## 4 A Routing Protocol for LLNs (RPL)
### RPL Objective Functions for Non-Malicious LLNs
#### 4.2.3 Fuzzy Logic Method  
The third group uses combined routing metrics based on fuzzy logic methods. [PERSON] first introduced fuzzy logic in [106] as a framework that can deal with uncertainty and approximation inputs. Unlike traditional logic based on binary true/false values, fuzzy logic allows for representing partial truth or partial membership in a set. In other words, it allows for a degree of \"fuzziness\" in the way of reason about things. Therefore, fuzzy logic is often used to solve problems that involve decision-making in uncertain or imprecise situations, resulting in making accurate and efficient decisions as possible [107]. As shown in Figure 7, fuzzy logic consists of four main components:  
1. Fuzzification--the process of converting specific input values into a certain degree of fuzzy set membership. 2. Fuzzy rules/knowledge base--the if-then rules to follow are often derived from human expert opinions. 3. Inference engine--the way of obtaining the final fuzzy conclusion based on the degree of membership of the input variables to fuzzy sets and detailed fuzzy rules. 4. Defuzzification--the process of converting the fuzzy conclusions into detailed output values. Similar to the second group, the combined routing metrics in fuzzy logic can belong to one or both of the metric categories. These objective functions include composite metric objective function (CMOF) [108], fuzzy-based mobility objective function (FMOF) [109], fuzzy analytic hierarchy process objective function (FAHP-OF) [110], optimisation fuzzy link quality estimation-based routing metric (Opt-FLQE) [111], objective function-based fuzzy (OF-Fuzzy) [112], objective function-based fuzzy logic (OF-FL) [113], objective function energy consumption (OF-EC) [114], and fuzzy logic-based objective function (FLEOF) [115]. [PERSON] et al. [108] proposed CMOF, a fuzzy logic-based objective function that combines ETX with latency. CMOF addresses the problem of reliability and latency requirements during path selection. The latency metric is measured by the time a packet spends in the transmit queue plus the time it takes to access the channel. By considering ETX and latency as routing metrics, CMOF can select paths with less congestion and good link quality. The following fuzzy rule characterises the highest quality of a link: IF the link has a high ETX value AND low latency, THEN it has high quality. Simulation results show improvement in terms of PDR and latency compared to MRHOF [85]. [PERSON] et al. [109] proposed FMOF, a fuzzy logic method that takes into consideration three routing metrics for path selection. The chosen routing metrics are (i) ETX to measure link quality, (ii) hop count to find the shortest path in terms of the hop, and (iii) RSSI to measure the received signal power. The following fuzzy rule obtains the quality of a link: IF the ETX value is small AND hop count is near AND RSSI is connected, THEN the link is excellent. Simulation results show that FMOF enhances the network performance in terms of PDR, average delay, and control overhead compared to MRHOF [85] and OF0 [81]. [PERSON] et al. [110] proposed FAHP-OF. This objective function harnesses fuzzy logic for soft-boundary decision-making and employs the Analytic Hierarchy Process (AHP) to combine multiple routing metrics. FAHP considers three routing metrics: ETX, RSSI, and hop count. The selected routing metrics for FAHP-OF are ETX, RSSI, and hop count. AHP uses a scale method table, which matches linguistic importance intensities to numerical numbers. Simulation results show that FAHP-OF maximises network performance in terms of PDR and network lifetime. A similar idea, as in [108, 109, 110], is also proposed by [PERSON] et al. [111], who suggested combining four-link quality estimators as routing metrics using the fuzzy logic method. The proposed OF, namely Opt-FLQE, aims to improve RPL performance in smart grid environments and overcome the limitations of ETX in terms of (i) reliability, (ii) stability, and (iii) reactivity.