离散合取聚合算子的迁移性

Migrativity of Discrete Conjunctive Aggregation Operations

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LukasieLwicz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LukasieLwicz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LukasieLwicz三角模的α-迁移当且仅当其是LukasieLwicz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LukasieLwicz三角模的α-迁移的条件。

This paper mainly solves the problem about the migrativity of conjunctive aggregation operations on a finite chain. Firstly, this paper discussesα-migrativity with respect to minimum triangular norm and？ukasiewicz triangular norm of divisible triangular norms. Then, this paper studiesα-migrativity with respect to minimum triangular norm and？ukasiewicz 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 fol-lowing propositions： （1） Divisible triangular norm is said to be α-migrativite with respect to minimum triangular norm if and only ifαis an idempotent element. （2） Divisible triangular norm is said to beα-migrativite with respect to？ukasiewicz triangular norm if and only if it is？ukasiewicz triangular norm. （3） The element in conjunctive aggre-gation operations which have an additive generator is the condition ofα-migrativity with respect to minimum trian-gular norm and？ukasiewicz triangular norm.