On some properties of α-planes of type-2 fuzzy sets

Title:

On some properties of α-planes of type-2 fuzzy sets

Creator:

Takáč, Zdenko

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3ab8e5b8-d367-4dcc-9def-c022a4547e57
uuid:3ab8e5b8-d367-4dcc-9def-c022a4547e57

Subject:

type-2 fuzzy sets, α-plane, intersection of type-2 fuzzy sets, union of type-2 fuzzy sets, and fuzzy sets

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Some basic properties of α-planes of type-2 fuzzy sets are investigated and discussed in connection with the similar properties of α-cuts of type-1 fuzzy sets. It is known, that standard intersection and standard union of type-1 fuzzy sets (it means intersection and union under minimum t-norm and maximum t-conorm, respectively) are the only cutworthy operations for type-1 fuzzy sets. Recently, a similar property was declared to be true also for α-planes of type-2 fuzzy sets in a few papers. Thus, we study under which t-norms and which \mbox{t-conorms} are intersection and union of the type-2 fuzzy sets preserved in the α-planes. Note that understanding of the term α-plane is somewhat confusing in recent type-2 fuzzy sets literature. We discuss this problem and show how it relates to obtained results.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[149]-163

Source:

Kybernetika | 2013 Volume:49 | Number:1

Harvested from:

CDK

Metadata only:

false