A new method for solving quadratic fractional programming problem in neutrosophic environment Article Swipe

PDF

Hamiden Abd El‐Wahed Khalifa , Majed Alharbi , Pavan Kumar ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1515/eng-2021-0088

In the current study, a neutrosophic quadratic fractional programming (NQFP) problem is investigated using a new method. The NQFP problem is converted into the corresponding quadratic fractional programming (QFP) problem. The QFP is formulated by using the score function and hence it is converted to the linear programming problem (LPP) using the Taylor series, which can be solved by LPP techniques or software (e.g., Lingo). Finally, an example is given for illustration.

Related Topics

Mathematics

Computer Science

Mathematical Analysis

Concepts

Quadratic programming Fractional programming Sequential quadratic programming Quadratic equation Mathematical optimization Mathematics Taylor series Linear programming Quadratic unconstrained binary optimization Series (stratigraphy) Applied mathematics Computer science Nonlinear programming Mathematical analysis Nonlinear system Physics Geometry Quantum mechanics Quantum Biology Paleontology Quantum computer

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.1515/eng-2021-0088
PDF: https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf
OA Status: gold
Cited By: 13
References: 32
Related Works: 10
OpenAlex ID: https://openalex.org/W3200639542

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W3200639542

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.1515/eng-2021-0088

Digital Object Identifier
Title: A new method for solving quadratic fractional programming problem in neutrosophic environment

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2021

Year of publication
Publication date: 2021-01-01

Full publication date if available
Authors: Hamiden Abd El‐Wahed Khalifa, Majed Alharbi, Pavan Kumar

List of authors in order
Landing page: https://doi.org/10.1515/eng-2021-0088

Publisher landing page
PDF URL: https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf

Direct OA link when available
Concepts: Quadratic programming, Fractional programming, Sequential quadratic programming, Quadratic equation, Mathematical optimization, Mathematics, Taylor series, Linear programming, Quadratic unconstrained binary optimization, Series (stratigraphy), Applied mathematics, Computer science, Nonlinear programming, Mathematical analysis, Nonlinear system, Physics, Geometry, Quantum mechanics, Quantum, Biology, Paleontology, Quantum computer

Top concepts (fields/topics) attached by OpenAlex
Cited by: 13

Total citation count in OpenAlex
Citations by year (recent): 2025: 1, 2024: 2, 2023: 6, 2022: 4

