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

图片模糊集（PFS）是模糊集（FSs）和直觉模糊集（IFS）的直接概括。PFS的概念适合于对涉及更多答案（是，否，弃权和拒绝）的情况进行建模。在这项研究中，我们在直接操作的基础上，基于成员，非成员，中立，拒绝和两个PFS成员功能的上限，引入了一种新颖的图片模糊（PF）距离度量。我们将提出的PF距离度量与现有的PF距离度量进行对比，并讨论了模式分类问题中的优点。模糊和非标准模糊模型在真实数据中的应用非常具有挑战性，因为真实数据总是以清晰的形式出现。在这里，我们还导出了一些转换公式，以将建议的方法应用于实际数据集。此外，我们使用提出的PF距离测度介绍了一种新的多属性决策（MADM）方法。另外，我们使用适当的反直觉示例来证明新提出的MADM方法的必要性。最后，我们将提出的MADM方法与经典MADM方法在PF环境中的性能进行了对比。