Abstract: This paper mainly solves the problem about the migrativity of conjunctive aggregation operations on a finite chain. Firstly, this paper discusses α-migrativity with respect to minimum triangular norm and Lukasiewicz triangular norm of divisible triangular norms. Then, this paper studies α-migrativity with respect to minimum triangular norm and Lukasiewicz triangular norm of conjunctive aggregation operations in a class which have an additive generator. This paper mainly uses additive generators to depict the migrativity of the element in this class. The results show following propositions: (1) Divisible triangular norm is said to be α-migrativite with respect to minimum triangular norm if and only if α is an idempotent element. (2) Divisible triangular norm is said to be α-migrativite with respect to Lukasiewicz triangular norm if and only if it is Lukasiewicz triangular norm. (3) The element in conjunctive aggregation operations which have an additive generator is the condition of α-migrativity with respect to minimum triangular norm and Lukasiewicz triangular norm.

Key words: discrete conjunctive aggregation operations, migrativity, finite chain, additive generator, triangular norm

摘要： 主要研究了有限链上合取聚合算子的迁移性问题；讨论了可分三角模关于取小三角模和Lukasiewicz三角模的α-迁移性；研究了含加法生成子的合取聚合算子类关于取小三角模和Lukasiewicz三角模的α-迁移性，其中主要利用了加法生成子来刻画此类中元素的迁移性。结果表明：（1）可分三角模是关于取小三角模的α-迁移当且仅当α是其幂等元；（2）可分三角模是关于?ukasiewicz三角模的α-迁移当且仅当其是Lukasiewicz三角模；（3）含加法生成子的合取聚合算子类中的元素是关于取小三角模和Lukasiewicz三角模的α-迁移的条件。

关键词: 离散合取聚合算子, 迁移性, 有限链, 加法生成子, 三角模