Per-year citation counts (last 5 years)
References (count): 32

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W3200639542
doi	https://doi.org/10.1515/eng-2021-0088
ids.doi	https://doi.org/10.1515/eng-2021-0088
ids.mag	3200639542
ids.openalex	https://openalex.org/W3200639542
fwci	1.59399491
type	article
title	A new method for solving quadratic fractional programming problem in neutrosophic environment
biblio.issue	1
biblio.volume	11
biblio.last_page	886
biblio.first_page	880
topics[0].id	https://openalex.org/T12709
topics[0].field.id	https://openalex.org/fields/22
topics[0].field.display_name	Engineering
topics[0].score	0.9987999796867371
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2207
topics[0].subfield.display_name	Control and Systems Engineering
topics[0].display_name	Optimization and Mathematical Programming
topics[1].id	https://openalex.org/T10050
topics[1].field.id	https://openalex.org/fields/18
topics[1].field.display_name	Decision Sciences
topics[1].score	0.9002000093460083
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	Multi-Criteria Decision Making
is_xpac	False
apc_list.value	1000
apc_list.currency	EUR
apc_list.value_usd	1078
apc_paid.value	1000
apc_paid.currency	EUR
apc_paid.value_usd	1078
concepts[0].id	https://openalex.org/C81845259
concepts[0].level	2
concepts[0].score	0.8160205483436584
concepts[0].wikidata	https://www.wikidata.org/wiki/Q290117
concepts[0].display_name	Quadratic programming
concepts[1].id	https://openalex.org/C169069869
concepts[1].level	4
concepts[1].score	0.7248866558074951
concepts[1].wikidata	https://www.wikidata.org/wiki/Q5477546
concepts[1].display_name	Fractional programming
concepts[2].id	https://openalex.org/C198927703
concepts[2].level	3
concepts[2].score	0.6557738184928894
concepts[2].wikidata	https://www.wikidata.org/wiki/Q4373881
concepts[2].display_name	Sequential quadratic programming
concepts[3].id	https://openalex.org/C129844170
concepts[3].level	2
concepts[3].score	0.5247340798377991
concepts[3].wikidata	https://www.wikidata.org/wiki/Q41299
concepts[3].display_name	Quadratic equation
concepts[4].id	https://openalex.org/C126255220
concepts[4].level	1
concepts[4].score	0.5214735269546509
concepts[4].wikidata	https://www.wikidata.org/wiki/Q141495
concepts[4].display_name	Mathematical optimization
concepts[5].id	https://openalex.org/C33923547
concepts[5].level	0
concepts[5].score	0.5133837461471558
concepts[5].wikidata	https://www.wikidata.org/wiki/Q395
concepts[5].display_name	Mathematics
concepts[6].id	https://openalex.org/C158946198
concepts[6].level	2
concepts[6].score	0.4880763292312622
concepts[6].wikidata	https://www.wikidata.org/wiki/Q131187
concepts[6].display_name	Taylor series
concepts[7].id	https://openalex.org/C41045048
concepts[7].level	2
concepts[7].score	0.4833254814147949
concepts[7].wikidata	https://www.wikidata.org/wiki/Q202843
concepts[7].display_name	Linear programming
concepts[8].id	https://openalex.org/C177179195
concepts[8].level	4
concepts[8].score	0.441747784614563
concepts[8].wikidata	https://www.wikidata.org/wiki/Q7268372
concepts[8].display_name	Quadratic unconstrained binary optimization
concepts[9].id	https://openalex.org/C143724316
concepts[9].level	2
concepts[9].score	0.43170446157455444
concepts[9].wikidata	https://www.wikidata.org/wiki/Q312468
concepts[9].display_name	Series (stratigraphy)
concepts[10].id	https://openalex.org/C28826006
concepts[10].level	1
concepts[10].score	0.4259393811225891
concepts[10].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[10].display_name	Applied mathematics
concepts[11].id	https://openalex.org/C41008148
concepts[11].level	0
concepts[11].score	0.41455161571502686
concepts[11].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[11].display_name	Computer science
concepts[12].id	https://openalex.org/C115527620
concepts[12].level	3
concepts[12].score	0.366489440202713
concepts[12].wikidata	https://www.wikidata.org/wiki/Q769909
concepts[12].display_name	Nonlinear programming
concepts[13].id	https://openalex.org/C134306372
concepts[13].level	1
concepts[13].score	0.1407647728919983
concepts[13].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[13].display_name	Mathematical analysis
concepts[14].id	https://openalex.org/C158622935
concepts[14].level	2
concepts[14].score	0.07459214329719543
concepts[14].wikidata	https://www.wikidata.org/wiki/Q660848
concepts[14].display_name	Nonlinear system
concepts[15].id	https://openalex.org/C121332964
concepts[15].level	0
concepts[15].score	0.055473774671554565
concepts[15].wikidata	https://www.wikidata.org/wiki/Q413
concepts[15].display_name	Physics
concepts[16].id	https://openalex.org/C2524010
concepts[16].level	1
concepts[16].score	0.050819337368011475
concepts[16].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[16].display_name	Geometry
