Linear Diophantine fuzzy graphs with new decision-making approach Article Swipe
Muhammad Zeeshan Hanif
,
Naveed Yaqoob
,
Muhammad Riaz
,
Muhammad Aslam
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3934/math.2022801
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3934/math.2022801
The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these operations with various illustrations. We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. We describe the idea of homomorphisms for LDF-graphs. We observe the equivalence relation via an isomorphism between LDF-graphs. Some significant results related to complement of LDF-graph are also investigated. Lastly, an algorithm based on LDFSs and LDF-relations is proposed for decision-making problems. A numerical example of medical diagnosis application is presented based on proposed approach.
Related Topics
Concepts
Mathematics
Discrete mathematics
Graph isomorphism
Line graph
Graph product
Symmetric graph
Diophantine equation
Graph
Pathwidth
Voltage graph
Combinatorics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3934/math.2022801
- OA Status
- gold
- Cited By
- 21
- References
- 47
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4285272186
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4285272186Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3934/math.2022801Digital Object Identifier
- Title
-
Linear Diophantine fuzzy graphs with new decision-making approachWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-01-01Full publication date if available
- Authors
-
Muhammad Zeeshan Hanif, Naveed Yaqoob, Muhammad Riaz, Muhammad AslamList of authors in order
- Landing page
-
https://doi.org/10.3934/math.2022801Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.3934/math.2022801Direct OA link when available
- Concepts
-
Mathematics, Discrete mathematics, Graph isomorphism, Line graph, Graph product, Symmetric graph, Diophantine equation, Graph, Pathwidth, Voltage graph, CombinatoricsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
21Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 7, 2023: 11, 2022: 1Per-year citation counts (last 5 years)
- References (count)
-
47Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4285272186 |
|---|---|
| doi | https://doi.org/10.3934/math.2022801 |
| ids.doi | https://doi.org/10.3934/math.2022801 |
| ids.openalex | https://openalex.org/W4285272186 |
| fwci | 4.21028906 |
| type | article |
| title | Linear Diophantine fuzzy graphs with new decision-making approach |
| biblio.issue | 8 |
| biblio.volume | 7 |
| biblio.last_page | 14556 |
| biblio.first_page | 14532 |
| topics[0].id | https://openalex.org/T10050 |
| topics[0].field.id | https://openalex.org/fields/18 |
| topics[0].field.display_name | Decision Sciences |
| topics[0].score | 0.9912999868392944 |
| topics[0].domain.id | https://openalex.org/domains/2 |
| topics[0].domain.display_name | Social Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1803 |
| topics[0].subfield.display_name | Management Science and Operations Research |
| topics[0].display_name | Multi-Criteria Decision Making |
| topics[1].id | https://openalex.org/T11671 |
| topics[1].field.id | https://openalex.org/fields/18 |
| topics[1].field.display_name | Decision Sciences |
| topics[1].score | 0.9884999990463257 |
| topics[1].domain.id | https://openalex.org/domains/2 |
| topics[1].domain.display_name | Social Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1803 |
| topics[1].subfield.display_name | Management Science and Operations Research |
| topics[1].display_name | Fuzzy and Soft Set Theory |
| topics[2].id | https://openalex.org/T11063 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9684000015258789 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1703 |
| topics[2].subfield.display_name | Computational Theory and Mathematics |
| topics[2].display_name | Rough Sets and Fuzzy Logic |
| is_xpac | False |
| apc_list.value | 1200 |
| apc_list.currency | USD |
| apc_list.value_usd | 1200 |
| apc_paid.value | 1200 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 1200 |
| concepts[0].id | https://openalex.org/C33923547 |
| concepts[0].level | 0 |
| concepts[0].score | 0.5473459362983704 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[0].display_name | Mathematics |
| concepts[1].id | https://openalex.org/C118615104 |
| concepts[1].level | 1 |
| concepts[1].score | 0.484195739030838 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[1].display_name | Discrete mathematics |
| concepts[2].id | https://openalex.org/C61665672 |
| concepts[2].level | 4 |
| concepts[2].score | 0.4777583181858063 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q303100 |
| concepts[2].display_name | Graph isomorphism |
| concepts[3].id | https://openalex.org/C203776342 |
