{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T21:43:09Z","timestamp":1755034989965},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p> In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann\u2019s hypergroupoids (AG-hypergroupoids). We define double-framed soft AG-hypergroupoids (DFS AG-hypergroupoids) and double-framed soft left (respectively, right) (briefly DFS-left (respectively, DFS-right)) hyperideals of AG-hypergroupoids. It is shown that an idempotent DFS-left hyperideal is a DFS-hyperideal. Also a DFS right hyperideal becomes DFS hyperideal when pure left identity is adjoined to an AG-hypergroupoid, but the converse is not true. We also discuss some properties of these hyperideals in regular AG-hypergroupoids. <\/jats:p>","DOI":"10.1142\/s1793005722500399","type":"journal-article","created":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T07:57:05Z","timestamp":1635148625000},"page":"819-841","source":"Crossref","is-referenced-by-count":2,"title":["Double-Framed Soft Set Theory Applied to Abel-Grassmann\u2019s Hypergroupoids"],"prefix":"10.1142","volume":"18","author":[{"given":"Muhammad","family":"Izhar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College Garhi Kapura Mardan, Khyber Pakhtunkhwa Pakistan"}]},{"given":"Tariq","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, University of Engineering and Technology, Taxila, Pakistan"}]},{"given":"Asghar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan"}]},{"given":"Muhammad","family":"Farooq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan"}]},{"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania"}]}],"member":"219","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"S1793005722500399BIB001","first-page":"45","volume-title":"8th Congres Mathematics Scandinaves","author":"Marty F.","year":"1934"},{"key":"S1793005722500399BIB002","first-page":"xii+322","volume-title":"Advances in Mathematics","volume":"5","author":"Corsini P.","year":"2003"},{"key":"S1793005722500399BIB003","unstructured":"P. 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