concepts[17].id	https://openalex.org/C62520636
concepts[17].level	1
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q944
concepts[17].display_name	Quantum mechanics
concepts[18].id	https://openalex.org/C84114770
concepts[18].level	2
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q46344
concepts[18].display_name	Quantum
concepts[19].id	https://openalex.org/C86803240
concepts[19].level	0
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q420
concepts[19].display_name	Biology
concepts[20].id	https://openalex.org/C151730666
concepts[20].level	1
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q7205
concepts[20].display_name	Paleontology
concepts[21].id	https://openalex.org/C58053490
concepts[21].level	3
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q176555
concepts[21].display_name	Quantum computer
keywords[0].id	https://openalex.org/keywords/quadratic-programming
keywords[0].score	0.8160205483436584
keywords[0].display_name	Quadratic programming
keywords[1].id	https://openalex.org/keywords/fractional-programming
keywords[1].score	0.7248866558074951
keywords[1].display_name	Fractional programming
keywords[2].id	https://openalex.org/keywords/sequential-quadratic-programming
keywords[2].score	0.6557738184928894
keywords[2].display_name	Sequential quadratic programming
keywords[3].id	https://openalex.org/keywords/quadratic-equation
keywords[3].score	0.5247340798377991
keywords[3].display_name	Quadratic equation
keywords[4].id	https://openalex.org/keywords/mathematical-optimization
keywords[4].score	0.5214735269546509
keywords[4].display_name	Mathematical optimization
keywords[5].id	https://openalex.org/keywords/mathematics
keywords[5].score	0.5133837461471558
keywords[5].display_name	Mathematics
keywords[6].id	https://openalex.org/keywords/taylor-series
keywords[6].score	0.4880763292312622
keywords[6].display_name	Taylor series
keywords[7].id	https://openalex.org/keywords/linear-programming
keywords[7].score	0.4833254814147949
keywords[7].display_name	Linear programming
keywords[8].id	https://openalex.org/keywords/quadratic-unconstrained-binary-optimization
keywords[8].score	0.441747784614563
keywords[8].display_name	Quadratic unconstrained binary optimization
keywords[9].id	https://openalex.org/keywords/series
keywords[9].score	0.43170446157455444
keywords[9].display_name	Series (stratigraphy)
keywords[10].id	https://openalex.org/keywords/applied-mathematics
keywords[10].score	0.4259393811225891
keywords[10].display_name	Applied mathematics
keywords[11].id	https://openalex.org/keywords/computer-science
keywords[11].score	0.41455161571502686
keywords[11].display_name	Computer science
keywords[12].id	https://openalex.org/keywords/nonlinear-programming
keywords[12].score	0.366489440202713
keywords[12].display_name	Nonlinear programming
keywords[13].id	https://openalex.org/keywords/mathematical-analysis
keywords[13].score	0.1407647728919983
keywords[13].display_name	Mathematical analysis
keywords[14].id	https://openalex.org/keywords/nonlinear-system
keywords[14].score	0.07459214329719543
keywords[14].display_name	Nonlinear system
keywords[15].id	https://openalex.org/keywords/physics
keywords[15].score	0.055473774671554565
keywords[15].display_name	Physics
keywords[16].id	https://openalex.org/keywords/geometry
keywords[16].score	0.050819337368011475
keywords[16].display_name	Geometry
language	en
locations[0].id	doi:10.1515/eng-2021-0088
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S2738317984
locations[0].source.issn	2391-5439
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2391-5439
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	Open Engineering
locations[0].source.host_organization	https://openalex.org/P4310313990
locations[0].source.host_organization_name	De Gruyter
locations[0].source.host_organization_lineage	https://openalex.org/P4310313990
locations[0].source.host_organization_lineage_names	De Gruyter
locations[0].license	cc-by
locations[0].pdf_url	https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf
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	Open Engineering
locations[0].landing_page_url	https://doi.org/10.1515/eng-2021-0088
locations[1].id	pmh:oai:doaj.org/article:be463538c9034e6a80e3123729961d7b
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	Open Engineering, Vol 11, Iss 1, Pp 880-886 (2021)
locations[1].landing_page_url	https://doaj.org/article/be463538c9034e6a80e3123729961d7b
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5050384109
authorships[0].author.orcid	https://orcid.org/0000-0002-8269-8822
authorships[0].author.display_name	Hamiden Abd El‐Wahed Khalifa
authorships[0].countries	EG, SA
authorships[0].affiliations[0].institution_ids	https://openalex.org/I145487455
