{"id":"https://openalex.org/W3038987649","doi":"https://doi.org/10.1109/tfuzz.2020.3006557","title":"An Understandable Way to Extend the Ordinary Linear Order on Real Numbers to a Linear Order on Interval Numbers","display_name":"An Understandable Way to Extend the Ordinary Linear Order on Real Numbers to a Linear Order on Interval Numbers","publication_year":2020,"publication_date":"2020-07-02","ids":{"openalex":"https://openalex.org/W3038987649","doi":"https://doi.org/10.1109/tfuzz.2020.3006557","mag":"3038987649"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2020.3006557","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.3006557","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","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/A5100697691","display_name":"Jing Yang","orcid":"https://orcid.org/0000-0002-9478-1519"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jing Yang","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, China","College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-9478-1519","affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102968426","display_name":"Sheng-Gang Li","orcid":"https://orcid.org/0000-0003-2998-726X"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shenggang Li","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, China","College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0003-2998-726X","affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeshui Xu","raw_affiliation_strings":["Business School, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-3547-2908","affiliations":[{"raw_affiliation_string":"Business School, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100392542","display_name":"Heng Liu","orcid":"https://orcid.org/0000-0003-3923-7526"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heng Liu","raw_affiliation_strings":["School of Science, Guangxi University of Nationalities, Nanning, China"],"raw_orcid":"https://orcid.org/0000-0003-3923-7526","affiliations":[{"raw_affiliation_string":"School of Science, Guangxi University of Nationalities, Nanning, China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083158084","display_name":"Wei Yao","orcid":"https://orcid.org/0000-0003-3320-7609"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Yao","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-3320-7609","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100697691"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":2.7866,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.90822694,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"9","first_page":"2675","last_page":"2688"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6066868901252747},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.59412682056427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5034753680229187},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47941848635673523},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4447345733642578},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4414343237876892},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38155731558799744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36384642124176025},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24726980924606323}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6066868901252747},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.59412682056427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5034753680229187},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47941848635673523},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4447345733642578},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4414343237876892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38155731558799744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36384642124176025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24726980924606323},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2020.3006557","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.3006557","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1804066553","display_name":null,"funder_award_id":"11771263","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6564907044","display_name":null,"funder_award_id":"61967001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W119888408","https://openalex.org/W1507872748","https://openalex.org/W1975503090","https://openalex.org/W1978889792","https://openalex.org/W1981107087","https://openalex.org/W1988053196","https://openalex.org/W2012430137","https://openalex.org/W2035386280","https://openalex.org/W2047161103","https://openalex.org/W2050262998","https://openalex.org/W2060907774","https://openalex.org/W2060924166","https://openalex.org/W2068069653","https://openalex.org/W2072002558","https://openalex.org/W2073714748","https://openalex.org/W2080344763","https://openalex.org/W2082088296","https://openalex.org/W2093397547","https://openalex.org/W2150546380","https://openalex.org/W2164734181","https://openalex.org/W2282429601","https://openalex.org/W2346443999","https://openalex.org/W2912349840"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W4301770943","https://openalex.org/W2288802435","https://openalex.org/W2283513731","https://openalex.org/W2071261821","https://openalex.org/W2952935049","https://openalex.org/W2042906530","https://openalex.org/W3194807151"],"abstract_inverted_index":{"Inspired":[0],"by":[1,93,106],"reflection":[2],"transformations":[3,6],"and":[4,10,69,88,108,190,203,238,242],"rotation":[5],"in":[7,13,16,261],"plane":[8,179],"geometry":[9],"dictionary":[11],"orders":[12,202,224],"lattice":[14],"theory,":[15],"this":[17,235],"article,":[18],"we":[19,84,157,191,205],"explore,":[20],"through":[21],"exposing":[22],"the":[23,50,89,123,138,152,164,178,197,200,215,239],"possible":[24,216],"motivation":[25],"of":[26,28,38,58,102,110,141,143,155,218,222],"definition":[27],"a":[29,63,171,193,212],"defined":[30],"linear":[31,52,64,125,166,172,223,236],"order":[32,53,65,91,167,173,237],"\u2264":[33,94,132,219],"on":[34,54,66,95,168,174,177,196,225,234],"R":[35,55,96,121,169,175,180],"(the":[36,56,100],"set":[37,57,101],"all":[39,59,103],"interval":[40,111,145],"numbers),":[41],"how":[42],"to":[43,48,62,136,162,170,210,228,251],"find":[44],"an":[45,76,144,159,230],"easy-to-understand":[46],"way":[47,161],"extend":[49,163],"ordinary":[51,124,165],"real":[60],"numbers)":[61],"R.":[67],"Theory":[68],"application":[70],"aspects":[71],"are":[72],"also":[73],"studied.":[74],"For":[75],"arbitrary":[77],"cardinal":[78],"number":[79,146],"\u03ba":[80,107],"(\u03ba":[81],"\u2260":[82],"0),":[83],"define":[85],"seven":[86],"operations":[87],"point-wise":[90],"induced":[92],"<sup":[97,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[98,182],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03ba</sup>":[99],"sequences":[104],"indexed":[105],"consisting":[109],"numbers).":[112],"It":[113],"is":[114,147],"found":[115],"that":[116],"(":[117],"R,\\\u2264),":[118],"much":[119],"like":[120],"(with":[122],"order),":[126],"has":[127],"some":[128,187],"desirable":[129],"properties;":[130],"particularly,":[131],"can":[133,248],"be":[134,249],"used":[135,250],"describe":[137],"corrected":[139],"degree":[140],"possibility":[142],"smaller":[148],"than":[149],"another.":[150],"Generalizing":[151],"discovery":[153],"process":[154],"\u2264,":[156],"provide":[158],"understandable":[160],"(even":[176],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[183],"),":[184],"which":[185,247],"meets":[186],"specific":[188],"requirement,":[189],"give":[192],"clear":[194],"description":[195],"relation":[198],"between":[199],"admissible":[201],"those":[204],"propose.":[206],"Those":[207],"urge":[208],"us":[209],"take":[211],"look":[213],"at":[214],"applications":[217],"(a":[220],"delegation":[221],"R).":[226],"Precisely,":[227],"propose":[229],"ordering":[231],"method":[232],"(based":[233],"matched":[240],"metric":[241],"weighted":[243],"averaging":[244],"aggregation":[245],"operator),":[246],"deal":[252],"with":[253],"very":[254],"complicated":[255],"generalized":[256],"interval-valued":[257],"preference":[258],"hesitant":[259],"relations":[260],"group":[262],"decision-making":[263],"problems.":[264]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
