## 5 Results
### Proposed MBFLR Models  
The LR model above cannot provide the minimum RSSI that influences disconnected communication, maximum RSSI, and interference to another network. Hence, MBFLR was applied. The individual RSSI measurements with all the antenna heights (0.2 m-1.2 m) were fuzzified and aggregated into a combined uncertainty for the RSSI-distance relationship based on the LOS short grass environment conditions. Two different groups of uncertainty in the RSSI measurements were considered before and after the breakpoint distances. The RSSI uncertainty was expressed herein as triangular fuzzy numbers with a membership level of 0 to 1. The fuzzy aggregation of the uncertainties was used in the fuzzy LR analysis with fuzzy output variables. For simplicity, the symmetrical triangular L-R fuzzy numbers for coefficients A1, B1, A2, and B2 (Equation (8) were equal to the left and right spreads, respectively. The decision variables for the fuzzy regression were reduced to eight, that is, central values Ca1, Ca2, Cb1, and Cb2 and spreads Ra1, Ra2, Rb1, and Rb2 for the distance before and after the breakpoint distance coefficients. An initial membership level (\(\mu_{AI}\)) was used for the modeling, which increased or decreased the spread of the fuzzy regression curve and the output spread. The uncertainty in the RSSI measurements was expressed by the wide spread of their fuzzy numbers; thus, the \(\mu_{AI}\) values can be varied for optimization. The fuzzy regression analysis result using the minimum spread criteria (Equation (16)) with 0.4 \(\mu_{AI}\) is expressed as:  
\[RSSI_{1}(d)=[-55.4,-18.2]+[-16.2,\ 0.2]\log(d);\ \mathrm{d}\ \leq\ \mathrm{d}_{ \mathrm{bp}} \tag{26}\]  
\[RSSI_{2}(d)=[-42.9,-22.5]+[-26.8,\ 4.9]\log(d);\ \mathrm{d}\ >\ \mathrm{d}_{ \mathrm{bp}} \tag{27}\]  
where the central and spread of fuzzy coefficients A and B are \(-55.4\), \(-18.2\) and \(-16.2\), 0.2 respectively for Equation (26), and are \(-42.9\), \(-22.5\) and \(-26.8\), 4.9 respectively for Equation (27). The analysis produced upper (U) and lower (L) curves bounding the fuzzy distance and RSSI data. The uncertainty bound curves for the different membership levels represented \(\mu_{AI}\) of belonging of the RSSI values corresponding to a particular measured distance. The closer the membership level was to one, the wider the boundaries were. The spread of the fuzzy regression curves depended on the \(\mu_{AI}\) used during the regression analysis, while that of the uncertainty bound curves depended on the \(\mu_{AI}\) of 0.4 and two different levels of belonging (i.e., 0.2 and 0.0) for the measured RSSI in different grass environments. The curves between the lower 0.4(L) and upper 0.4(U) bounds represent the total uncertainty of the RSSI-distance relationship in the normal short grass area (see Figure 9). Meanwhile, those between 0.2(L) and 0.2(U) represent the uncertainty in the short and tall grass and weed (see Figure 10). Similarly, the curves between 0.0 L and 0.0 U covered all the uncertainties in the available data set of the short and tall grass uncertainties, including the effect of the one moving person (see Figure 11). However, the RSSI fell to the lower bound (0.0 L) in the case with two people blocking because the radio waves were mostly blocked at both nodes (see Figure 12). This case cannot influence the WSN disconnection because of the limited low signal (\(>\)\(-\)91 dB) and very large change of signal. Almost all RSSIs were between the central line (1.0) and the lower boundary (0.0 L) (see Figure 13).  
Figure 10: FLR curves for tall grass and weed with membership level 0.2.  
Figure 9: FLR curves for short grass with membership level 0.4.