Fine dust is a harmful particulate substance floating in the air and is divided into PM10 (which is 10 um in diameter or less) and PM2.5 (which is 2.5 um in diameter or less). Fine dust is a major cause of chronic respiratory diseases, which may occur naturally through forest fires or yellow dust, but it is mainly caused by combustion of fossil fuels such as oil and coal, or by automobile exhaust gases. When this type of bad outdoor fine dust flows into buildings, the indoor air becomes polluted, making it easier for workers or students who spend a lot of time indoors to be at risk for chronic respiratory diseases. To minimize this risk, recent research and development has focused on systems to purify indoor air by filtering fine dust. In this paper, we introduce a Wireless Sensor Networks (WSNs)-based Internet of Things (IoT) air purification system. In the WSNs-based IoT air purification system, it is important to maintain the integrity of the sensing data because the IoT air purifier operates based on the sensing data detected by sensor nodes. To defend the IoT air purifier against false report injection attacks, the existing fuzzy-based Interleaved Hop-by-Hop Authentication (IHA) detects false report injection attacks through Data Calibration. In addition to the existing fuzzy-based IHA sets, the security limit changes according to the network situation using fuzzy logic and adjusts the security and energy. However, the existing fuzzy-based IHA executes a fuzzy system every time it detects a normal event or false report injection attack, which requires additional message overhead and increases the transmission/reception energy, which increases the energy burden of the sensor nodes. To address this problem, we propose a method to control the operation cycle of the fuzzy system using the evaluation function. This proposed method has the advantage that the trade-off relationship between energy and security can be appropriately used to adjust the operation cycle and increase the lifetime of the network.