| concepts[3].level | 3 |
| concepts[3].score | 0.44106587767601013 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q1378376 |
| concepts[3].display_name | Line graph |
| concepts[4].id | https://openalex.org/C68103157 |
| concepts[4].level | 5 |
| concepts[4].score | 0.42806482315063477 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q569347 |
| concepts[4].display_name | Graph product |
| concepts[5].id | https://openalex.org/C14201764 |
| concepts[5].level | 5 |
| concepts[5].score | 0.415374219417572 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1205074 |
| concepts[5].display_name | Symmetric graph |
| concepts[6].id | https://openalex.org/C206530611 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4109340310096741 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q905896 |
| concepts[6].display_name | Diophantine equation |
| concepts[7].id | https://openalex.org/C132525143 |
| concepts[7].level | 2 |
| concepts[7].score | 0.3968387842178345 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q141488 |
| concepts[7].display_name | Graph |
| concepts[8].id | https://openalex.org/C43517604 |
| concepts[8].level | 4 |
| concepts[8].score | 0.3766240179538727 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q7144893 |
| concepts[8].display_name | Pathwidth |
| concepts[9].id | https://openalex.org/C22149727 |
| concepts[9].level | 4 |
| concepts[9].score | 0.36763182282447815 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q7940747 |
| concepts[9].display_name | Voltage graph |
| concepts[10].id | https://openalex.org/C114614502 |
| concepts[10].level | 1 |
| concepts[10].score | 0.3436998128890991 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[10].display_name | Combinatorics |
| keywords[0].id | https://openalex.org/keywords/mathematics |
| keywords[0].score | 0.5473459362983704 |
| keywords[0].display_name | Mathematics |
| keywords[1].id | https://openalex.org/keywords/discrete-mathematics |
| keywords[1].score | 0.484195739030838 |
| keywords[1].display_name | Discrete mathematics |
| keywords[2].id | https://openalex.org/keywords/graph-isomorphism |
| keywords[2].score | 0.4777583181858063 |
| keywords[2].display_name | Graph isomorphism |
| keywords[3].id | https://openalex.org/keywords/line-graph |
| keywords[3].score | 0.44106587767601013 |
| keywords[3].display_name | Line graph |
| keywords[4].id | https://openalex.org/keywords/graph-product |
| keywords[4].score | 0.42806482315063477 |
| keywords[4].display_name | Graph product |
| keywords[5].id | https://openalex.org/keywords/symmetric-graph |
| keywords[5].score | 0.415374219417572 |
| keywords[5].display_name | Symmetric graph |
| keywords[6].id | https://openalex.org/keywords/diophantine-equation |
| keywords[6].score | 0.4109340310096741 |
| keywords[6].display_name | Diophantine equation |
| keywords[7].id | https://openalex.org/keywords/graph |
| keywords[7].score | 0.3968387842178345 |
| keywords[7].display_name | Graph |
| keywords[8].id | https://openalex.org/keywords/pathwidth |
| keywords[8].score | 0.3766240179538727 |
| keywords[8].display_name | Pathwidth |
| keywords[9].id | https://openalex.org/keywords/voltage-graph |
| keywords[9].score | 0.36763182282447815 |
| keywords[9].display_name | Voltage graph |
| keywords[10].id | https://openalex.org/keywords/combinatorics |
| keywords[10].score | 0.3436998128890991 |
| keywords[10].display_name | Combinatorics |
| language | en |
| locations[0].id | doi:10.3934/math.2022801 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210179087 |
| locations[0].source.issn | 2473-6988 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2473-6988 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | AIMS Mathematics |
| locations[0].source.host_organization | https://openalex.org/P4310315844 |
| locations[0].source.host_organization_name | American Institute of Mathematical Sciences |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310315844 |
| locations[0].source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | AIMS Mathematics |
| locations[0].landing_page_url | https://doi.org/10.3934/math.2022801 |
| locations[1].id | pmh:oai:doaj.org/article:3a5a9353c4a44b568c5741e3d326fe43 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | cc-by-sa |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by-sa |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | AIMS Mathematics, Vol 7, Iss 8, Pp 14532-14556 (2022) |
| locations[1].landing_page_url | https://doaj.org/article/3a5a9353c4a44b568c5741e3d326fe43 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5037915584 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-1457-6954 |
| authorships[0].author.display_name | Muhammad Zeeshan Hanif |