authorships[0].affiliations[0].raw_affiliation_string	Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University , Giza , Egypt
authorships[0].affiliations[1].institution_ids	https://openalex.org/I156216236
authorships[0].affiliations[1].raw_affiliation_string	Mathematics Department, College of Science and Arts , Al-Badaya , Qassim University , Saudi Arabia
authorships[0].institutions[0].id	https://openalex.org/I145487455
authorships[0].institutions[0].ror	https://ror.org/03q21mh05
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I145487455
authorships[0].institutions[0].country_code	EG
authorships[0].institutions[0].display_name	Cairo University
authorships[0].institutions[1].id	https://openalex.org/I156216236
authorships[0].institutions[1].ror	https://ror.org/01wsfe280
authorships[0].institutions[1].type	education
authorships[0].institutions[1].lineage	https://openalex.org/I156216236
authorships[0].institutions[1].country_code	SA
authorships[0].institutions[1].display_name	Qassim University
authorships[0].author_position	first
authorships[0].raw_author_name	Hamiden Abd El-Wahed Khalifa
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	Mathematics Department, College of Science and Arts , Al-Badaya , Qassim University , Saudi Arabia, Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University , Giza , Egypt
authorships[1].author.id	https://openalex.org/A5075392453
authorships[1].author.orcid
authorships[1].author.display_name	Majed Alharbi
authorships[1].countries	SA
authorships[1].affiliations[0].institution_ids	https://openalex.org/I156216236
authorships[1].affiliations[0].raw_affiliation_string	Mathematics Department, College of Science and Arts , Methnab , Qassim University , Saudi Arabia
authorships[1].institutions[0].id	https://openalex.org/I156216236
authorships[1].institutions[0].ror	https://ror.org/01wsfe280
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I156216236
authorships[1].institutions[0].country_code	SA
authorships[1].institutions[0].display_name	Qassim University
authorships[1].author_position	middle
authorships[1].raw_author_name	Majed Alharbi
authorships[1].is_corresponding	True
authorships[1].raw_affiliation_strings	Mathematics Department, College of Science and Arts , Methnab , Qassim University , Saudi Arabia
authorships[2].author.id	https://openalex.org/A5101398697
authorships[2].author.orcid	https://orcid.org/0000-0001-5340-7777
authorships[2].author.display_name	Pavan Kumar
authorships[2].countries	IN
authorships[2].affiliations[0].institution_ids	https://openalex.org/I464993
authorships[2].affiliations[0].raw_affiliation_string	Department of Mathematics, School of Advanced Science and Languages, VIT Bhopal University , Sehore , MP, 466114 , India
authorships[2].institutions[0].id	https://openalex.org/I464993
authorships[2].institutions[0].ror	https://ror.org/02ax13658
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I464993
authorships[2].institutions[0].country_code	IN
authorships[2].institutions[0].display_name	Barkatullah University
authorships[2].author_position	last
authorships[2].raw_author_name	Pavan Kumar
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Department of Mathematics, School of Advanced Science and Languages, VIT Bhopal University , Sehore , MP, 466114 , India
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2021-09-27T00:00:00
display_name	A new method for solving quadratic fractional programming problem in neutrosophic environment
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T12709
primary_topic.field.id	https://openalex.org/fields/22
primary_topic.field.display_name	Engineering
primary_topic.score	0.9987999796867371
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2207
primary_topic.subfield.display_name	Control and Systems Engineering
primary_topic.display_name	Optimization and Mathematical Programming
related_works	https://openalex.org/W2128461291, https://openalex.org/W2589412911, https://openalex.org/W4206704743, https://openalex.org/W2081101031, https://openalex.org/W2010155752, https://openalex.org/W2098918699, https://openalex.org/W1997448496, https://openalex.org/W165108556, https://openalex.org/W2328936146, https://openalex.org/W3200639542
cited_by_count	13
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	1
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	2
counts_by_year[2].year	2023
counts_by_year[2].cited_by_count	6
counts_by_year[3].year	2022
counts_by_year[3].cited_by_count	4
locations_count	2
best_oa_location.id	doi:10.1515/eng-2021-0088
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S2738317984
best_oa_location.source.issn	2391-5439
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2391-5439
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	Open Engineering
