{"id":"https://openalex.org/W2972205455","doi":"https://doi.org/10.1142/s179300572050012x","title":"Fuzzification of Zero Forcing Process","display_name":"Fuzzification of Zero Forcing Process","publication_year":2019,"publication_date":"2019-09-06","ids":{"openalex":"https://openalex.org/W2972205455","doi":"https://doi.org/10.1142/s179300572050012x","mag":"2972205455"},"language":"en","primary_location":{"id":"doi:10.1142/s179300572050012x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179300572050012x","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/A5072356626","display_name":"R. A. Borzooei","orcid":"https://orcid.org/0000-0001-7538-7885"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"R. A. Borzooei","raw_affiliation_strings":["Department of Mathematics, Shahid Beheshti University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003004244","display_name":"B. Sheikh Hoseini","orcid":null},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"B. Sheikh Hoseini","raw_affiliation_strings":["Department of Mathematics, Shahid Beheshti University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060639819","display_name":"M. Golmohammadian","orcid":null},"institutions":[{"id":"https://openalex.org/I1516879","display_name":"Tarbiat Modares University","ror":"https://ror.org/03mwgfy56","country_code":"IR","type":"education","lineage":["https://openalex.org/I1516879"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Golmohammadian","raw_affiliation_strings":["Department of Mathematics, Tarbiat Modares University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tarbiat Modares University, Tehran, Iran","institution_ids":["https://openalex.org/I1516879"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010062036","display_name":"Zeinab Montazeri","orcid":"https://orcid.org/0000-0002-2846-9535"},"institutions":[{"id":"https://openalex.org/I67080706","display_name":"Alzahra University","ror":"https://ror.org/013cdqc34","country_code":"IR","type":"education","lineage":["https://openalex.org/I67080706"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Z. Montazeri","raw_affiliation_strings":["Department of Mathematics, Alzahra University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Alzahra University, Tehran, Iran","institution_ids":["https://openalex.org/I67080706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082321731","display_name":"M. Mohseni Takallo","orcid":"https://orcid.org/0000-0002-4113-3657"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Mohseni Takallo","raw_affiliation_strings":["Department of Mathematics, Shahid Beheshti University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahid Beheshti University, Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072356626"],"corresponding_institution_ids":["https://openalex.org/I48379061"],"apc_list":null,"apc_paid":null,"fwci":0.2262,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57007097,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"01","first_page":"195","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11476","display_name":"Graph theory and applications","score":0.9731000065803528,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9682999849319458,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.8212085962295532},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6454226970672607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.582383394241333},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5520322322845459},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5377213358879089},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46474072337150574},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44537100195884705},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.40397369861602783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36820313334465027},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31801027059555054},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1101280152797699},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10329192876815796}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8212085962295532},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6454226970672607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.582383394241333},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5520322322845459},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5377213358879089},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46474072337150574},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44537100195884705},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.40397369861602783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36820313334465027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31801027059555054},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1101280152797699},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10329192876815796},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s179300572050012x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179300572050012x","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"},{"id":"pmh:oai:RePEc:wsi:nmncxx:v:16:y:2020:i:01:n:s179300572050012x","is_oa":false,"landing_page_url":"https://www.worldscientific.com/doi/abs/10.1142/S179300572050012X","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.550000011920929,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1544632947","https://openalex.org/W1601092472","https://openalex.org/W1988353915","https://openalex.org/W2061820396","https://openalex.org/W2091222603","https://openalex.org/W2099618798","https://openalex.org/W2147493617","https://openalex.org/W2296563105","https://openalex.org/W2304896639","https://openalex.org/W2791064953","https://openalex.org/W2792624398","https://openalex.org/W2953303692"],"related_works":["https://openalex.org/W2971214053","https://openalex.org/W2081900870","https://openalex.org/W2021517900","https://openalex.org/W2949231297","https://openalex.org/W2060606417","https://openalex.org/W2045623209","https://openalex.org/W13367279","https://openalex.org/W152327667","https://openalex.org/W2243116742","https://openalex.org/W4301155280"],"abstract_inverted_index":{"In":[0],"this":[1,45,71],"paper,":[2],"we":[3,14,50,66],"investigate":[4],"the":[5],"fuzzification":[6],"of":[7,19,32,40,44,58],"zero":[8,29,46,55],"forcing":[9,30,42,47,56],"process.":[10],"For":[11],"this,":[12],"first":[13],"introduce":[15],"a":[16,20,27,52,59],"new":[17],"embedding":[18],"graph":[21,60],"[Formula:":[22,33],"see":[23,34],"text]":[24,35],"by":[25,61],"considering":[26],"minimal":[28],"set":[31],"and":[36],"an":[37,68],"arbitrary":[38],"list":[39],"maximal":[41],"chains":[43],"set.":[48],"Then":[49],"get":[51],"comparison":[53],"between":[54],"sets":[57],"using":[62],"fuzzy":[63],"concepts.":[64],"Finally,":[65],"give":[67],"application":[69],"for":[70],"procedure.":[72]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}