| authorships[0].countries | PK |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I195024194 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan |
| authorships[0].institutions[0].id | https://openalex.org/I195024194 |
| authorships[0].institutions[0].ror | https://ror.org/02kdm5630 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I195024194 |
| authorships[0].institutions[0].country_code | PK |
| authorships[0].institutions[0].display_name | Riphah International University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Muhammad Zeeshan Hanif |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan |
| authorships[1].author.id | https://openalex.org/A5026211730 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-5362-9916 |
| authorships[1].author.display_name | Naveed Yaqoob |
| authorships[1].countries | PK |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I195024194 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan |
| authorships[1].institutions[0].id | https://openalex.org/I195024194 |
| authorships[1].institutions[0].ror | https://ror.org/02kdm5630 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I195024194 |
| authorships[1].institutions[0].country_code | PK |
| authorships[1].institutions[0].display_name | Riphah International University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Naveed Yaqoob |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan |
| authorships[2].author.id | https://openalex.org/A5049665961 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-8115-9168 |
| authorships[2].author.display_name | Muhammad Riaz |
| authorships[2].countries | PK |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I172780181 |
| authorships[2].affiliations[0].raw_affiliation_string | Department of Mathematics, University of the Punjab, Lahore, Pakistan |
| authorships[2].institutions[0].id | https://openalex.org/I172780181 |
| authorships[2].institutions[0].ror | https://ror.org/011maz450 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I172780181 |
| authorships[2].institutions[0].country_code | PK |
| authorships[2].institutions[0].display_name | University of the Punjab |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Muhammad Riaz |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Department of Mathematics, University of the Punjab, Lahore, Pakistan |
| authorships[3].author.id | https://openalex.org/A5033770251 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-6443-4962 |
| authorships[3].author.display_name | Muhammad Aslam |
| authorships[3].countries | PK, SA |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I195024194 |
| authorships[3].affiliations[0].raw_affiliation_string | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan |
| authorships[3].affiliations[1].institution_ids | https://openalex.org/I82952536 |
| authorships[3].affiliations[1].raw_affiliation_string | Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia |
| authorships[3].affiliations[2].institution_ids | https://openalex.org/I172780181 |
| authorships[3].affiliations[2].raw_affiliation_string | Department of Mathematics, University of the Punjab, Lahore, Pakistan |
| authorships[3].institutions[0].id | https://openalex.org/I195024194 |
| authorships[3].institutions[0].ror | https://ror.org/02kdm5630 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I195024194 |
| authorships[3].institutions[0].country_code | PK |
| authorships[3].institutions[0].display_name | Riphah International University |
| authorships[3].institutions[1].id | https://openalex.org/I172780181 |
| authorships[3].institutions[1].ror | https://ror.org/011maz450 |
| authorships[3].institutions[1].type | education |
| authorships[3].institutions[1].lineage | https://openalex.org/I172780181 |
| authorships[3].institutions[1].country_code | PK |
| authorships[3].institutions[1].display_name | University of the Punjab |
| authorships[3].institutions[2].id | https://openalex.org/I82952536 |
| authorships[3].institutions[2].ror | https://ror.org/052kwzs30 |
| authorships[3].institutions[2].type | education |
| authorships[3].institutions[2].lineage | https://openalex.org/I82952536 |
| authorships[3].institutions[2].country_code | SA |
| authorships[3].institutions[2].display_name | King Khalid University |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Muhammad Aslam |
| authorships[3].is_corresponding | True |
| authorships[3].raw_affiliation_strings | Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan, Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia, Department of Mathematics, University of the Punjab, Lahore, Pakistan |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.3934/math.2022801 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Linear Diophantine fuzzy graphs with new decision-making approach |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10050 |
