Soft Computing Thisbookexploressoftcomputingtechniquesinasystematicmannerstartingfrom theirinitialstagetorecentdevelopmentsinthisarea.Thebookpresentsasurveyof theexistingknowledgeandthecurrentstate-of-the-artdevelopmentthroughcutting- edgeoriginalnewcontributionsfromtheresearchers. SoftComputing:RecentAd- vancesandApplicationsinEngineeringandMathematicalSciencespresentsasur- veyoftheexistingknowledgeandthecurrentstate-of-the-artdevelopmentthrough cutting-edgeoriginalnewcontributionsfromtheresearchers. As suggested by the title, this book particularly focuses on the recent advances andapplicationsofsoftcomputingtechniquesinengineeringandmathematicalsci- ences. Chapter 1 describes the contribution of soft computing techniques towards a new paradigm shift. The subsequent chapters present a systematic application of fuzzylogicinmathematicalsciencesanddecision-making.Newresearchdirections are also provided at the end of each chapter. The application of soft computing in healthsciencesandinthemodelingofepidemicsincludingtheeffectsofvaccination arealsoexamined.Sustainabilityofgreenproductdevelopment,optimumdesignof 3Dsteelframe,digitalizationinvestmentanalysisinthemaritimeindustry,forecast- ing return rates of individual pension funds are among some of the topics where engineering and industrial applications of soft computing have been studied in the book.Thereadersofthisbookwillrequireminimumprerequisitesofundergraduate studiesincomputationandmathematics. Thisbookismeantforgraduatestudents,faculty,andresearcherswhoareapply- ingsoftcomputinginengineeringandmathematics.Newresearchdirectionsarealso providedattheendofeachchapter. Edge AI in Future Computing SeriesEditors: ArunKumarSangaiah SCOPE,VITUniversity,TamilNadu MamtaMittal G.B.PantGovernmentEngineeringCollege,Okhla,NewDelhi SoftComputingTechniquesinEngineering,Health,Mathematical andSocialSciences PradipDebnathandS.A.Mohiuddine MachineLearningforEdgeComputing:Frameworks,Patterns andBestPractices AmitojSingh,VinayKukreja,andTaghiJavdaniGandomani InternetofThings:FrameworksforEnablingandEmergingTechnologies BharatBhushan,SudhirKumarSharma,BhuvanUnhelkar,MuhammadFazalIjaz, andLamiaKarim SoftComputing:RecentAdvancesandApplicationsinEngineeringand MathematicalSciences PradipDebnath,OscarCastillo,andPoomKumam Formoreinformationaboutthisseries,pleasevisit: https://www.routledge.com/Edge-AI-in-Future-Computing/book-series/EAIFC Soft Computing Recent Advances and Applications in Engineering and Mathematical Sciences Editedby Pradip Debnath Department of Applied Science and Humanities, Assam University Silchar, India Oscar Castillo Tijuana Institute of Technology, Mexico Poom Kumam Department of Mathematics, King Mongkut’s University of Technology Thonburi, Thailand MATLAB®isatrademarkofTheMathWorks,Inc.andisusedwithpermission.TheMathWorksdoesnot warranttheaccuracyofthetextorexercisesinthisbook.Thisbook’suseordiscussionofMATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particularpedagogicalapproachorparticularuseoftheMATLAB®software. Firsteditionpublished2023 byCRCPress 6000BrokenSoundParkwayNW,Suite300,BocaRaton,FL33487-2742 andbyCRCPress 4ParkSquare,MiltonPark,Abingdon,Oxon,OX144RN CRCPressisanimprintofTaylor&FrancisGroup,LLC ©2023Taylor&FrancisGroup,LLC Reasonableeffortshavebeenmadetopublishreliabledataandinformation,buttheauthorandpublisher cannotassumeresponsibilityforthevalidityofallmaterialsortheconsequencesoftheiruse.Theauthors andpublishershaveattemptedtotracethecopyrightholdersofallmaterialreproducedinthispublication andapologizetocopyrightholdersifpermissiontopublishinthisformhasnotbeenobtained.Ifany copyrightmaterialhasnotbeenacknowledgedpleasewriteandletusknowsowemayrectifyinany futurereprint. ExceptaspermittedunderU.S.CopyrightLaw,nopartofthisbookmaybereprinted,reproduced,trans- mitted,orutilizedinanyformbyanyelectronic,mechanical,orothermeans,nowknownorhereafter invented,includingphotocopying,microfilming,andrecording,orinanyinformationstorageorretrieval system,withoutwrittenpermissionfromthepublishers. Forpermissiontophotocopyorusematerialelectronicallyfromthiswork,accesswww.