| Title:
|
A note on resolving inconsistency of fuzzy relational equations on Łukasiewicz algebra (English) |
| Author:
|
Li, Pingke |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2026 |
| Pages:
|
735-754 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The inconsistency of fuzzy relational equations is frequently encountered when modelling an inference system with fuzzy logic. A polynomial-time direct search procedure is designed to resolve the inconsistency for fuzzy relational equations on Łukasiewicz algebra by minimizing the maximum absolute deviation to the right-hand side vector. Alternatively, a reformulation approach is proposed by minimizing instead the sum of absolute deviations. It results in a polynomial-sized mixed integer linear programming problem and hence, may be readily solved with the aid of an off-the-shelf optimization solver. This reformulation approach is flexible in nature and can be adjusted to deal with some other problems related to the inconsistency of fuzzy relational equations. (English) |
| Keyword:
|
fuzzy relational equations |
| Keyword:
|
inconsistency |
| Keyword:
|
optimal approximation |
| Keyword:
|
mixed integer linear programming |
| MSC:
|
08A72 |
| MSC:
|
15B15 |
| MSC:
|
90C11 |
| DOI:
|
10.14736/kyb-2026-4-0735 |
| . |
| Date available:
|
2026-10-07T10:24:26Z |
| Last updated:
|
2026-10-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153781 |
| . |
| Reference:
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