Publication Information

{'id': 'https://openalex.org/W4213091376', 'doi': 'https://doi.org/10.3390/axioms11020077', 'title': 'The Relationships among Three Kinds of Divisions of Type-1 Fuzzy Numbers', 'display_name': 'The Relationships among Three Kinds of Divisions of Type-1 Fuzzy Numbers', 'publication_year': 2022, 'publication_date': '2022-02-15', 'ids': {'openalex': 'https://openalex.org/W4213091376', 'doi': 'https://doi.org/10.3390/axioms11020077'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.3390/axioms11020077', 'pdf_url': 'https://www.mdpi.com/2075-1680/11/2/77/pdf?version=1644930647', 'source': {'id': 'https://openalex.org/S4210173132', 'display_name': 'Axioms', 'issn_l': '2075-1680', 'issn': ['2075-1680'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310310987', 'host_organization_name': 'Multidisciplinary Digital Publishing Institute', 'host_organization_lineage': ['https://openalex.org/P4310310987'], 'host_organization_lineage_names': ['Multidisciplinary Digital Publishing Institute'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref', 'doaj'], 'open_access': {'is_oa': True, 'oa_status': 'gold', 'oa_url': 'https://www.mdpi.com/2075-1680/11/2/77/pdf?version=1644930647', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5036332719', 'display_name': 'Yadan Jiang', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I10535382', 'display_name': 'Chongqing University of Posts and Telecommunications', 'ror': 'https://ror.org/03dgaqz26', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I10535382']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Yadan Jiang', 'raw_affiliation_strings': ['College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China'], 'affiliations': [{'raw_affiliation_string': 'College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China', 'institution_ids': ['https://openalex.org/I10535382']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5023158018', 'display_name': 'Dong Qiu', 'orcid': 'https://orcid.org/0000-0002-4088-5371'}, 'institutions': [{'id': 'https://openalex.org/I10535382', 'display_name': 'Chongqing University of Posts and Telecommunications', 'ror': 'https://ror.org/03dgaqz26', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I10535382']}], 'countries': ['CN'], 'is_corresponding': True, 'raw_author_name': 'Dong Qiu', 'raw_affiliation_strings': ['College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China'], 'affiliations': [{'raw_affiliation_string': 'College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China', 'institution_ids': ['https://openalex.org/I10535382']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5023158018'], 'corresponding_institution_ids': ['https://openalex.org/I10535382'], 'apc_list': {'value': 1400, 'currency': 'CHF', 'value_usd': 1515, 'provenance': 'doaj'}, 'apc_paid': {'value': 1400, 'currency': 'CHF', 'value_usd': 1515, 'provenance': 'doaj'}, 'fwci': 1.04, 'has_fulltext': False, 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.999784, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 80, 'max': 83}, 'biblio': {'volume': '11', 'issue': '2', 'first_page': '77', 'last_page': '77'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12135', 'display_name': 'Fuzzy Systems and Optimization', 'score': 0.9998, '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': 0.9998, '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': 0.9959, '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/T10820', 'display_name': 'Fuzzy Logic and Control Systems', 'score': 0.9937, 'subfield': {'id': 'https://openalex.org/subfields/1702', 'display_name': 'Artificial Intelligence'}, '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/division-ring', 'display_name': 'Division ring', 'score': 0.5089667}], 'concepts': [{'id': 'https://openalex.org/C60798267', 'wikidata': 'https://www.wikidata.org/wiki/Q1226939', 'display_name': 'Division (mathematics)', 'level': 2, 'score': 0.9516574}, {'id': 'https://openalex.org/C2780595030', 'wikidata': 'https://www.wikidata.org/wiki/Q3860309', 'display_name': 'Multiplication (music)', 'level': 2, 'score': 0.7552446}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.72000635}, {'id': 'https://openalex.org/C96442724', 'wikidata': 'https://www.wikidata.org/wiki/Q242188', 'display_name': 'Invertible matrix', 'level': 2, 'score': 0.61151767}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.59004676}, {'id': 'https://openalex.org/C31671303', 