Dual hesitant fuzzy sets (DHFSs) is the refinement and extension of hesitant fuzzy sets and encompasses fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as a special case. DHFSs have two parts, that is, the membership function and the non-membership function, in which each function is defined by two sets of some feasible values. Therefore, according to the practical demand, DHFSs are more adjustable than the existing ones and provide the information regarding different objects in much better way. The set pair analysis (SPA) illustrates unsureness in three angles, called ''identity'', ''discrepancy'' and ''contrary'', and the connection number (CN) is one of its main features. In the present article, the axiom definition of distance measure between DHFSs and CN is introduced. The distance measures are established on the basis of Hamming distance, Hausdorff distance and Euclidean distance. The previous identities and relationship between them are discussed in detail. On the basis of the geometric distance model, the settheoretic approach, and the matching functions several novel distance formulas of CN are introduced. The novel distance formulas are then applied to multiple-attribute decision making for dual hesitant fuzzy environments. Finally, to demonstrate the validity of the introduced measures, a practical example of decisionmaking is presented. The benefits of the new measures over the past measures are additionally talked about.

Objectives/Methods: Taking into account the impreciseness and subjectiveness of decision makers (DMs) in complex decision-making situations, the assessment datum over alternatives given by DMs is consistently vague and uncertain. In meantime, to evaluate human's hesitance, the q-rung orthopair dual hesitant fuzzy sets (q-RODHFSs) are defined which are more accurate for manipulation real MADM matters. To merge the datum in q-RODHFSs more precisely, in this research script, some Bonferroni mean (BM) operators in light of q-RODHFSs datum, which includes arbitrary number of being merged arguments, are developed and examined. Findings: Obviously, the novel defined operators can produce much accurate results than already existing methods. Additionally, some important measures of said BM operators are talked about and all the peculiar cases of them are studied which expresses that the BM operator is more dominant than others. Eventually, the MADM algorithm is furnished and the operators are utilized to choose the best alternative under q-rung orthopair dual hesitant fuzzy numbers (q-RODHFNs). Taking advantage of the novel operators and constructed algorithm, the developed operators are utilized in the MADM problems.