{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T07:22:42Z","timestamp":1772263362004,"version":"3.50.1"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,7,10]],"date-time":"2018-07-10T00:00:00Z","timestamp":1531180800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2018,7,10]]},"abstract":"<jats:p>The intuitionistic fuzzification in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>algebras about the concepts of ideals and subalgebras given with several related characterizations is considered. Some new concepts like intuitionistic fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>ideal (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>I<\/mml:mi><mml:mi>F<\/mml:mi><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:math>), intuitionistic fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>subalgebra (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>I<\/mml:mi><mml:mi>F<\/mml:mi><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mi>s<\/mml:mi><\/mml:math>), <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>homomorphism, and intuitionistic fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mover accent=\"false\"><mml:mrow><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><mml:mo>-<\/mml:mo><\/mml:math>ideal (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mi>I<\/mml:mi><mml:mi>F<\/mml:mi><mml:mover accent=\"false\"><mml:mrow><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><mml:mi>i<\/mml:mi><\/mml:math>) are introduced and some of their descriptions are given in this work. Further, we show some applications on the family of all intuitionistic fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>subalgebras <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mi>I<\/mml:mi><mml:mi>F<\/mml:mi><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"fraktur\">R<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>algebra like the binary relations <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:munder><mml:mrow><mml:mo>\u2248<\/mml:mo><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">\u03bc<\/mml:mi><\/mml:mrow><\/mml:munder><\/mml:mrow><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:munder><mml:mrow><mml:mo>\u2248<\/mml:mo><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">\u03bd<\/mml:mi><\/mml:mrow><\/mml:munder><\/mml:mrow><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\"><mml:mi>I<\/mml:mi><mml:mi>F<\/mml:mi><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u03c1<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"fraktur\">R<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>. Also, their equivalence classes are given and studied.<\/jats:p>","DOI":"10.1155\/2018\/5712676","type":"journal-article","created":{"date-parts":[[2018,7,10]],"date-time":"2018-07-10T19:34:54Z","timestamp":1531251294000},"page":"1-6","source":"Crossref","is-referenced-by-count":23,"title":["New Branch of Intuitionistic Fuzzification in Algebras with Their Applications"],"prefix":"10.1155","volume":"2018","author":[{"given":"Samaher Adnan","family":"Abdul-Ghani","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Basrah University, Basrah 61004, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7635-3553","authenticated-orcid":true,"given":"Shuker Mahmood","family":"Khalil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Basrah University, Basrah 61004, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mayadah Abd","family":"Ulrazaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Basrah University, Basrah 61004, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abu Firas Muhammad","family":"Jawad Al-Musawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Basrah University, Basrah 61004, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793005709001544"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.07.047"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.fiae.2016.11.003"},{"issue":"3","key":"14","first-page":"589","volume":"9","year":"2001","journal-title":"Journal of Fuzzy Mathematics"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"issue":"12","key":"5","first-page":"349","volume":"10","year":"2014","journal-title":"European Scientific Journal"},{"issue":"2","key":"10","first-page":"221","volume":"10","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"issue":"3","key":"13","first-page":"677","volume":"9","year":"2001","journal-title":"Journal of Fuzzy Mathematics"},{"key":"9","first-page":"119","volume":"6","journal-title":"International Journal of Applications of Fuzzy Sets and Artificial Intelligence"},{"issue":"1","key":"7","first-page":"117","volume":"66","year":"2007","journal-title":"Scientiae Mathematicae Japonicae"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195522169"},{"issue":"1","key":"15","first-page":"19","volume":"49","year":"1999","journal-title":"Mathematica Slovaca"},{"issue":"4","key":"8","first-page":"152","volume":"7","year":"2017","journal-title":"American Journal of Mathematics and Statistics"},{"key":"12","first-page":"231","volume":"7","year":"2017","journal-title":"International Journal of Applications of Fuzzy Sets and Artificial Intelligence"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.12.008"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2018\/5712676.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2018\/5712676.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2018\/5712676.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,7,10]],"date-time":"2018-07-10T19:34:57Z","timestamp":1531251297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2018\/5712676\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,10]]},"references-count":16,"alternative-id":["5712676","5712676"],"URL":"https:\/\/doi.org\/10.1155\/2018\/5712676","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,10]]}}}