THE BEST SOLUTION FOR INEQUALITIES OF A O CROSS X LOWER THAN X FROM B O DOT X USING HIGH MATRIX RESIDUATION OF IDEMPOTENT SEMIRING

Eka Susilowati; Ari Suparwanto

doi:10.21831/jsd.v5i1.12663

THE BEST SOLUTION FOR INEQUALITIES OF A O CROSS X LOWER THAN X FROM B O DOT X USING HIGH MATRIX RESIDUATION OF IDEMPOTENT SEMIRING

Eka Susilowati, Jurusan Matematika, Universitas PGRI Adibuana, Surabaya
Ari Suparwanto, Jurusan Matematika, Fakultas MIPA, Universitas Gadjah Mada, Yogyakarta

10.21831/jsd.v5i1.12663

Abstract

Abstract

A complete idempotent semiring has a structure which is called 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 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 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 .

Keywords: complete lattice, complete idempotent semiring, dual Kleene Star, dual product, residuation theory

Keywords

complete lattice, complete idempotent semiring, dual Kleene Star, dual product, residuation theory

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DOI: https://doi.org/10.21831/jsd.v5i1.12663