Decision-making under uncertainty, especially when dealing with incomplete or linguistically described data, remains a significant challenge in various fields of science and industry. The increasing complexity of real-world problems necessitates the development of mathematical models and data processing techniques that effectively address uncertainty and incompleteness. Aggregators play a key role in solving these problems, particularly in fuzzy systems, where they constitute fundamental tools for decision-making, data analysis, and information fusion. Aggregation functions have been extensively studied and applied in many fields of science and engineering. Recent research has explored their usefulness in fuzzy control systems, highlighting both their advantages and limitations. One promising approach is the use of ordered fuzzy numbers (OFNs), which can represent directional tendencies in data. Previous studies have introduced the property of direction sensitivity and the corresponding determinant parameter, which enables the analysis of correspondence between OFNs and facilitates inference operations. The aim of this paper is to examine existing aggregate functions for fuzzy set numbers and assess their suitability within OFNs. By analyzing the properties, theoretical foundations, and practical applications of these functions, we aim to identify a suitable aggregation operator that complies with the principles of OFN while ensuring consistency and efficiency in decision-making based on fuzzy structures. This paper introduces a novel aggregation approach that preserves the expected mathematical properties while incorporating the directional components inherent to OFN. The proposed method aims to improve the robustness and interpretability of fuzzy reasoning systems under uncertainty.
Kozielski et al. (Sat,) studied this question.