Grouping functions, as one new case of not necessarily associative particular binary aggregation functions, have been proposed in the literature for their vast applications in fuzzy community detection problems, image processing and decision making. On the other hand, due to the wide applications in fuzzy reasoning, fuzzy control and approximate reasoning, the investigations of fuzzy implications derived from specific binary aggregation functions become a natural and hot research topic. In this paper, we focus on this research area and consider the ${\mathcal{ℐ}}_{\mathcal{𝒢},\mathcal{𝒩}}$-implications induced from quasi-grouping functions and negations on bounded lattices. To be precise, firstly, by removing the continuity condition, we extend the notion of grouping functions on the unit closed interval to the so-called quasi-grouping functions on bounded lattices. Secondly, we give some basic properties and two construction methods of quasi-grouping functions on bounded lattices. Finally, we give the concept of ${\mathcal{ℐ}}_{\mathcal{𝒢},\mathcal{𝒩}}$-implications and focus on the conditions under which they can satisfy the certain algebraic properties possessed by implications on bounded lattices.

分组函数作为不一定关联的特定二进制聚合函数的一种新情况，因其在模糊社区检测问题、图像处理和决策制定中的广泛应用而在文献中被提出。另一方面，由于模糊推理、模糊控制和近似推理等领域的广泛应用，研究特定二元聚合函数的模糊含义成为自然而然的研究热点。在本文中，我们专注于该研究领域并考虑${\mathcal{ℐ}}_{\mathcal{𝒢},\mathcal{𝒩}}$- 由准分组函数和有界格上的否定引起的影响。确切地说，首先，通过去除连续性条件，我们将单位闭区间上的群函数的概念扩展为所谓的有界格上的拟群函数。其次，我们给出了有界格上拟群函数的一些基本性质和两种构造方法。最后，我们给出一个概念${\mathcal{ℐ}}_{\mathcal{𝒢},\mathcal{𝒩}}$-蕴涵并关注它们可以满足有界格蕴涵所具有的某些代数性质的条件。