SOLUSI TERBESAR PERTIDAKSAMAAN A X ? X ? B ?X DENGAN MENGGUNAKAN RESIDUASI MATRIKS ATAS SEMIRING IDEMPOTEN; THE GREATEST SOLUTION OF INEQUALITY A X ? X ? B ? X BY USING MATRIX RESIDUATION OVER IDEMPOTENT SEMIRING

EKA SUSILOWATI, Ari Suparwanto

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

A complete idempotent semiring has the structure as a complete lattice. Because of the same structure as the complete lattice then inequality of the complete idempotent semiring can be solved a solution by using residuation theory. One of the inequality which is explained is A X ? B where matrices A;X;B with entries in the complete idempotent semiring S. Furthermore, introduced dual product ?, i.e. binary operation endowed in a complete idempotent semirings S and not included in the standard definition of complete idempotent semirings. A solution of inequality A ? X ? B can be solved by using residuation theory. Because of the guarantee that for each isotone mapping in complete lattice always has a fixed point, then is also exist in a complete idempotent semirings. This of the characteristics is used in order to obtain the greatest solution of inequality A X ? X ? B ? X.

Kata Kunci : SOLUTION, INEQUALITY, MATRIX RESIDUATION, IDEMPOTENT SEMIRING