论文标题
关于模糊关系方程的弱线性系统的溶解度
On the solvability of weakly linear systems of fuzzy relation equations
论文作者
论文摘要
模糊关系方程式和未知模糊关系的不等式的系统在方程或不平等的一侧是线性系统。它们是研究最多的文献，有关线性系统的大量文献着重于寻找此类系统的解决方案和可溶性标准。所谓的弱线性系统有很大的不同，在该系统中，方程式或不平等的两侧都有未知的模糊关系。确切地说，学者仅鉴于对此类系统的精确解决方案的表征。本文描述了一系列模糊关系，该关系在一定程度上解决了弱线性系统，并提供了计算它们的方法。我们特别注意开发用于计算模糊预订和模糊等价的算法，这些算法在某种程度上是解决弱线性系统的解决方案。我们在某些特定类型的完整残留晶格上建立了此类近似解决方案集的其他属性。我们通过许多示例来证明这种方法的优势，这些示例来自模糊网络的聚集问题。
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on finding solutions and solvability criteria for such systems. The situation is quite different with the so-called weakly linear systems, in which an unknown fuzzy relation is on both sides of the equation or inequality. Precisely, the scholars have only given the characterization of the set of exact solutions to such systems. This paper describes the set of fuzzy relations that solve weakly linear systems to a certain degree and provides ways to compute them. We pay special attention to developing the algorithms for computing fuzzy preorders and fuzzy equivalences that are solutions to some extent to weakly linear systems. We establish additional properties for the set of such approximate solutions over some particular types of complete residuated lattices. We demonstrate the advantage of this approach via many examples that arise from the problem of aggregation of fuzzy networks.
