{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T16:30:36Z","timestamp":1773851436872,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","doi-asserted-by":"publisher","award":["PNURSP2026R231"],"award-info":[{"award-number":["PNURSP2026R231"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces the concept of interval-valued intuitionistic fuzzy n-fold implicative filters in hoop algebras and explores their fundamental properties. We establish several new and equivalent characterizations, investigate their closure properties, and provide explicit algorithms for their construction and verification. Furthermore, we examine the relationships between interval-valued intuitionistic fuzzy n-fold implicative filters, interval-valued intuitionistic fuzzy filters, and classical n-fold implicative filters. The results presented here extend beyond straightforward generalizations, offering both practical tools and theoretical insights that are not previously available in the literature. The results presented here build upon earlier studies by systematically characterizing interval-valued intuitionistic fuzzy n-fold implicative filters in hoop algebras. Several new equivalent conditions and computational methods are introduced, and relationships with existing filter concepts are clarified.<\/jats:p>","DOI":"10.3390\/axioms15030221","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T13:32:07Z","timestamp":1773667927000},"page":"221","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interval-Valued Intuitionistic Fuzzy n-Fold Implicative Filters in Hoop Algebra"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal","family":"S. Alali","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6514-4027","authenticated-orcid":false,"given":"Tahsin","family":"Oner","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-7914","authenticated-orcid":false,"given":"Ravi Kumar","family":"Bandaru","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0921-6054","authenticated-orcid":false,"given":"Rajesh","family":"Neelamegarajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8296-2796","authenticated-orcid":false,"given":"Ibrahim","family":"Senturk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, T\u00fcrkiye"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,16]]},"reference":[{"key":"ref_1","unstructured":"H\u00e1jek, P. 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