best_oa_location.source.host_organization	https://openalex.org/P4310313990
best_oa_location.source.host_organization_name	De Gruyter
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310313990
best_oa_location.source.host_organization_lineage_names	De Gruyter
best_oa_location.license	cc-by
best_oa_location.pdf_url	https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf
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	Open Engineering
best_oa_location.landing_page_url	https://doi.org/10.1515/eng-2021-0088
primary_location.id	doi:10.1515/eng-2021-0088
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S2738317984
primary_location.source.issn	2391-5439
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2391-5439
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	Open Engineering
primary_location.source.host_organization	https://openalex.org/P4310313990
primary_location.source.host_organization_name	De Gruyter
primary_location.source.host_organization_lineage	https://openalex.org/P4310313990
primary_location.source.host_organization_lineage_names	De Gruyter
primary_location.license	cc-by
primary_location.pdf_url	https://www.degruyter.com/document/doi/10.1515/eng-2021-0088/pdf
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	Open Engineering
primary_location.landing_page_url	https://doi.org/10.1515/eng-2021-0088
publication_date	2021-01-01
publication_year	2021
referenced_works	https://openalex.org/W2156577211, https://openalex.org/W2089197052, https://openalex.org/W1966757346, https://openalex.org/W2053641094, https://openalex.org/W2007464938, https://openalex.org/W2010364067, https://openalex.org/W2003610871, https://openalex.org/W1788709585, https://openalex.org/W2974586822, https://openalex.org/W2893440933, https://openalex.org/W3135796150, https://openalex.org/W3006728051, https://openalex.org/W4234250338, https://openalex.org/W3142236006, https://openalex.org/W2512921275, https://openalex.org/W4211007335, https://openalex.org/W6702266818, https://openalex.org/W1874009099, https://openalex.org/W4241914201, https://openalex.org/W3159501514, https://openalex.org/W3091984800, https://openalex.org/W3014207952, https://openalex.org/W1980564456, https://openalex.org/W6602379895, https://openalex.org/W2297362139, https://openalex.org/W2905308477, https://openalex.org/W2127470768, https://openalex.org/W2322281151, https://openalex.org/W2609588521, https://openalex.org/W2412080945, https://openalex.org/W2912565176, https://openalex.org/W2330022088
referenced_works_count	32
abstract_inverted_index.a	5, 15
abstract_inverted_index.In	1
abstract_inverted_index.an	67
abstract_inverted_index.be	57
abstract_inverted_index.by	35, 59
abstract_inverted_index.is	12, 21, 33, 43, 69
abstract_inverted_index.it	42
abstract_inverted_index.or	62
abstract_inverted_index.to	45
abstract_inverted_index.LPP	60
abstract_inverted_index.QFP	32
abstract_inverted_index.The	18, 31
abstract_inverted_index.and	40
abstract_inverted_index.can	56
abstract_inverted_index.for	71
abstract_inverted_index.new	16
abstract_inverted_index.the	2, 24, 37, 46, 52
abstract_inverted_index.NQFP	19
abstract_inverted_index.into	23
abstract_inverted_index.(LPP)	50
abstract_inverted_index.(QFP)	29
abstract_inverted_index.given	70
abstract_inverted_index.hence	41
abstract_inverted_index.score	38
abstract_inverted_index.using	14, 36, 51
abstract_inverted_index.which	55
abstract_inverted_index.(NQFP)	10
abstract_inverted_index.(e.g.,	64
abstract_inverted_index.Taylor	53
abstract_inverted_index.linear	47
abstract_inverted_index.solved	58
abstract_inverted_index.study,	4
abstract_inverted_index.Lingo).	65
abstract_inverted_index.current	3
abstract_inverted_index.example	68
abstract_inverted_index.method.	17
abstract_inverted_index.problem	11, 20, 49
abstract_inverted_index.series,	54
abstract_inverted_index.Abstract	0
abstract_inverted_index.Finally,	66
abstract_inverted_index.function	39
abstract_inverted_index.problem.	30
abstract_inverted_index.software	63
abstract_inverted_index.converted	22, 44
abstract_inverted_index.quadratic	7, 26
abstract_inverted_index.formulated	34
abstract_inverted_index.fractional	8, 27
abstract_inverted_index.techniques	61
abstract_inverted_index.programming	9, 28, 48
abstract_inverted_index.investigated	13
abstract_inverted_index.neutrosophic	6
abstract_inverted_index.corresponding	25
abstract_inverted_index.illustration.	72
cited_by_percentile_year.max	98
cited_by_percentile_year.min	91
corresponding_author_ids	https://openalex.org/A5075392453
countries_distinct_count	3
institutions_distinct_count	3
corresponding_institution_ids	https://openalex.org/I156216236
citation_normalized_percentile.value	0.84296868
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False