{"id":"https://openalex.org/W4408310712","doi":"https://doi.org/10.1142/s1793005726500511","title":"An Innovative Unique Factorization Approach of Fuzzy Fractional Ideals in Dedekind Domains","display_name":"An Innovative Unique Factorization Approach of Fuzzy Fractional Ideals in Dedekind Domains","publication_year":2025,"publication_date":"2025-03-11","ids":{"openalex":"https://openalex.org/W4408310712","doi":"https://doi.org/10.1142/s1793005726500511"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005726500511","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005726500511","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107291531","display_name":"Tasaduk Rashid Mir","orcid":null},"institutions":[{"id":"https://openalex.org/I59475050","display_name":"Jamia Millia Islamia","ror":"https://ror.org/00pnhhv55","country_code":"IN","type":"education","lineage":["https://openalex.org/I59475050"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tasaduk Rashid Mir","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"],"raw_orcid":"https://orcid.org/0009-0009-4740-4022","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India","institution_ids":["https://openalex.org/I59475050"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046570244","display_name":"Mohammad Yahya Abbasi","orcid":"https://orcid.org/0000-0002-3283-1410"},"institutions":[{"id":"https://openalex.org/I59475050","display_name":"Jamia Millia Islamia","ror":"https://ror.org/00pnhhv55","country_code":"IN","type":"education","lineage":["https://openalex.org/I59475050"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"M. Yahya Abbasi","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"],"raw_orcid":"https://orcid.org/0000-0002-3283-1410","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India","institution_ids":["https://openalex.org/I59475050"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056996250","display_name":"Kostaq Hila","orcid":"https://orcid.org/0000-0001-6425-2619"},"institutions":[{"id":"https://openalex.org/I193184871","display_name":"Polytechnic University of Tirana","ror":"https://ror.org/05aec4025","country_code":"AL","type":"education","lineage":["https://openalex.org/I193184871"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Kostaq Hila","raw_affiliation_strings":["Department of Mathematical Engineering, Polytechnic University of Tirana, Tiran\u00eb, Albania"],"raw_orcid":"https://orcid.org/0000-0001-6425-2619","affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Polytechnic University of Tirana, Tiran\u00eb, Albania","institution_ids":["https://openalex.org/I193184871"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059847111","display_name":"Shahnawaz Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I59475050","display_name":"Jamia Millia Islamia","ror":"https://ror.org/00pnhhv55","country_code":"IN","type":"education","lineage":["https://openalex.org/I59475050"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shahnawaz Ali","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"],"raw_orcid":"https://orcid.org/0009-0005-5746-0619","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India","institution_ids":["https://openalex.org/I59475050"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08066826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"03","first_page":"1025","last_page":"1038"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.948199987411499,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.948199987411499,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9444000124931335,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7201442122459412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6289419531822205},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5874737501144409},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.5640719532966614},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5293812155723572},{"id":"https://openalex.org/keywords/unique-factorization-domain","display_name":"Unique factorization domain","score":0.4455045759677887},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.429651141166687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30194124579429626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17108860611915588},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16017299890518188}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7201442122459412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6289419531822205},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5874737501144409},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.5640719532966614},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5293812155723572},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.4455045759677887},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.429651141166687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30194124579429626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17108860611915588},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16017299890518188}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793005726500511","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005726500511","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W648107711","https://openalex.org/W1970498753","https://openalex.org/W1970802566","https://openalex.org/W1972723563","https://openalex.org/W1973375121","https://openalex.org/W2002680690","https://openalex.org/W2006571464","https://openalex.org/W2008987438","https://openalex.org/W2020394756","https://openalex.org/W2027654459","https://openalex.org/W2036632353","https://openalex.org/W2037999488","https://openalex.org/W2044315800","https://openalex.org/W2060660016","https://openalex.org/W2079811768","https://openalex.org/W2100579677","https://openalex.org/W2142293051","https://openalex.org/W2148549553","https://openalex.org/W2885675431","https://openalex.org/W4210778630","https://openalex.org/W4211007335","https://openalex.org/W4380202458"],"related_works":["https://openalex.org/W122992567","https://openalex.org/W2060844765","https://openalex.org/W2947171056","https://openalex.org/W4212806998","https://openalex.org/W2316516874","https://openalex.org/W4282930157","https://openalex.org/W4298073638","https://openalex.org/W2949457045","https://openalex.org/W4300191954","https://openalex.org/W2355470482"],"abstract_inverted_index":{"A":[0],"solid":[1],"mathematical":[2],"technique":[3],"for":[4,22,46],"handling":[5],"uncertainty":[6],"is":[7,114],"offered":[8],"by":[9],"the":[10,23,34,44,50,85,97,115],"Zadeh-conceived":[11],"notion":[12],"of":[13,20,25,36,52,87,117],"fuzzy":[14,40,53,63,75,93,123],"sets,":[15],"provides":[16],"a":[17,26,67,71,80,88,110,118],"convenient":[18],"point":[19],"departure":[21],"construction":[24],"conceptual":[27],"framework.":[28],"In":[29],"this":[30],"paper,":[31],"we":[32],"explore":[33],"advantages":[35],"applying":[37],"techniques":[38],"from":[39],"set":[41],"theory,":[42],"paving":[43],"way":[45],"innovative":[47],"approaches":[48],"in":[49,66],"study":[51,58],"multiplicative":[54],"ideal":[55,65],"theory.":[56],"This":[57],"investigates":[59],"that":[60,109],"every":[61],"nonzero":[62],"fractional":[64,94,124],"Dedekind":[68],"domain":[69,90,120],"has":[70],"unique":[72],"factorization":[73],"into":[74],"prime":[76],"ideals.":[77,95,125],"We":[78],"demonstrate":[79],"few":[81],"intermediate":[82],"findings":[83],"about":[84],"localization":[86,116],"noetherian":[89,119],"at":[91,121],"its":[92,122],"Introducing":[96],"new":[98],"concepts":[99],"and":[100],"provide":[101],"some":[102],"examples":[103],"via":[104],"discrete":[105,111],"valuation":[106,112],"ring":[107,113],"illustrates":[108]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}