论文标题
通过严格的三角形规范和多标准决策的应用图片模糊互动聚合操作员
Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making
论文作者
论文摘要
图片模糊集的特征是三个会员学位，是多标准决策（MCDM）的有用工具。本文研究了图片模糊数（PFN）中封闭的操作定律的结构，并提出了有效的图片模糊MCDM方法。我们首先引入了可允许的PFN订单，并证明所有PFN在此订单下构成一个完整的晶格。然后，我们给出一些具体的示例，以显示某些现有图片模糊聚合操作员的不闭合性。为了确保PFN中操作定律的亲密关系，我们基于严格的三角形规范构建了一类新的图片模糊操作员，这些规范考虑了正度（负度）和中性程度之间的相互作用。基于这些新操作员，我们获得图片模糊交互加权平均（PFIWA）操作员和图片模糊交互性加权几何（PFIWG）操作员。事实证明，它们是单调的，有势的，有界的，不变的和同质的。我们还在应用PFIWA和PFIWG操作员的图片模糊环境下建立了一种新颖的MCDM方法。此外，我们提出了一个说明性的例子，以清楚了解我们的方法。我们还通过六类著名的三角形规范引起的操作员进行了比较分析。
The picture fuzzy set, characterized by three membership degrees, is a helpful tool for multi-criteria decision making (MCDM). This paper investigates the structure of the closed operational laws in the picture fuzzy numbers (PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an admissible order for PFNs and prove that all PFNs form a complete lattice under this order. Then, we give some specific examples to show the non-closeness of some existing picture fuzzy aggregation operators. To ensure the closeness of the operational laws in PFNs, we construct a new class of picture fuzzy operators based on strict triangular norms, which consider the interaction between the positive degrees (negative degrees) and the neutral degrees. Based on these new operators, we obtain the picture fuzzy interactional weighted average (PFIWA) operator and the picture fuzzy interactional weighted geometric (PFIWG) operator. They are proved to be monotonous, idempotent, bounded, shift-invariant, and homogeneous. We also establish a novel MCDM method under the picture fuzzy environment applying PFIWA and PFIWG operators. Furthermore, we present an illustrative example for a clear understanding of our method. We also give the comparative analysis among the operators induced by six classes of famous triangular norms.
