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Dioieds and semirings: Links to fuzzy sets and other applications

机译：Dioieds和semirings：链接到模糊集和其他应用程序

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摘要

Besides the classical algebraic structures of groups, rings and fields which have long been the almost exclusive reference concepts used in mathematical modelling, other algebraic structures such as dioieds and semirings have emerged in the last two or three decades in connection with modelling and solving a rich variety of non-classical problems, e.g. in Decision Analysis, Fuzzy Set Theory, Operations Research, Automatic Control and Mathematical Physics. The present paper aims at providing an overview of applications of dioied and semiring structures, stressing links with Fuzzy Sets and emphasizing linear algebraic problems (solving linear systems, computing eigenvalues and eigenvectors), non-classical path-finding problems (using algebras of endomorphisms) and connections between dioied structure and nonlinear analysis (in view of solving problems in Mathematical Physics).
机译：除了群，环和场的经典代数结构（它们一直以来是数学建模中几乎排他的参考概念）外，在过去的两，三十年中，与建模和求解丰富函数有关的其他代数结构（如dioieds和semirings）也应运而生。各种非经典问题，例如在决策分析，模糊集理论，运筹学，自动控制和数学物理领域。本文旨在概述二环和半环结构的应用，强调具有模糊集的链接并强调线性代数问题（求解线性系统，计算特征值和特征向量），非经典路径查找问题（使用内同形代数）透视结构与非线性分析之间的联系（考虑到解决数学问题）。

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