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400.ForworksthatarenotavailableonCCCpleasecontactmpkbookspermissions@tandf.co.uk Trademarknotice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks,andareused onlyforidentificationandexplanationwithoutintenttoinfringe. ISBN:978-1-032-31831-8(hbk) ISBN:978-1-032-31917-9(pbk) ISBN:978-1-003-31201-7(ebk) DOI:10.1201/9781003312017 TypesetinTimes bycodeMantra Contents Preface......................................................................................................................vii Editors.......................................................................................................................ix Contributor................................................................................................................xi Chapter1 AStudyonApproximateFixedPointPropertyin IntuitionisticFuzzyn-NormedLinearSpaces.................................1 PradipDebnath Chapter2 SequentialExtendedParametricandSequentialExtended Fuzzyb-MetricswithanApplicationinIntegralEquations..........15 MarijaV.Paunovic´,SamiraHadiBonab,VahidParvaneh, andFarhanGolkarmanesh Chapter3 AnalyticalSequelofRational-TypeFuzzyContractionin Fuzzyb-MetricSpaces..................................................................29 NabanitaKonwar Chapter4 Weak-WardowskiContractionsinGeneralized Triple-ControlledModularMetricSpacesandGeneralized Triple-ControlledFuzzyMetricSpaces........................................45 MarijaV.Paunovic´,SamiraHadiBonab,andVahidParvaneh Chapter5 SomeFirst-Order-LikeMethodsforSolvingSystemsof NonlinearEquations......................................................................67 SaniAji,PoomKumam,andWiyadaKumam Chapter6 CubicInverseSoftSet...................................................................87 SrinivasanVijayabalajiandKaliyaperumalPunniyamoorthy v vi Contents Chapter7 InverseSoft-RoughMatrices.........................................................97 SrinivasanVijayabalaji Chapter8 NewObservationsonLacunaryI-InvariantConvergence forSequencesinFuzzyConeNormedSpaces............................107 O¨merKisi,MehmetGu¨rdal,andErhanGu¨ler Chapter9 SomeConvergentSequenceSpacesofFuzzyStar-Shaped Numbers......................................................................................125 ErhanGu¨lerandO¨merKisi Chapter10 DigitalizationInvestmentAnalysisinMaritime IndustrywithInterval−ValuedPythagoreanFuzzyPresent WorthAnalysis............................................................................141 EdaBoltu¨rk Chapter11 CompositeMappingonHesitantFuzzySoftClasses..................153 ManashJyotiBorahandBipanHazarika Chapter12 UlamStabilityofMixedTypeFunctionalEquation inNon-ArchimedeanIFN-Space.................................................167 K.Tamilvanan,S.A.Mohiuddine,andN.Revathi Chapter13 OptimumDesignof3DSteelFrameswithComposite SlabsUsingAdaptiveHarmonySearchMethod.........................179 MehmetPolatSaka,IbrahimAydogdu,RefikBurakTaymus, andZongWooGeem Chapter14 FosteringSustainabilityinOpenInnovation,toSelect theRightPartneronGreenProductDevelopment......................211 RicardoSantos,PolinhoKatina,Jose´ Soares, AnouarHallioui,JoaoMatias,andFernandaMendes Index.......................................................................................................................233 Preface Thisbookcollectschaptersfromeminentcontemporaryresearchersacrossthecoun- triesworkingonthetheoryandapplicationsofsoftcomputingtechniques.Thebook presents a survey of the existing knowledge and also current state of the art devel- opment through cutting-edge original new contributions from the researchers. As suggestedbythetitle,thisbookparticularlyfocusesontherecentadvancesandap- plications of soft computing techniques in engineering and mathematical sciences. The first Chapter presents a study on approximate fixed point property in a gen- eralized fuzzy normed space. Chapters 2–4 consist of new fixed point results and thier applications in different types of metric spaces such as fuzzy b-metric spaces and controlled fuzzy metric spaces. Chapter 5 describes new first order-like meth- ods for solving