Abstract As two important methods used to deal with uncertainty, the rough set theory and the evidence theory have close connections with each other. The purpose of this paper is to examine relationships between the relation-based rough set theory and the evidence theory, and to present interpretations of belief structures in relation-based rough set algebras. The probabilities of relation lower and upper approximations from a serial relation yield a pair of belief and plausibility functions and its belief structure. Properties of the belief structures induced by different relation-based rough set algebras are explored in this paper. The belief structure induced from a reflexive (serial and transitive, serial and symmetric, serial and Euclidean, respectively) relation is reflexive (transitive, symmetric, Euclidean, respectively). Conversely, for a reflexive (transitive, symmetric, Euclidean, respectively) belief structure, there exist a probability and a reflexive (serial and transitive, serial and symmetric, serial and Euclidean, respectively) relation such that the belief and plausibility functions defined by the known belief structure are, respectively, the belief and plausibility functions induced by the relation approximation operators. Then, necessary and sufficient conditions for a belief structure to be the belief structure induced by the relation approximation operators from different binary relations are presented.

中文翻译：

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基于关系的粗糙集和信念结构之间的关系

摘要 作为处理不确定性的两种重要方法，粗糙集理论和证据理论有着密切的联系。本文的目的是检验基于关系的粗糙集理论和证据理论之间的关系，并展示对基于关系的粗糙集代数中信念结构的解释。来自序列关系的关系上下近似的概率产生一对置信度和似真度函数及其置信度结构。本文探讨了由不同的基于关系的粗糙集代数引起的信念结构的性质。从自反（分别为串行和传递、串行和对称、串行和欧几里德）关系引发的信念结构是自反的（分别是传递、对称、欧几里得）。反过来，对于自反（分别为传递、对称、欧几里德）信念结构，存在概率和自反（分别为串行和传递、串行和对称、串行和欧几里德）关系，使得由已知信念定义的信念和似然函数结构分别是由关系逼近算子引起的置信度和似真度函数。然后，给出了一个信念结构成为由不同二元关系的关系逼近算子归纳出的信念结构的充要条件。分别）关系使得由已知信念结构定义的信念和似然函数分别是由关系逼近算子导出的信念和似然函数。然后，给出了一个信念结构成为由不同二元关系的关系逼近算子归纳出的信念结构的充要条件。分别）关系使得由已知信念结构定义的信念和似然函数分别是由关系逼近算子导出的信念和似然函数。然后，给出了一个信念结构成为由不同二元关系的关系逼近算子归纳出的信念结构的充要条件。