On the T-transitivity of fuzzy similarity measures

He, Xiaoqiong; Li, Yingfang; Qin, Keyun; Meng, Dan

doi:10.1016/j.fss.2016.06.017

Cited by 10 publications

(1 citation statement)

References 29 publications

(62 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In other words, the problem is determining conditions guarantee that the output has the same structure. Preservation of structures under aggregation has been widely studied in recent decades (see [12][13][14][15][16][17][18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

On Self-Aggregations of Min-Subgroups

Bejines

Ardanza-Trevijano

Elorza

2021

Axioms

View full text Add to dashboard Cite

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

show abstract