Interval-valued seminormed fuzzy operators based on admissible orders

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 motivated 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. (c) 2021 Elsevier Inc. All rights reserved.