| primary_topic.field.id | https://openalex.org/fields/18 |
| primary_topic.field.display_name | Decision Sciences |
| primary_topic.score | 0.9912999868392944 |
| primary_topic.domain.id | https://openalex.org/domains/2 |
| primary_topic.domain.display_name | Social Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1803 |
| primary_topic.subfield.display_name | Management Science and Operations Research |
| primary_topic.display_name | Multi-Criteria Decision Making |
| related_works | https://openalex.org/W2962948643, https://openalex.org/W2280002837, https://openalex.org/W2256054477, https://openalex.org/W2312623659, https://openalex.org/W86257524, https://openalex.org/W1769730578, https://openalex.org/W2006394420, https://openalex.org/W3001787527, https://openalex.org/W2325085986, https://openalex.org/W2213134860 |
| cited_by_count | 21 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 2 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 7 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 11 |
| counts_by_year[3].year | 2022 |
| counts_by_year[3].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | doi:10.3934/math.2022801 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210179087 |
| best_oa_location.source.issn | 2473-6988 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2473-6988 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | AIMS Mathematics |
| best_oa_location.source.host_organization | https://openalex.org/P4310315844 |
| best_oa_location.source.host_organization_name | American Institute of Mathematical Sciences |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310315844 |
| best_oa_location.source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | AIMS Mathematics |
| best_oa_location.landing_page_url | https://doi.org/10.3934/math.2022801 |
| primary_location.id | doi:10.3934/math.2022801 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210179087 |
| primary_location.source.issn | 2473-6988 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2473-6988 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | AIMS Mathematics |
| primary_location.source.host_organization | https://openalex.org/P4310315844 |
| primary_location.source.host_organization_name | American Institute of Mathematical Sciences |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310315844 |
| primary_location.source.host_organization_lineage_names | American Institute of Mathematical Sciences |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | AIMS Mathematics |
| primary_location.landing_page_url | https://doi.org/10.3934/math.2022801 |
| publication_date | 2022-01-01 |
| publication_year | 2022 |
| referenced_works | https://openalex.org/W3049148438, https://openalex.org/W3011105088, https://openalex.org/W2903466805, https://openalex.org/W2899158091, https://openalex.org/W4211007335, https://openalex.org/W2002541167, https://openalex.org/W2131273007, https://openalex.org/W2016168196, https://openalex.org/W1980564456, https://openalex.org/W2031241748, https://openalex.org/W2109689583, https://openalex.org/W1531907347, https://openalex.org/W2091275864, https://openalex.org/W1565315122, https://openalex.org/W2028649872, https://openalex.org/W1995972849, https://openalex.org/W2157746846, https://openalex.org/W2571719847, https://openalex.org/W1980345052, https://openalex.org/W2179485815, https://openalex.org/W2083480711, https://openalex.org/W2273289985, https://openalex.org/W2156662032, https://openalex.org/W2031345712, https://openalex.org/W2010276308, https://openalex.org/W2304896639, https://openalex.org/W4234428270, https://openalex.org/W1601092472, https://openalex.org/W2296563105, https://openalex.org/W2342014178, https://openalex.org/W2079457935, https://openalex.org/W1668569279, https://openalex.org/W2514754342, https://openalex.org/W3096131456, https://openalex.org/W2907855553, https://openalex.org/W3107959253, https://openalex.org/W2941162238, https://openalex.org/W3124245353, https://openalex.org/W2973775716, https://openalex.org/W3044339214, https://openalex.org/W3125697874, https://openalex.org/W3164521590, https://openalex.org/W3139668460, https://openalex.org/W3127095498, https://openalex.org/W2888024370, https://openalex.org/W3097542744, https://openalex.org/W2907615575 |
| referenced_works_count | 47 |
| abstract_inverted_index.A | 161 |
| abstract_inverted_index.a | 9, 46, 100, 108, 117 |
| abstract_inverted_index.We | 35, 64, 81, 88, 119, 127 |
| abstract_inverted_index.an | 133, 149 |
| abstract_inverted_index.as | 45 |
| abstract_inverted_index.is | 8, 25, 99, 107, 116, 156, 168 |
| abstract_inverted_index.of | 2, 22, 30, 39, 48, 68, 79, 96, 104, 113, 123, 143, 164 |
| abstract_inverted_index.on | 152, 171 |
| abstract_inverted_index.to | 26, 141 |
