The fuzzy integral is a well-known class of aggregation operators, which includes the Sugeno integral and Shilkret integral. When performing fuzzy integration over vectors of interval values, recent literature showed that using a simplistic method to independently deal with the lower and upper bounds of interval-valued inputs is sometimes not reasonable in practice. This motivate us to conduct a necessary and thorough study of the possible structures and properties of interval-valued fuzzy operators. This study investigated concepts and revealed some related properties of admissible orders and cones such that interval-valued seminormed fuzzy operator (ISFO) is then well defined. We introduce the relevant set and systematically examine some of its main properties, which forms the basis of the fundamental structural analysis of the ISFO. Furthermore, relationships between the proposed concepts are discussed, and several Jensen-type inequalities for the ISFO are examined.

模糊积分是一类众所周知的聚合算子，包括 Sugeno 积分和 Shilkret 积分。在对区间值向量执行模糊积分时，最近的文献表明，使用简单的方法来独立处理区间值输入的下界和上界在实践中有时是不合理的。这促使我们对区间值模糊算子的可能结构和性质进行必要和彻底的研究。这项研究调查了概念并揭示了可容许阶数和锥体的一些相关属性，从而可以很好地定义区间值半规范模糊算子 (ISFO)。我们介绍了相关集合并系统地研究了它的一些主要属性，这些属性构成了 ISFO 基本结构分析的基础。此外，