| Title:
|
On the $T$-conditionality of $T$-power based implications (English) |
| Author:
|
Peng, Zuming |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
43-63 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of $T$-conditionality. In this paper, the $T$-conditionality for $T$-power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication $I^{T}$ being $T$-conditional are obtained. Moreover, the sufficient conditions under which a power based implication $I^{T}$ is $T^{\ast}$-conditional are discussed, this discussions give an ideas to construct a t-norm $T^{\ast}$ such that the power based implication $I^{T}$ is $T^{\ast}$-conditional. (English) |
| Keyword:
|
$T$-power based implications |
| Keyword:
|
$T$-conditionality |
| Keyword:
|
t-norms |
| Keyword:
|
generalized modus ponens |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| idZBL:
|
Zbl 07511610 |
| idMR:
|
MR4405946 |
| DOI:
|
10.14736/kyb-2022-1-0043 |
| . |
| Date available:
|
2022-04-08T07:49:43Z |
| Last updated:
|
2022-08-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149601 |
| . |
| Reference:
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