{"id":"https://openalex.org/W2908721168","doi":"https://doi.org/10.1007/s13042-018-00909-y","title":"Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making","display_name":"Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making","publication_year":2019,"publication_date":"2019-01-10","ids":{"openalex":"https://openalex.org/W2908721168","doi":"https://doi.org/10.1007/s13042-018-00909-y","mag":"2908721168"},"language":"en","primary_location":{"id":"doi:10.1007/s13042-018-00909-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13042-018-00909-y","pdf_url":null,"source":{"id":"https://openalex.org/S2764999920","display_name":"International Journal of Machine Learning and Cybernetics","issn_l":"1868-8071","issn":["1868-8071","1868-808X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Machine Learning and Cybernetics","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/A5101908597","display_name":"Muhammad Shakeel","orcid":"https://orcid.org/0000-0002-8475-7101"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"M. Shakeel","raw_affiliation_strings":["Department of Mathematics, Hazara University Mansehra Kpk, Dhodial, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra Kpk, Dhodial, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077817609","display_name":"Saleem Abdullah","orcid":"https://orcid.org/0000-0002-7474-5115"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"S. Abdullah","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan Kpk, Mardan, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan Kpk, Mardan, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005220352","display_name":"Muhammad Shahzad","orcid":"https://orcid.org/0000-0002-2290-804X"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Shahzad","raw_affiliation_strings":["Department of Mathematics, Hazara University Mansehra Kpk, Dhodial, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra Kpk, Dhodial, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081970325","display_name":"Nasir Siddiqui","orcid":"https://orcid.org/0000-0002-0612-4835"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Nasir Siddiqui","raw_affiliation_strings":["Department of Mathematics, University of Engineering and Technology Taxila, Taxila, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Engineering and Technology Taxila, Taxila, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101908597"],"corresponding_institution_ids":["https://openalex.org/I263208278"],"apc_list":{"value":2790,"currency":"EUR","value_usd":3590},"apc_paid":null,"fwci":2.8816,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.90559991,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"10","first_page":"2867","last_page":"2886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9728999733924866,"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"}},{"id":"https://openalex.org/T11634","display_name":"Water Quality and Pollution Assessment","score":0.9538000226020813,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.942898154258728},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6344062089920044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6170667409896851},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.6160449385643005},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5439233779907227},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5412051677703857},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.48308590054512024},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.46379026770591736},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.4207574129104614},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3482632040977478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3387712836265564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3093775510787964},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.30588704347610474},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23334619402885437},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17602071166038513},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15008074045181274},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14197775721549988},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.05690509080886841}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.942898154258728},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6344062089920044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6170667409896851},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.6160449385643005},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5439233779907227},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5412051677703857},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.48308590054512024},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.46379026770591736},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.4207574129104614},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3482632040977478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3387712836265564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3093775510787964},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.30588704347610474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23334619402885437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17602071166038513},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15008074045181274},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14197775721549988},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05690509080886841},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s13042-018-00909-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13042-018-00909-y","pdf_url":null,"source":{"id":"https://openalex.org/S2764999920","display_name":"International Journal of Machine Learning and Cybernetics","issn_l":"1868-8071","issn":["1868-8071","1868-808X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Machine Learning and Cybernetics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8199999928474426}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1489487994","https://openalex.org/W1668569279","https://openalex.org/W1829951598","https://openalex.org/W1916037859","https://openalex.org/W1965777053","https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1987814547","https://openalex.org/W2008103229","https://openalex.org/W2013932252","https://openalex.org/W2041346764","https://openalex.org/W2042377845","https://openalex.org/W2073275126","https://openalex.org/W2075368401","https://openalex.org/W2078423530","https://openalex.org/W2079457935","https://openalex.org/W2087991154","https://openalex.org/W2104077967","https://openalex.org/W2122732477","https://openalex.org/W2160185911","https://openalex.org/W2311142332","https://openalex.org/W2345848912","https://openalex.org/W2376743315","https://openalex.org/W2379318532","https://openalex.org/W2412590235","https://openalex.org/W2611273622","https://openalex.org/W2624109864","https://openalex.org/W2725695898","https://openalex.org/W2739712640","https://openalex.org/W2756768858","https://openalex.org/W2765829946","https://openalex.org/W2769278513","https://openalex.org/W2772679429","https://openalex.org/W2784166218","https://openalex.org/W2784303153","https://openalex.org/W2796572160","https://openalex.org/W2912565176","https://openalex.org/W4205912702","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4378767041","https://openalex.org/W4210969441","https://openalex.org/W2943864676","https://openalex.org/W2765931357","https://openalex.org/W2906568202","https://openalex.org/W2774486171","https://openalex.org/W1985678092","https://openalex.org/W4223890462"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}