The existing approaches for maintenance strategy selection cannot usually account for the intrinsic complexities, uncertainties, and bipolarities that are prevalent in critical engineering systems. This highlights the necessity of novel multi-attribute decision-making (MADM) models that can deal with ambiguity, imprecision, and conflicting objectives effectively. The research on bipolar complex fuzzy sets (BCFSs) and the construction of specialized aggregation operators (AOs) are the steps that can serve as a solid mathematical foundation to blend and integrate expert knowledge and complex systems to obtain more rational and well-balanced decisions concerning the maintenance of complex assets. To solve the hierarchical decision-making in the case of bipolar complex fuzzy (BCF) information, several prioritized AOs are formulated, such as BCF prioritized weighted averaging (BCFPWA), BCF prioritized ordered weighted averaging (BCFPOWA), BCF prioritized hybrid averaging (BCFPHA), BCF prioritized weighted geometric (BCFPWG), BCF prioritized ordered weighted geometric (BCFPOWG), and BCF prioritized hybrid geometric (BCFPHG) operators. The prioritized weighted operators represent the predetermined importance relationships between the criteria, the prioritized ordered weighted operators represent the various decision attitudes by reordering mechanisms, and the prioritized hybrid operators combine both the importance and attitudinal features, which provide more flexibility in complex maintenance decision settings. After that, we devise the notion of MADM within BCFS by employing these AOs, and then we analyze a case study, “maintenance strategy selection for engineering systems”. Finally, we carry out the comparative study of the deduced theory with a few existing theories to demonstrate the authenticity and capability of the developed theories.
Xu et al. (Tue,) studied this question.