nonlinear equations. Cubic inverse soft sets have been studied in Chapter 6, whereas inverse soft-rough matrices are introduced in Chapter 7. Some new convergence results concerning fuzzy normed spaces and fuzzy numbers have beendescribedinChapters8and9,respectively.Digitalizationinvestmentanalysis in maritime industry with picture fuzzy sets are studied in Chapter 10. Chapter 11 containsastudyoncompositemappingonhesitantfuzzysoftclasses.InChapter12 we have Ulam stability of mixed type functional equation in fuzzy normed space. An interesting investigation on optimum design of 3D steel frames with composite slabshasbeenpresentedinChapter13.Finally,inChapter14,wediscussfostering sustainabilityinopeninnovationtoselecttherightpartnerongreenproductdevel- opment. Thisbookismeantforgraduatestudents,facultiesandresearcherswillingtolearn and apply fuzziness and soft computing in engineering and mathematics. New re- searchdirectionshavebeenpresented withinthechapterstoenabletheresearchers to further advance their research. The readers of this book will require minimum pre-requisitesofundergraduatestudiesincomputationandmathematics. vii Editors Pradip Debnath is an Assistant Professor (in Mathematics) at the Department of Applied Science and Humanities, Assam University, Silchar (a central university), India.HereceivedhisPh.D.inMathematicsfromtheNationalInstituteofTechnol- ogySilchar,India.Hisresearchinterestsincludefixedpointtheory,nonlinearfunc- tional analysis, soft computing and mathematical statistics. He has published more than 60 papers in various journals of international repute and is reviewer for more than40internationaljournals.Dr.Debnathisalsoareviewerfor“MathematicalRe- views” published by the American Mathematical Society. He is the Lead Editor of the books “Metric Fixed Point Theory - Applications in Science, Engineering and BehaviouralSciences”(2021,SpringerNature),“SoftComputingTechniquesinEn- gineering,Health,MathematicalandSocialSciences”(2021,CRCPress)and“Fixed Point Theory and Fractional Calculus: Recent Advances and Applications” (2022, Springer Nature). He has successfully guided Ph.D. students in the areas of fuzzy logic,softcomputingandfixedpointtheory.HehasrecentlycompletedaBasicSci- ence Research Project on fixed point theory funded by the UGC, the Government of India. Having been an academic gold medalist during his post-graduation stud- iesfromAssamUniversity,Silchar,Dr.Debnathhasqualifiedseveralnational-level examinationsinmathematicsinIndia. Oscar Castillo holds the Doctor in Science degree (Doctor Habilitatus) in Com- puter Science from the Polish Academy of Sciences (with the Dissertation “Soft Computing and Fractal Theory for Intelligent Manufacturing”). He is a Professor ofComputerScienceintheGraduateDivision,TijuanaInstituteofTechnology,Ti- juana,Mexico.Inaddition,heisservingasResearchDirectorofComputerScience andheadoftheresearchgrouponHybridFuzzyIntelligentSystems.Currently,heis PresidentofHAFSA(HispanicAmericanFuzzySystemsAssociation)andPastPres- identofIFSA(InternationalFuzzySystemsAssociation).Prof.CastilloisalsoChair ofthe MexicanChapter oftheComputational IntelligenceSociety(IEEE). Healso belongstotheTechnicalCommitteeonFuzzySystemsofIEEEandtotheTaskForce on“ExtensionstoType-1FuzzySystems”.HeisalsoamemberofNAFIPS,IFSA andIEEE.HebelongstotheMexicanResearchSystem(SNILevel3).Hisresearch interestsareinType-2FuzzyLogic,FuzzyControl,Neuro-FuzzyandGenetic-Fuzzy hybridapproaches.Hehaspublishedover300journalpapers,10authoredbooks,40 editedbooks,200papersinconferenceproceedings,andmorethan300chaptersin editedbooks,intotal910publicationsaccordingtoScopus(Hindex=63,andmore than1050publicationsaccordingtoResearchGate(Hindex=74inGoogleScholar). He has been Guest Editor of several successful Special Issues in the past, like in the following journals: Applied Soft Computing, Intelligent Systems, Information Sciences, Non-Linear Studies, Fuzzy Sets and Systems, JAMRIS and Engineering Letters. He is currently Associate Editor of the Information Sciences Journal, Ap- plied Soft Computing Journal, Engineering Applications of Artificial Intelligence, ix