This paper deals with the resolutions of fuzzy relation equations with
addition-min composition. When the fuzzy relation equations have a solution, we
first propose an algorithm to find all minimal solutions of the fuzzy relation
equations and also supply an algorithm to find all maximal solutions of the
fuzzy relation equations, which will be illustrated, respectively, by numeral
examples. Then we prove that every solution of the fuzzy relation equations is
between a minimal solution and a maximal one, so that we describe the solution
set of the fuzzy relation equations completely.

本文研究了带有加法 - 最小合成的模糊关系方程的解决方案。当模糊关系方程有解时，我们首先提出了一个算法来找到所有模糊关系方程的最小解，并提供了一个算法来找到所有最大解，分别通过数字例子进行说明。然后我们证明了模糊关系方程的每个解都在最小解和最大解之间，使得我们完全描述了模糊关系方程的解集。

具有加法 - 最小合成的模糊关系方程的解集

The solution set of fuzzy relation equations with addition-min composition

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.

本文研究了未知模糊关系在方程或不等式中出现的模糊关系方程和不等式的问题，并提供了解决方案，特别关注计算它们的算法，发现它们在模糊网络聚合问题中具有优势。