| abstract_inverted_index.The | 20 |
| abstract_inverted_index.aim | 21 |
| abstract_inverted_index.and | 17, 60, 77, 110, 154 |
| abstract_inverted_index.are | 145 |
| abstract_inverted_index.for | 13, 125, 158 |
| abstract_inverted_index.new | 10 |
| abstract_inverted_index.set | 6 |
| abstract_inverted_index.the | 28, 37, 94, 111, 121, 129 |
| abstract_inverted_index.two | 97, 105, 114 |
| abstract_inverted_index.via | 132 |
| abstract_inverted_index.Some | 137 |
| abstract_inverted_index.also | 146 |
| abstract_inverted_index.idea | 38, 122 |
| abstract_inverted_index.join | 112 |
| abstract_inverted_index.soft | 15 |
| abstract_inverted_index.some | 90 |
| abstract_inverted_index.that | 93 |
| abstract_inverted_index.this | 23 |
| abstract_inverted_index.tool | 12 |
| abstract_inverted_index.with | 85 |
| abstract_inverted_index.LDFSs | 153 |
| abstract_inverted_index.based | 151, 170 |
| abstract_inverted_index.crisp | 69 |
| abstract_inverted_index.fuzzy | 5, 42, 55, 58, 62 |
| abstract_inverted_index.graph | 31, 43, 70 |
| abstract_inverted_index.join, | 76 |
| abstract_inverted_index.these | 83 |
| abstract_inverted_index.union | 78 |
| abstract_inverted_index.(LDFS) | 7 |
| abstract_inverted_index.LDFSs. | 34 |
| abstract_inverted_index.extend | 27, 65 |
| abstract_inverted_index.graph, | 56, 59 |
| abstract_inverted_index.graph. | 63 |
| abstract_inverted_index.linear | 3, 40 |
| abstract_inverted_index.notion | 29 |
| abstract_inverted_index.q-rung | 53 |
| abstract_inverted_index.theory | 32, 71 |
| abstract_inverted_index.Lastly, | 148 |
| abstract_inverted_index.analyze | 89 |
| abstract_inverted_index.article | 24 |
| abstract_inverted_index.between | 135 |
| abstract_inverted_index.certain | 49, 66 |
| abstract_inverted_index.concept | 1 |
| abstract_inverted_index.example | 163 |
| abstract_inverted_index.medical | 165 |
| abstract_inverted_index.observe | 128 |
| abstract_inverted_index.product | 103 |
| abstract_inverted_index.related | 140 |
| abstract_inverted_index.results | 92, 139 |
| abstract_inverted_index.towards | 33, 72 |
| abstract_inverted_index.various | 86 |
| abstract_inverted_index.concepts | 51 |
| abstract_inverted_index.decision | 18 |
| abstract_inverted_index.describe | 120 |
| abstract_inverted_index.initiate | 36 |
| abstract_inverted_index.proposed | 157, 172 |
| abstract_inverted_index.relation | 131 |
| abstract_inverted_index.LDF-graph | 73, 144 |
| abstract_inverted_index.algorithm | 150 |
| abstract_inverted_index.analysis. | 19 |
| abstract_inverted_index.cartesian | 102 |
| abstract_inverted_index.diagnosis | 166 |
| abstract_inverted_index.elucidate | 82 |
| abstract_inverted_index.numerical | 162 |
| abstract_inverted_index.orthopair | 54 |
| abstract_inverted_index.presented | 169 |
| abstract_inverted_index.problems. | 160 |
| abstract_inverted_index.LDF-graph, | 101, 109 |
| abstract_inverted_index.LDF-graph. | 118 |
| abstract_inverted_index.LDF-graphs | 98, 106, 115 |
| abstract_inverted_index.complement | 142 |
| abstract_inverted_index.computing, | 16 |
| abstract_inverted_index.including, | 52, 74 |
| abstract_inverted_index.operations | 84 |
| abstract_inverted_index.properties | 67 |
| abstract_inverted_index.(LDF-graph) | 44 |
| abstract_inverted_index.Diophantine | 4, 41 |
| abstract_inverted_index.LDF-graphs. | 80, 126, 136 |
| abstract_inverted_index.Pythagorean | 57 |
| abstract_inverted_index.application | 167 |
| abstract_inverted_index.composition | 95 |
| abstract_inverted_index.equivalence | 130 |
| abstract_inverted_index.interesting | 91 |
| abstract_inverted_index.isomorphism | 134 |
| abstract_inverted_index.significant | 138 |
| abstract_inverted_index.theoretical | 50 |
| abstract_inverted_index.composition, | 75 |
| abstract_inverted_index.mathematical | 11 |
| abstract_inverted_index.LDF-relations | 155 |
| abstract_inverted_index.homomorphisms | 124 |
| abstract_inverted_index.investigated. | 147 |
| abstract_inverted_index.optimization, | 14 |
| abstract_inverted_index.generalization | 47 |
| abstract_inverted_index.illustrations. | 87 |
| abstract_inverted_index.intuitionistic | 61 |
| abstract_inverted_index.decision-making | 159 |
| abstract_inverted_index.<abstract><p>The | 0 |
| abstract_inverted_index.approach.</p></abstract> | 173 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 89 |
| corresponding_author_ids | https://openalex.org/A5033770251 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 4 |
| corresponding_institution_ids | https://openalex.org/I172780181, https://openalex.org/I195024194, https://openalex.org/I82952536 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.7799999713897705 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.93415533 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |