{"id":"https://openalex.org/W2028305097","doi":"https://doi.org/10.1016/s0020-0255(97)10070-6","title":"Operations of fuzzy numbers with step form membership function using function principle","display_name":"Operations of fuzzy numbers with step form membership function using function principle","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2028305097","doi":"https://doi.org/10.1016/s0020-0255(97)10070-6","mag":"2028305097"},"language":"en","primary_location":{"id":"doi:10.1016/s0020-0255(97)10070-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0020-0255(97)10070-6","pdf_url":null,"source":{"id":"https://openalex.org/S192650101","display_name":"Information Sciences","issn_l":"0020-0255","issn":["0020-0255","1872-6291"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Sciences","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/A5083613180","display_name":"Shan-Huo Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I153512688","display_name":"National Taiwan Ocean University","ror":"https://ror.org/03bvvnt49","country_code":"TW","type":"education","lineage":["https://openalex.org/I153512688"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Shan-Huo Chen","raw_affiliation_strings":["Department of Shipping and Transportation Management, National Taiwan Ocean University, Keelung, 20224, Taiwan, ROC"],"affiliations":[{"raw_affiliation_string":"Department of Shipping and Transportation Management, National Taiwan Ocean University, Keelung, 20224, Taiwan, ROC","institution_ids":["https://openalex.org/I153512688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083613180"],"corresponding_institution_ids":["https://openalex.org/I153512688"],"apc_list":{"value":3330,"currency":"USD","value_usd":3330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.14616882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"108","issue":"1-4","first_page":"149","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9991999864578247,"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":0.9991999864578247,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9921000003814697,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9699000120162964,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6714128851890564},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.670269250869751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6185842156410217},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6029742360115051},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5825566649436951},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5557088255882263},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.47686538100242615},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.469693660736084},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4464412331581116},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.42959925532341003},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4011261761188507},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3749324083328247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3726075291633606},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3723706007003784},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3373284637928009},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26647713780403137},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17214041948318481}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6714128851890564},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.670269250869751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6185842156410217},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6029742360115051},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5825566649436951},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5557088255882263},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.47686538100242615},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.469693660736084},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4464412331581116},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.42959925532341003},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4011261761188507},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3749324083328247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3726075291633606},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3723706007003784},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3373284637928009},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26647713780403137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17214041948318481},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0020-0255(97)10070-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0020-0255(97)10070-6","pdf_url":null,"source":{"id":"https://openalex.org/S192650101","display_name":"Information Sciences","issn_l":"0020-0255","issn":["0020-0255","1872-6291"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1494039286","https://openalex.org/W1898259180","https://openalex.org/W2025162503","https://openalex.org/W2043814432","https://openalex.org/W2045114196","https://openalex.org/W2069069851","https://openalex.org/W2071884542","https://openalex.org/W2496352033","https://openalex.org/W4211007335","https://openalex.org/W4213071690","https://openalex.org/W4289255536"],"related_works":["https://openalex.org/W1487720066","https://openalex.org/W1975005191","https://openalex.org/W2781808531","https://openalex.org/W3186561448","https://openalex.org/W2253053392","https://openalex.org/W3107001035","https://openalex.org/W4361984403","https://openalex.org/W3207735076","https://openalex.org/W1501518539","https://openalex.org/W2674573885"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}