Research Article
ANovelApproachofComplexDualHesitantFuzzySetsandTheir
ApplicationsinPatternRecognitionandMedicalDiagnosis
UbaidUrRehman ,
1
TahirMahmood ,
1
ZeeshanAli ,
1
andThammaratPanityakul
2
1
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
2
Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, ailand
CorrespondenceshouldbeaddressedtoammaratPanityakul;thammarat.p@psu.ac.th
Received 14 October 2020; Revised 10 November 2020; Accepted 28 November 2020; Published 28 April 2021
AcademicEditor:AhmedMostafaKhalil
Copyright©2021UbaidUrRehmanetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Complexdualhesitantfuzzyset(CDHFS)isanassortmentofcomplexfuzzyset(CFS)anddualhesitantfuzzyset(DHFS).Inthis
manuscript, the notion of the CDHFS is explored and its operational laws are discussed. e new methodology of the complex
interval-valueddualhesitantfuzzyset(CIvDHFS)anditsnecessarylawsareintroducedandarealsodefensiblewiththehelpof
examples.Further,theantilogarithmicandwith-outexponential-basedsimilaritymeasures,generalizedsimilaritymeasures,and
theirimportantcharacteristicsarealsodeveloped.esesimilaritymeasuresareappliedintheenvironmentofpatternrecognition
and medical diagnosis to evaluate the proficiency and feasibility of the established measures. We also solved some numerical
examplesusingtheestablishedmeasurestoexaminethereliabilityandvalidityoftheproposedmeasuresbycomparingthesewith
existingmeasures.Tostrengthentheproposedstudy,thecomparativeanalysisismadeanditisconferredthattheproposedstudy
is much more superior to the existing studies.
1.Introduction
Zadeh [1] presented the theory of fuzzy sets (FSs), which
containthegradeoftruthbelongingtounitinterval.But,in
some cases, the theory of FSs has been failed. For instance,
when a decision-maker faced information in the form of
truth and falsity grades, then the FSs are not able to cope
withit.Inreality,thesesetshavegivendifferentapproaches
toallottheparticipationdegreeorthenonmembershiplevel
of a component to a given set portrayed by various prop-
erties. IFSs [2], otherwise called IVFSs from a numerical
perspective, can be demonstrated with two capacities that
characterize a stretch to mirror some vulnerability on the
enrollment work of the components. IVFSs are the specu-
lationofFSsandcandemonstratevulnerabilityfortheneed
ofdata,inwhichaclosedsubintervalof[0,1]isrelegatedto
the participation degree. Atanassov and Gargov [3] dem-
onstratedthatIFSsandIVFSsareequipollentspeculationsof
FSs and proposed the thought of IVIFS, which has been
examined and utilized broadly [4–8].
T2FSs,depictedbyenrollmentworkthatisportrayedby
more boundaries, grant the fuzzy enrollment as a fuzzy set
improving the demonstrating ability compared to the
original one. Scientifically, IFSs can be viewed as a specific
instanceofT2FSs,wheretheparticipant’sworkrestoresalot
offreshstretches.InspiteofthewideusesofT2FSs[9–12],
they experience issues in building up the optional enroll-
ment capacities and troubles in control [13–15]. FMSs are
also the extension of the FSs, which contains the grade of
truthintheformofthefinitesubsetoftheunitinterval.Note
thatinspiteofthefactthatthehighlightsofFMSspermitthe
application to data recovery on the internet, where a web
index recovers different events of the same subjects with
conceivable various degrees of significance [16], they have
issues with the fundamental tasks, for example, the defini-
tions for association and crossing point, which do not sum
uptheonesforFSs.Rickard[17]gaveanelectivedefinition
thatunderlinesthevalueofacommutativepropertybetween
a set activity and an α-cut, settling this issue. HFSs were
initiallypresentedbyTorra[4].etheoryofhesitantfuzzy
Hindawi
Journal of Mathematics
Volume 2021, Article ID 6611782, 31 pages
https://doi.org/10.1155/2021/6611782