In a hyper structure \((X,\star )\), \(x\star y\) is a non-empty subset of X. For a state s, \(s(x\star y)\) need not be well defined. In this paper, by defining \(s^*(x\star y)=sup\{s(z)\mid z\in x\star y\}\), we introduce notions of sup-Bosbach states, state-morphisms and sup-Riečan states on a bounded hyper EQ-algebra and discuss the related properties. The states on bounded hyper EQ-algebras are the generalization of states on EQ-algebras. Then we discuss the relations among sup-Bosbach states, state-morphisms and sup-Riečan states on bounded hyper EQ-algebras. By giving a counter example, we show that a sup-Bosbach state may not be a sup-Riečan state on a hyper EQ-algebra. We give conditions in which each sup-Bosbach state becomes a sup-Riečan state on bounded hyper EQ-algebras. Moreover, we introduce several kinds of congruences on bounded hyper EQ-algebras, by which we construct the quotient hyper EQ-algebras. By use of the state s on a bounded hyper EQ-algebra H, we set up a state \({\bar{s}}\) on the quotient hyper EQ-algebra \(H/\theta \). We also give the condition, by which a bounded hyper EQ-algebra admits a sup-Bosbach state.

在超结构\（（X，\ star）\）中，\（x \ star y \）是X的非空子集。对于状态s，\（s（x \ star y）\）不需要很好地定义。在本文中，通过定义\（s ^ *（x \ star y）= sup \ {s（z）\ mid z \ in x \ star y \} \），我们介绍了有界超EQ代数上的sup-Bosbach状态，状态同态和sup-Riečan状态的概念，并讨论了相关的性质。有界超EQ代数上的状态是EQ代数上的状态的推广。然后，我们讨论了有界超EQ代数上sup-Bosbach态，状态同态和sup-Riečan态之间的关系。通过给出一个反例，我们证明了超Bosbach状态可能不是超EQ代数上的sup-Riečan状态。我们给出了条件，其中每个sup-Bosbach状态成为有界超EQ代数上的sup-Riečan状态。此外，我们介绍了有界超EQ代数上的几种同余，以此构造商超EQ代数。通过使用状态小号上有界超EQ-代数^ h，我们成立了一个状态商超EQ代数\（H / \ theta \）上的\（{\ bar {s}} \）。我们还给出了一个条件，即有界超EQ代数承认sup-Bosbach状态。