{"id":"https://openalex.org/W4317937619","doi":"https://doi.org/10.1142/s1793005724500042","title":"Soft Homotopy Classes and Their Fundamental Group","display_name":"Soft Homotopy Classes and Their Fundamental Group","publication_year":2023,"publication_date":"2023-01-25","ids":{"openalex":"https://openalex.org/W4317937619","doi":"https://doi.org/10.1142/s1793005724500042"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005724500042","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s1793005724500042","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/A5063204543","display_name":"Sk. Nazmul","orcid":"https://orcid.org/0000-0001-6674-1459"},"institutions":[{"id":"https://openalex.org/I3131729800","display_name":"Kazi Nazrul University","ror":"https://ror.org/02qy8xv65","country_code":"IN","type":"education","lineage":["https://openalex.org/I3131729800"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sk. Nazmul","raw_affiliation_strings":["Department of Mathematics, Kazi Nazrul University, Asansol, Paschim Burdwan 713340, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kazi Nazrul University, Asansol, Paschim Burdwan 713340, West Bengal, India","institution_ids":["https://openalex.org/I3131729800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044267348","display_name":"Golam Biswas","orcid":"https://orcid.org/0009-0003-7278-1344"},"institutions":[{"id":"https://openalex.org/I3131729800","display_name":"Kazi Nazrul University","ror":"https://ror.org/02qy8xv65","country_code":"IN","type":"education","lineage":["https://openalex.org/I3131729800"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Golam Biswas","raw_affiliation_strings":["Department of Mathematics, Kazi Nazrul University, Asansol, Paschim Burdwan 713340, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kazi Nazrul University, Asansol, Paschim Burdwan 713340, West Bengal, India","institution_ids":["https://openalex.org/I3131729800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063204543"],"corresponding_institution_ids":["https://openalex.org/I3131729800"],"apc_list":null,"apc_paid":null,"fwci":0.9592,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76301525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"20","issue":"01","first_page":"45","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.7374280691146851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6778058409690857},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5140898823738098},{"id":"https://openalex.org/keywords/soft-set","display_name":"Soft set","score":0.5071382522583008},{"id":"https://openalex.org/keywords/homotopy-group","display_name":"Homotopy group","score":0.4963834881782532},{"id":"https://openalex.org/keywords/n-connected","display_name":"n-connected","score":0.4677097201347351},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"Fundamental group","score":0.4395415484905243},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43390488624572754},{"id":"https://openalex.org/keywords/homotopy-lifting-property","display_name":"Homotopy lifting property","score":0.42269501090049744},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4126468896865845},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3980979323387146},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.329345166683197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22297894954681396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15432968735694885},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07733255624771118},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06063377857208252}],"concepts":[{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7374280691146851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6778058409690857},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5140898823738098},{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.5071382522583008},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.4963834881782532},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.4677097201347351},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.4395415484905243},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43390488624572754},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.42269501090049744},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4126468896865845},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3980979323387146},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.329345166683197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22297894954681396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15432968735694885},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07733255624771118},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06063377857208252},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793005724500042","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s1793005724500042","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:20:y:2024:i:01:n:s1793005724500042","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S1793005724500042","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1978352585","https://openalex.org/W1994126463","https://openalex.org/W2023769726","https://openalex.org/W2069754181","https://openalex.org/W2071796503","https://openalex.org/W3190941578","https://openalex.org/W3214077557","https://openalex.org/W4210457345","https://openalex.org/W4213100037","https://openalex.org/W4244518645"],"related_works":["https://openalex.org/W3211691158","https://openalex.org/W4252076429","https://openalex.org/W4327495897","https://openalex.org/W939169393","https://openalex.org/W4242991709","https://openalex.org/W1540127744","https://openalex.org/W2164345227","https://openalex.org/W1610601528","https://openalex.org/W2963333616","https://openalex.org/W4302781545"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"our":[3],"prime":[4],"aim":[5],"is":[6],"to":[7],"develop":[8],"the":[9,67],"concept":[10],"of":[11,29,42,69],"fundamental":[12,70],"group":[13,71],"structure":[14],"in":[15,83],"soft":[16,27,31,33,35,38,43,45,51,55,75,85],"set":[17],"theoretic":[18],"approach.":[19],"To":[20],"execute":[21],"this,":[22],"first,":[23],"we":[24,64],"have":[25,65],"defined":[26],"homotopy":[28,46,76],"maps,":[30],"path,":[32],"loop,":[34],"path":[36],"homotopy,":[37,40],"loop":[39],"product":[41],"loops,":[44],"class,":[47],"etc.,":[48],"at":[49],"a":[50],"element":[52],"using":[53],"generalized":[54],"mappings":[56],"and":[57],"their":[58],"important":[59],"behaviors":[60],"are":[61,74,80],"studied.":[62],"Finally,":[63],"introduced":[66],"notion":[68],"whose":[72],"members":[73],"classes.":[77],"Some":[78],"examples":[79],"also":[81],"discussed":[82],"different":[84],"topological":[86],"spaces.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
