论文标题
连续三角形规范的力量，并应用于直觉模糊信息聚合
Power of Continuous Triangular Norms with Application to Intuitionistic Fuzzy Information Aggregation
论文作者
论文摘要
连续的阿基米德三角形规范（T-norms）的功率操作对于在连续的Archimedean t-norms框架内概括了直觉模糊集（IFSS）的乘法和功率操作。但是，由于缺乏对理论上一般连续T-norm的功率运行的系统研究，因此它极大地限制了IFSS通过一般连续T-norms的乘法和功率操作的进一步概括。本文旨在研究连续T-norms的功率操作，并开发一些信息聚合方法。从理论上讲，事实证明，当且仅当每个点都是一个功率稳定点时，并且仅当它是最小t-norm或严格的情况下，或者仅是严格的，或者是严格的T-norm的序数总和时，连续的T-norm是稳定的。此外，连续T-norms的表示定理用于获得连续T-norms幂的计算公式。基于T-norms的功率操作，引入了IFSS连续T-norm引起的四个基本操作。此外，根据这四个基本操作，即加权平均（IFWA），如果加权几何（IFWG），以及平均加权平均值和几何（IFMWAG）操作员，则定义了各种IF聚合操作员，即定义的。在应用程序中，基于IFMWAG操作员设计了一种新的决策算法，该算法可以消除某些经典集合操作员的边界的不可分辨性的障碍。提供了使用其他决策方法的研究的实际适用性，比较分析和优势，以确定设计方法的功效。
The power operation of continuous Archimedean triangular norms (t-norms) is fundamental for generalizing the multiplication and power operations of intuitionistic fuzzy sets (IFSs) within the framework of continuous Archimedean t-norms. However, due to the lack of systematic research on the power operation of general continuous t-norms in theory, it greatly limits the further generalization of the multiplication and power operations for IFSs via general continuous t-norms. This paper aims to investigate the power operation of continuous t-norms and develop some IF information aggregation methods. In theory, it is proved that a continuous t-norm is power stable if and only if every point is a power stable point, and if and only if it is the minimum t-norm, or it is strict, or it is an ordinal sum of strict t-norms. Moreover, the representation theorem of continuous t-norms is used to obtain the computational formula for the power of continuous t-norms. Based on the power operation of t-norms, four fundamental operations induced by a continuous t-norm for the IFSs are introduced. Furthermore, various IF aggregation operators based on these four fundamental operations, namely the IF weighted average (IFWA), IF weighted geometric (IFWG), and IF mean weighted average and geometric (IFMWAG) operators, are defined, and their properties are analyzed. In application, a new decision-making algorithm is designed based on the IFMWAG operator, which can remove the hindrance of indiscernibility on the boundaries of some classical aggregation operators. The practical applicability, comparative analysis, and advantages of the study with other decision-making methods are furnished to ascertain the efficacy of the designed method.
