The homomorphism and isomorphism of rough groups","volume":"24","author":"Goldhaber J.K.","year":"2001","unstructured":"GoldhaberJ.K. and EnrichG., The homomorphism and isomorphism of rough groups, Academy of Shanxi University 24 (2001), 303\u2013305.","journal-title":"Academy of Shanxi University"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40840-015-0136-y"},{"key":"e_1_3_2_15_2","doi-asserted-by":"crossref","unstructured":"HilaK. DineJ. On hyperideals in left almost ihypergroups ISRN Algebra Article ID 953124 (2011) p. 8.","DOI":"10.5402\/2011\/953124"},{"key":"e_1_3_2_16_2","first-page":"95","article-title":"Polygroups et certains de leurs properietes","volume":"22","author":"Ioulidis S.","year":"1981","unstructured":"IoulidisS., Polygroups et certains de leurs properietes, Bull Greek Math Soc 22 (1981), 95\u2013104.","journal-title":"Bull Greek Math Soc"},{"key":"e_1_3_2_17_2","first-page":"1","article-title":"On almost-igroup","volume":"2","author":"Kazim M.A.","year":"1972","unstructured":"KazimM.A. and NaseerudinM., On almost-igroup, Alig Bull Math 2 (1972), 1\u20137.","journal-title":"Alig Bull Math"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.05.009"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.030"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-162041"},{"key":"e_1_3_2_21_2","unstructured":"MartyF. Sur une generalization de la notion de group 8th Congress Math Scandenaves (1934) pp. 45\u201349 Stockholm."},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498815500607"},{"key":"e_1_3_2_23_2","first-page":"65","article-title":"On LA-igroups","volume":"8","author":"Mushtaq Q.","year":"1978","unstructured":"MushtaqQ. and YusufS.M., On LA-igroups, Alig Bull Math 8 (1978), 65\u201370.","journal-title":"Alig Bull Math"},{"key":"e_1_3_2_24_2","first-page":"331","article-title":"Partial ordering and congruences on LA-igroups","volume":"22","author":"Mushtaq Q.","year":"1991","unstructured":"MushtaqQ. and IqbalM., Partial ordering and congruences on LA-igroups, Indian J Pure Appl Math 22 (1991), 331\u2013336.","journal-title":"Indian J Pure Appl Math"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/09720502.2008.10700573"},{"key":"e_1_3_2_26_2","first-page":"321","article-title":"M-systems in LA-igroups","volume":"33","author":"Mushtaq Q.","year":"2009","unstructured":"MushtaqQ. and KhanM., M-systems in LA-igroups, Southeast Asian Bull Math 33 (2009), 321\u2013327.","journal-title":"Southeast Asian Bull Math"},{"key":"e_1_3_2_27_2","first-page":"1","article-title":"On left almost groups","volume":"33","author":"Mushtaq Q.","year":"1996","unstructured":"MushtaqQ. and KamranM.S., On left almost groups, Proc Pak Acad Sci 33 (1996), 1\u20132.","journal-title":"Proc Pak Acad Sci"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"e_1_3_2_29_2","first-page":"1085201","article-title":"Generalized rough fuzzy ideals in quantales,11. Article ID","volume":"2018","author":"Qurashi M.S.","year":"2018","unstructured":"QurashiM.S. and ShabirM., Generalized rough fuzzy ideals in quantales,11. Article ID, Disc Dyn Nature Soc 2018 (2018), 1085201.","journal-title":"Disc Dyn Nature Soc"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","unstructured":"QurashiS.M. and ShabirM. Roughness in quantale module J Intell Fuzzy Syst doi: 10.3233\/jifs-17886.","DOI":"10.3233\/jifs-17886"},{"key":"e_1_3_2_31_2","first-page":"84","article-title":"Roughness in ordered igroups","volume":"22","author":"Shabir M.","year":"2013","unstructured":"ShabirM. and IrshadS., Roughness in ordered igroups, World Appl Sci J 22 (2013), 84\u2013105.","journal-title":"World Appl Sci J"},{"issue":"2","key":"e_1_3_2_32_2","first-page":"331","article-title":"Roughness in ternary igroups","volume":"19","author":"Shabir M.","year":"2011","unstructured":"ShabirM. and RehmanN., Roughness in ternary igroups, Quasigroups Relt Syst 19(2) (2011), 331\u2013338.","journal-title":"Quasigroups Relt Syst"},{"key":"e_1_3_2_33_2","volume-title":"Hyperstructures and their representations","author":"Vougiouklis T.","year":"1994","unstructured":"VougiouklisT. Hyperstructures and their representations, Hadronic Press, Florida, 1994."},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.06.024"},{"key":"e_1_3_2_35_2","first-page":"465","article-title":"Left almost polygroups","volume":"39","author":"Yaqoob N.","year":"2018","unstructured":"YaqoobN., CristeaI., GulistanM. and NawazS., Left almost polygroups, Italian J Pure Appl Math 39 (2018), 465\u2013474.","journal-title":"Italian J Pure Appl Math"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-012-0809-5"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1713167Y"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141214"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems: Applications in Engineering and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18776","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18776","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18776","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:01Z","timestamp":1777455721000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18776"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,29]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2,16]]}},"alternative-id":["10.3233\/JIFS-18776"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18776","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,29]]}}}