{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:22Z","timestamp":1777703902812,"version":"3.51.4"},"reference-count":31,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,9,14]],"date-time":"2019-09-14T00:00:00Z","timestamp":1568419200000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2019,10,25]]},"abstract":"\n In this paper, we introduce the notion of co-annihilator in hoops and investigate some related properties of them. Then we prove that the set of filters\n \n \n F<\/mml:mi>\n (<\/mml:mo>\n A<\/mml:mi>\n )<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n form two pseudo-complemented lattices (with \u2217 and \u22a4) that if\n A<\/jats:italic>\n has (DNP), then the two pseudo-complemented lattices are the same. Moreover, by defining the operation \u2192 on the lattice\n \n \n F<\/mml:mi>\n (<\/mml:mo>\n A<\/mml:mi>\n )<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n , we prove that\n \n \n F<\/mml:mi>\n (<\/mml:mo>\n A<\/mml:mi>\n )<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n is a Heyting algebra and by defining of the product operation, we show that\n \n \n F<\/mml:mi>\n (<\/mml:mo>\n A<\/mml:mi>\n )<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n is a bounded hoop. Finally, we define the\n C<\/jats:italic>\n \u00a0-\u00a0\n Ann<\/jats:italic>\n \u00a0(\n A<\/jats:italic>\n ) to be the set of all co-annihilators of\n A<\/jats:italic>\n , then we have that it had made a Boolean algebra. Also, we give an extension of a filter, which leads to a useful characterization of\n \u03b1<\/jats:italic>\n -filters on hoops. For instance, we obtain a series of characterizations of\n \u03b1<\/jats:italic>\n -filters. In addition, we show that there are no non-trivial\n \u03b1<\/jats:italic>\n -filters on hoop-chains. That implies the structure of all\n \u03b1<\/jats:italic>\n -filters contains only trivial\n \u03b1<\/jats:italic>\n -filters on hoops. On hoops, we prove that the set of all\n \u03b1<\/jats:italic>\n -filters is a pseudo-complemented lattice. Moreover, the structure of all\n \u03b1<\/jats:italic>\n -filters can form a Boolean algebra under certain conditions.\n <\/jats:p>","DOI":"10.3233\/jifs-190565","type":"journal-article","created":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T14:42:43Z","timestamp":1572360163000},"page":"5471-5485","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["On co-annihilators in hoops"],"prefix":"10.1177","volume":"37","author":[{"given":"M.","family":"Aaly Kologani","sequence":"first","affiliation":[{"name":"Hatef Higher Education Institute, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.B.","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Korea"},{"name":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"X.L.","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.H.","family":"Roh","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Chinju National University of Education, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.A.","family":"Borzooei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,9,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.21136\/MB.2019.0140-17"},{"key":"e_1_3_2_3_2","unstructured":"Aglian\u00f3P. 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