ResearchArticle Multifuzzy Cubic Sets and Their Correlation Coefficients for Multicriteria Group Decision-Making Jun Ye , Shigui Du, and Rui Yong School of Civil and Environmental Engineering, Ningbo University, Ningbo 315211, China CorrespondenceshouldbeaddressedtoJunYe;yejun1@nbu.edu.cn Received 12 January 2021; Revised 28 January 2021; Accepted 1 February 2021; Published 18 February 2021 AcademicEditor:HarishGarg Copyright©2021JunYeetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e notion of multifuzzy sets (MFSs) or multi-interval-valued fuzzy sets (MIVFSs) provides a new method to represent some problemswithasequenceofthedifferentand/orsamefuzzy/interval-valuedfuzzymembershipvaluesofanelementtotheset. en,afuzzycubicset(FCS)consistsofacertainpart(afuzzyvalue)andanuncertainpart(aninterval-valuedfuzzyvalue)but cannot represent hybrid information of both MFS and MIVFS. To adequately depict the opinion of several experts/decision- makersbyusingaunion/sequenceofthedifferentand/orsamefuzzycubicvaluesforanobjectassessedingroupdecision-making (GDM)problems,thispaperproposesamultifuzzycubicset(MFCS)notionastheconceptualextensionofFCStoexpressthe hybrid information of both MFS and MIVFS in the fuzzy setting of both uncertainty and certainty. en, we propose three correlationcoefficientsofMFCSsandthenintroducecorrelationcoefficientsofMFSsandMIVFSsasspecialcasesofthethree correlation coefficients of MFCSs. Further, the multicriteria GDM methods using three weighted correlation coefficients of MFCSs are developed under the environment of MFCSs, which contains the MFS and MIVFS GDM methods. Lastly, these multicriteriaGDMmethodsareappliedinanillustrativeexampleontheselectionproblemofequipmentsuppliers;thentheir decisionresultsandcomparativeanalysisindicatethatthedevelopedGDMmethodsaremorepracticableandeffectiveandreflect thateitherdifferentcorrelationcoefficientsordifferentinformationexpressionscanalsoimpactontherankingofalternatives. erefore,thisstudyindicatesthemaincontributionofthemultifuzzycubicinformationexpression,correlationcoefficients,and GDM methods in the multifuzzy setting of both uncertainty and certainty. 1. Introduction Fuzzy set (FS) [1] is usually depicted by a membership degree in the interval [0, 1], where only indicate one oc- currence of each element. Hence, FSs have been wildly applied in various areas [2–10] regarding vague and in- completerealproblems.AstheextensionofFSs,Yager[11] and Sebastian and Ramakrishnan [12] presented a fuzzy multiset/bag/multifuzzy set (MFS), which provides a better methodtorepresentthenumbersofcopiesofanelementto the set by the different and/or same membership values. us, fuzzy multisets/MFSs have been utilized for various applications [13–17]. By extending the fuzzy multiset/MFS totheinterval-valuedfuzzyset(IVFS)[18],Kreinovichand Sriboonchitta [19] defined the notion of a multi-interval- valued fuzzy set (MIVFS), where each element can be repeated more than once with the different and/or same interval-valuedmembershipvaluestoadequatelydescribea union/sequence of interval-valued fuzzy values (IVFVs). en,thereexistthecertaintyanduncertaintyofhuman judgments regarding complicated real-world problems. Hence,Junetal.[20]proposedanotionofafuzzycubicset (FCS),whichcandepictthehybridfuzzyinformationofthe partial certainty (fuzzy value) and partial uncertainty (IVFV). Afterward, some researchers [21–24] also intro- ducedsometheoryandapplicationsofFCSssinceFCSisa very useful tool for expressing potentially uncertain and certainty information provided by the decision-makers. BasedonthehybridnotionofFCSandahesitantFS[25], someresearchersproposedhesitantFCSsandtheirdecision- making methods [26, 27] due to the hesitancy of human judgments in the setting of FCSs; then some researchers Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 5520335, 9 pages https://doi.org/10.1155/2021/5520335