Among these, [PERSON]'s index [21] is particularly effective in reflecting the significance of each input variable on output performance and has seen wider application. In practical reliability engineering, the failure probability of structures is often the primary focus, as it is more closely linked to the tail distribution of the model output. The influence that input variables exert on the overall distribution may not correspond directly to their impact on the failure probability [25]. To tackle this discrepancy, [PERSON] et al. [26] introduced a moment-independent index that specifically assesses the effect of input random variables on the probability of failure. Compared to conventional output distribution analysis, this approach offers more straightforward and practical information for dependability design. At present, the established IM technology primarily focuses on scenarios where the input variables are random. However, for the fuzzy uncertainty problems in practical engineering, a perfect fuzzy structural IM technological system has not been established. [PERSON] et al. [27] drew on the idea of the independent index of IM under probability theory. To investigate the effects of input fuzzy variables on the output response, the authors proposed a generalized moment-independent index derived from the change in the output response's membership function. They further proposed using an optimization technique to solve the moment-independent index. To inquire into how input fuzzy factors influence the likelihood of failure, [PERSON] et al. [28] developed an entropy-based importance measure index, which quantifies the change in entropy associated with the failure probability of the membership function. [PERSON] et al. [29] proposed an importance measure index for fuzzy structural systems based on failure credibility and discussed its mathematical properties. The primary objective of this study is to propose an efficient novel fuzzy structural IM technique based on the fuzzy failure probability (FFP) approach. This technique, referred to as the FFP-based importance measure (FFP-IM), evaluates the effects of input fuzzy variables on structural systems from a probabilistic perspective. The contributions of this work are threefold: (1) the derivation and proposal of the FFP-IM index, which assesses the influence of input fuzzy variables on structural systems from a probabilistic standpoint; (2) the development of an efficient algorithm for solving the FFP-IM using state-dependent parameter (SDP) [25; 30; 31]; and (3) the validation of the proposed method through typical examples, demonstrating its theoretical soundness, computational efficiency, and practical applicability to complex structural systems. The subsequent structure of this paper unfolds as follows: Section 2 briefly reviews the process of modeling the failure probability for fuzzy structural systems from a probabilistic perspective. Section 3 defines the IM index on the FFP and derives its basic properties. Section 4 transforms the unconditional and conditional FFP into the mathematical expectation of the index function of the failure domain and proposes an efficient algorithm for solving the FFP-IM using the SDP method. Section 5 utilizes typical examples to validate the theoretical soundness and engineering relevance of the FFP-IM, alongside demonstrating the precision and efficacy of the algorithm proposed. The paper concludes with Section 6.