Certain scholars have generalized the theory of fuzzy set, but picture hesitant set (PHFS) has received massive attention from distinguished scholars. PHFS is combination (PFS) and (HFS) to cope with awkward complicated information in real-life issues. The well-known characteristic that sum maximum membership, abstinence, non-membership degree limited unit interval. This manuscript aims develop...

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets,...

Multi-granularity unbalanced hesitant fuzzy linguistic term set (MGUHFLTS) is an effective expression of information, which applied in multi-attribute group decision-making (MAGDM), meanwhile Dempster-Shafer evidence theory (DSET) profound method representing and aggregating uncertain information. In order to combine the advantages from both, a new MAGDM approach based on with MGUHFLTSs propose...

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher general...