'wikidata': 'https://www.wikidata.org/wiki/Q650741', 'display_name': 'Division ring', 'level': 3, 'score': 0.5089667}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.34851477}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3019873}, {'id': 'https://openalex.org/C94375191', 'wikidata': 'https://www.wikidata.org/wiki/Q11205', 'display_name': 'Arithmetic', 'level': 1, 'score': 0.2546845}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.11005151}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', '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': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.3390/axioms11020077', 'pdf_url': 'https://www.mdpi.com/2075-1680/11/2/77/pdf?version=1644930647', 'source': {'id': 'https://openalex.org/S4210173132', 'display_name': 'Axioms', 'issn_l': '2075-1680', 'issn': ['2075-1680'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310310987', 'host_organization_name': 'Multidisciplinary Digital Publishing Institute', 'host_organization_lineage': ['https://openalex.org/P4310310987'], 'host_organization_lineage_names': ['Multidisciplinary Digital Publishing Institute'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': False, 'landing_page_url': 'https://doaj.org/article/bb9c1edff8e84860b0189f3299e22fdf', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306401280', 'display_name': 'DOAJ (DOAJ: Directory of Open Access Journals)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.3390/axioms11020077', 'pdf_url': 'https://www.mdpi.com/2075-1680/11/2/77/pdf?version=1644930647', 'source': {'id': 'https://openalex.org/S4210173132', 'display_name': 'Axioms', 'issn_l': '2075-1680', 'issn': ['2075-1680'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310310987', 'host_organization_name': 'Multidisciplinary Digital Publishing Institute', 'host_organization_lineage': ['https://openalex.org/P4310310987'], 'host_organization_lineage_names': ['Multidisciplinary Digital Publishing Institute'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 27, 'referenced_works': ['https://openalex.org/W1531645310', 'https://openalex.org/W1549880700', 'https://openalex.org/W1551251595', 'https://openalex.org/W1605890184', 'https://openalex.org/W18761891', 'https://openalex.org/W1975593923', 'https://openalex.org/W1982606567', 'https://openalex.org/W1987010138', 'https://openalex.org/W1995123739', 'https://openalex.org/W2003403943', 'https://openalex.org/W2030626585', 'https://openalex.org/W2038020290', 'https://openalex.org/W2038354216', 'https://openalex.org/W2070545443', 'https://openalex.org/W2095292012', 'https://openalex.org/W2144873543', 'https://openalex.org/W2160780842', 'https://openalex.org/W2533997743', 'https://openalex.org/W2563209315', 'https://openalex.org/W2580890888', 'https://openalex.org/W2968458585', 'https://openalex.org/W2988517722', 'https://openalex.org/W3122881245', 'https://openalex.org/W3138790204', 'https://openalex.org/W3169602177', 'https://openalex.org/W4211007335', 'https://openalex.org/W607489306'], 'related_works': ['https://openalex.org/W4294168466', 'https://openalex.org/W3094080891', 'https://openalex.org/W3093500249', 'https://openalex.org/W2991811627', 'https://openalex.org/W2886205627', 'https://openalex.org/W2095090051', 'https://openalex.org/W2063343791', 'https://openalex.org/W2038759377', 'https://openalex.org/W2022472189', 'https://openalex.org/W1584559800'], 'abstract_inverted_index': {'The': [0], 'division': [1, 39, 50, 61, 64], 'operation': [2], 'for': [3, 14], 'type-1': [4], 'fuzzy': [5], 'numbers': [6], 'in': [7, 23], 'its': [8], 'original': [9], 'form': [10], 'is': [11, 19, 51], 'not': [12], 'invertible': [13], 'the': [15, 34, 46, 54], 'multiplication': [16], 'operation.': [17], 'This': [18], 'an': [20], 'essential': [21], 'drawback': [22, 29], 'some': [24], 'applications.': [25], 'To': [26], 'eliminate': [27], 'this': [28, 44], 'several': [30], 'approaches': [31], 'are': [32, 65], 'proposed:': [33], 'generalized': [35, 38, 57, 60], 'Hukuhara': [36, 58], 'division,': [37, 59], 'and': [40, 53, 62], 'granular': [41, 49, 63], 'division.': [42], 'In': [43], 'paper,': [45], 'expression': [47], 'of': [48], 'introduced,': [52], 'relationships': [55], 'among': [56], 'clarified.': [66]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4213091376', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 1}], 'updated_date': '2024-12-08T13:44:25.194016', 'created_date': '2022-02-24'}