广义分组(重叠)函数关于三角模和三角余模的迁移性

Migrativity of general grouping (overlap) functions over t-norms and t-conorms

摘要

聚合函数的迁移性在决策分析和图像处理等方面有着广泛应用。本文以存在非平凡单位元的广义分组函数和广义重叠函数为研究对象,主要研究这两类函数关于三角模和三角余模的迁移性,刻画满足此类迁移性方程广义分组函数和广义重叠函数的结构特征。

Abstract

The migrativity of aggregation functions plays a pivotal role in various applications, including decision making and image processing. In this paper, we take general grouping functions and general overlap functions, which possess non-trivial neutral elements, the aim is to study the migrativity of these functions over t-norm and t-conorms, and to provide the structures of general grouping functions and general overlap functions that satisfy such migrative functional equations.

关键词

广义分组函数 / 广义重叠函数 / 三角模 / 三角余模 / 迁移性

Key words

general grouping function / general overlap function / t-norm / t-conorm / migrativity

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基金资助

国家自然科学基金资助项目(12171292)

陕西省杰出青年科学基金项目(2024JC-JCQN-01)

陕西师范大学研究生领航人才培养项目(LHRCTS23059)