An innovative picture fuzzy distance measure and novel multi-attribute decision-making method

Abstract Picture fuzzy set (PFS) is a direct generalization of the sets (FSs) and intuitionistic (IFSs). The concept PFS suitable to model situations that involve more answers type yes, no, abstain, refuse. In this study, we introduce novel picture (PF) distance measure on basis operation functions membership, non-membership, neutrality, refusal, upper bound function membership two PFSs. We contrast proposed PF with existing measures discuss advantages in pattern classification problems. application non-standard models real data very challenging as always found crisp form. Here, also derive some conversion formulae apply method set. Moreover, new multi-attribute decision-making (MADM) using measure. addition, justify necessity newly MADM appropriate counterintuitive examples. Finally, performance classical methods environment.