## 1 Introduction
To meet the detection requirements under various environmental conditions, an adaptive variability index CFAR detector (VI-CFAR) was proposed in Ref. [13], which integrates the advantages of CA-CFAR, GO-CFAR, and SO-CFAR. It selects the appropriate detection algorithm by computing the variability index (_VI_) and mean ratio (_MR_) from reference cells in both the leading and lagging windows. However, due to the limited robustness of CA-CFAR, GO-CFAR, and SO-CFAR, the detection performance of VI-CFAR significantly degrades when the environmental type is misjudged, when a multiple-target environment is mistaken for clutter edge environments [14]. To enhance robustness, several improved strategies based on VI-CFAR have been developed [15; 16; 17; 18; 19; 20]. Among them, the VIHCEMOS-CFAR detector was introduced in Ref. [15], in which the GO algorithm of VI-CFAR is replaced with the heterogeneous clutter estimate (HCE) algorithm, and in multiple-target environments, the CA detection algorithm is substituted by the Modified Ordered Statistics (MOS) detection algorithm. Although VIHEMOS-CFAR performs better than VI-CFAR in multiple-target environments, it is less effective at controlling false alarms in environments with clutter edges. The NVI-CFAR was designed by Ref. [16]. In NVI-CFAR, the SO detection algorithm in VI-CFAR is replaced by the OSSO detection algorithm, and in multiple-target environments, the CA detection algorithm is replaced by the OS detection algorithm. Compared to VI-CFAR, the performance of NVI-CFAR is improved in multiple-target environments, as the OS detection algorithm performs better than the CA detection algorithm in this context. However, its robustness remains poor when the environmental type is misjudged, as the threshold selection method in the OSSO detection algorithm is fixed and cannot adapt to the detection requirements in various environments. Additionally, an adaptive CFAR detector with fuzzy rules is introduced in Ref. [17], which is designed to enhance detection in multiple-target environments by utilizing the KLQ-CFAR and the CFVI-CFAR. Although it is found to be effective in complex environments, its performance is degraded in uniform backgrounds. Ref. [18] combines VI-CFAR with CNN for high-frequency surface wave radar, which improves detection in complex environments through dual-detection map fusion. However, misclassification may occur under low Signal-to-Noise Ratio (SNR) conditions. Ref. [19] presents RWVI-CFAR, a robust VI-CFAR for Weibull clutter, which incorporates AOCML-CFAR to improve detection in multi-target and clutter-edge scenarios. Its performance is, however, lower in uniform clutter environments. Ref. [20] proposes the CM-CM CFAR algorithm, which combines CMLD-CFAR and CM-CFAR to efficiently handle clutter environments with low resource consumption on an FPGA. Nevertheless, challenges such as target masking in complex multiple-target environments or clutter edge environments remain. In recent years, fuzzy theory has demonstrated powerful modeling capabilities in handling uncertainty, vagueness, and incomplete information. These methodologies have been widely applied in fields such as data mining, control systems, and intelligent decision-making. For example, [PERSON]. [21] proposed a method to incorporate fuzziness into the rough approximation framework, providing a theoretical foundation for bridging continuous and discrete information. In addition, [PERSON]. [22] explored the algebraic structures derived from rough approximations in incomplete information systems, offering a new perspective for information fusion using fuzzy systems in complex environments. Furthermore, [PERSON]. [23] demonstrated that Type-2 fuzzy set theory possesses good capabilities in representing uncertainty boundaries and managing the complexity of fuzzy inference. These studies indicate that fuzzy theory is particularly well-suited for addressing problems characterized by vague boundaries and high uncertainty.