Abstract The monotonicity of the system function of a fuzzy relational inference (FRI) system is one of the most important issues that need attention. The unavailability of monotonicity of the system function of an FRI system is not desirable in many practical settings. Works existing in the literature have dealt with monotonicity of the system function of an FRI system where fuzzy implications have been widely used and those fuzzy implications are known to come from a residuated lattice structure. Moreover, there are very few studies where monotonicity has been studied under a non-residuated lattice structure. Building on our recent work on monotonicity under a non-residuated setting, in this work, we ensure that the system function of a certain type of FRI system with a Single-Input Single-Output (SISO) implicative rule base and ordering property preserving fuzzy implications is monotonic. Towards doing this, we represent the monotone fuzzy rule base by a fuzzy relation that involves fuzzy implications which satisfy the so-called neutrality property and ordering property, simultaneously. It should be highlighted that this work generalizes the class of fuzzy implications that can be employed in an FRI system without modifying the rule base to ensure the monotonic nature of the system function, giving more choices to the practitioners.

中文翻译：

---

SISO FRI 系统的系统函数的单调性，具有中立性和保持有序性的模糊含义

摘要 模糊关系推理（FRI）系统系统函数的单调性是最需要关注的问题之一。在许多实际环境中，FRI 系统的系统函数单调性的不可用性是不可取的。文献中存在的工作已经处理了 FRI 系统的系统函数的单调性，其中模糊含义已被广泛使用，并且已知这些模糊含义来自剩余的晶格结构。此外，很少有研究在非残留晶格结构下研究单调性。基于我们最近关于非剩余环境下单调性的工作，在这项工作中，我们确保具有单输入单输出（SISO）蕴涵规则库和保持排序属性的模糊蕴涵的某种类型的 FRI 系统的系统函数是单调的。为此，我们通过模糊关系表示单调模糊规则库，该关系涉及同时满足所谓的中性属性和排序属性的模糊含义。应该强调的是，这项工作概括了可以在 FRI 系统中使用的模糊含义类别，而无需修改规则库以确保系统功能的单调性，为从业者提供更多选择。我们通过一个模糊关系来表示单调模糊规则库，该关系涉及同时满足所谓的中性属性和排序属性的模糊含义。应该强调的是，这项工作概括了可以在 FRI 系统中使用的模糊含义类别，而无需修改规则库以确保系统功能的单调性，为从业者提供更多选择。我们通过一个模糊关系来表示单调模糊规则库，该关系涉及同时满足所谓的中性属性和排序属性的模糊含义。应该强调的是，这项工作概括了可以在 FRI 系统中使用的模糊含义类别，而无需修改规则库以确保系统功能的单调性，为从业者提供更多选择。