幂等半环上的对偶与区间分析
Duality and interval analysis over idempotent semirings
摘要：
本文考虑了具有幂等元加法的半环。这些代数结构被赋予了偏序。这允许考虑剩余映射来解决不等式系统$A \otimes X \preceq B$。本文的目的是考虑一个对偶积，记作$\odot$，和矩阵的对偶剩余，以解决下列不等式$ A \otimes X \preceq X \preceq B \odot X$。给出了保证解集中存在非线性投影的充分条件。将所得结果推广到区间半环。
英文摘要：
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $ A \otimes X \preceq X \preceq B \odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
