| Title:
|
On some properties of $\alpha $-planes of type-2 fuzzy sets (English) |
| Author:
|
Takáč, Zdenko |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
149-163 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some basic properties of $\alpha$-planes of type-2 fuzzy sets are investigated and discussed in connection with the similar properties of $\alpha$-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 $\alpha$-planes of type-2 fuzzy sets in a few papers. Thus, we study under which t-norms and which t-conorms are intersection and union of the type-2 fuzzy sets preserved in the $\alpha$-planes. Note that understanding of the term $\alpha$-plane is somewhat confusing in recent type-2 fuzzy sets literature. We discuss this problem and show how it relates to obtained results. (English) |
| Keyword:
|
type-2 fuzzy sets |
| Keyword:
|
$\alpha $-plane |
| Keyword:
|
intersection of type-2 fuzzy sets |
| Keyword:
|
union of type-2 fuzzy sets |
| Keyword:
|
fuzzy sets |
| MSC:
|
03E72 |
| MSC:
|
68T37 |
| . |
| Date available:
|
2013-03-05T15:14:30Z |
| Last updated:
|
2013-07-31 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143246 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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