On the algebraic structures of the space of interval-valued intuitionistic fuzzy numbers
This work provides a theoretical foundation for ranking IVIFNs in fuzzy set theory, which is incremental as it builds on prior ranking techniques.
The paper tackles the problem of ordering interval-valued intuitionistic fuzzy numbers (IVIFNs) by proving that the space of all IVIFNs with a specific relation based on score and entropy functions is a complete chain and an admissible order, and demonstrates this for relations based on additional functions like accuracy and uncertainty indices.
This study is inspired by those of Huang et al. (Soft Comput. 25, 2513--2520, 2021) and Wang et al. (Inf. Sci. 179, 3026--3040, 2009) in which some ranking techniques for interval-valued intuitionistic fuzzy numbers (IVIFNs) were introduced. In this study, we prove that the space of all IVIFNs with the relation in the method for comparing any two IVIFNs based on a score function and three types of entropy functions is a complete chain and obtain that this relation is an admissible order. Moreover, we demonstrate that IVIFNs are complete chains to the relation in the comparison method for IVIFNs on the basis of score, accuracy, membership uncertainty index, and hesitation uncertainty index functions.