The q-Fractional Fuzzy Sets (q-FrFSs) offers information in Membership Grade (MG) and Non-membership Grade (NMG) of an object; however, both grades have the hesitancy factor because complex information usually does not give single MG and single NMG. Therefore, in this study we initiate the concept of q-Fractional Hesitant Fuzzy Sets (q-FrHFSs) and its basic properties. In q-FrHFSs not only hesitancy factor is taken into account but it also consider all possible values of uncertainties in {0,1}× {0,1}. Thus Correlation Coefficients (CCs) on q-FrHFSs are necessary to cope uncertain information with hesitancy, MGs and NMGs. In this study we introduce two types of CCs namely CCs on q-FrHFSs and weighted CCs on q-FrHFSs. We investigate underlying properties of these CCs and give a MCDM method on q-FrHFSs environment. We consider an application of our method to agricultural land selection across a set of cities for cultivation of apples crop. At the end, we compare our method of q-FrHFSs to some existing frameworks.

Decision makers (DMs) continually demonstrate shortcomings in their approaches to analyzing information through fuzzy systems; nevertheless, a model that integrates many dimensions of uncertainty is generally substantial. Normal wiggly dual hesitant fuzzy sets (NWDHFSs) incorporate a range of DMs' preferences for membership grades (MGs) and non-membership grades (NMGs). For complicated and multifaceted problems, one can apply the dynamic framework of NWDHFSs. To illustrate the relationship between NWDHFSs, correlation coefficients (CCs) on NWDHFSs, as well as weighted CCs on NWDHFSs, are presented in this work. These CCs are built up using means of values in hesitant fuzzy elements of NWDHFSs. Some fundamental axioms and thresholds of CCs on NWDHFSs are examined. A multi-criteria decision-making (MCDM) technique and associated algorithms based on these CCs are introduced. Because of the competitive real estate market, choosing a real estate agent is a challenging task for organizations. Through the consideration of a real estate case study, we select an appropriate real estate agent for a real estate firm utilizing proposed CCs on NWDHFSs. We examine the methodologies and outcomes of our approach to previous strategies.