Solving fuzzy linear systems using a block representation of generalized inverses: The group inverse
| Autor: | Branko Malesevic, Biljana Mihailovic, Vera Miler Jerkovic |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Logic Group (mathematics) Drazin inverse Linear system Block (permutation group theory) Inverse 020206 networking & telecommunications 02 engineering and technology Square (algebra) Matrix (mathematics) Artificial Intelligence 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Coefficient matrix Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 353:66-85 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2018.04.015 |
| Popis: | We present an efficient method for solving a singular, n × n fuzzy linear system (FLS), A X ˜ = Y ˜ , where the coefficient matrix A is a real matrix, singular or non-singular, using the block structure of the group inverse or any {1}-inverse. A characterization of the block structure of {1}-inverses, in particular, the group inverse, but also the Drazin inverse of the matrix associated to a square FLS is given. Based on the presented necessary and sufficient condition for the existence of a solution, the general solution of a square FLS is obtained. Finally, infinitely many solutions of a singular FLS are presented through many interesting examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect