###### Abstract  
Path loss models are essential tools for estimating expected large-scale signal fading in a specific propagation environment during wireless sensor network (WSN) design and optimization. However, variations in the environment may result in prediction errors due to uncertainty caused by vegetation growth, random obstruction or climate change. This study explores the capability of multi-boundary fuzzy linear regression (MBFLR) to establish uncertainty relationships between related variables for path loss predictions of WSN in agricultural farming. Measurement campaigns along various routes in an agricultural area are conducted to obtain terrain profile data and path losses of radio signals transmitted at 433 MHz. Proposed models are fitted using measured data with \"initial membership level\" (\(\mu_{AI}\)). The boundaries are extended to cover the uncertainty of the received signal strength indicator (RSSI) and distance relationship. The uncertainty not captured in normal measurement datasets between transmitter and receiving nodes (e.g., tall grass, weed, and moving humans and/or animals) may cause low-quality signal or disconnectivity. The results show the possibility of RSSI data in MBFLR supported at an \(\mu_{AI}\) of 0.4 with root mean square error (RMSE) of 0.8, 1.2, and 2.6 for short grass, tall grass, and people motion, respectively. Breakpoint optimization helps provide prediction accuracy when uncertainty occurs. The proposed model determines the suitable coverage for acceptable signal quality in all environmental situations. open rural area; RSSI model; multi-boundary fuzzy linear regression; wireless sensor network; initial membership level  
very important design factors for node placement in a specific area, which require suitable mathematic path loss models for certain environments. There are many studies about the received signal strength indicator (RSSI) and path loss models in agricultural and forest areas. The RSSI studies focus on accurate positioning of WSNs in smart farming [5]. An empirical path loss model in forest environments at 2.4 GHz showed the predicted results of high grass-bushes, low grass, and bushes without grass at 65 m [6]. Rapidly growing weeds can cause problems with wireless communication. Therefore, the problem of wave propagation was studied in a grass area of a field. Accurate positioning was based on the received signal strength (RSS) and the angle of arrival at an agricultural farm (i.e., short and tall grass) [7]. Various changes in the farm environment lead to difficult problems in modeling optimal conditions. To solve this problem, the intelligent model can be trained to recognize different environments through machine learning (ML). Then, the ML path loss models can be studied for mobile communication and WSNs in agriculture because of the nonlinear property and uncertainty of path loss models. Artificial neural networks (ANNs) are used in ML by providing a learning environment. The ANNs for predicting the path loss of a macro cell showed accuracy compared to traditional models [8]. However, the path loss of the wave also depends on the terrain and frequency, which are very different. A ML-based urban canyon path loss prediction model based on extensive 28 GHz measurements from Manhattan achieved a prediction error (root-mean-square error; RMSE) of 4.8 \(\pm\) 1.1 dB compared to 10.6 \(\pm\) 4.4 dB and 6.5 \(\pm\) 2.0 dB for the 3 GPP line of sight (LOS) prediction [9]. There are many different architectures of neural networks used to model path loss prediction, such as a convolutional neural network for fixed wireless access in suburban areas, obtaining an 8.59 dB RMSE [10]. An ANN-based path loss prediction for the wireless communication network at 2.5 GHz presented the rules for training and accuracy prediction [11]. The ANN and the adaptive neuro fuzzy interference system were studied to build very high frequency and ultra-high frequency path loss models.