Supporting mobility in wireless sensor networks is one of the major requirements for future Internet of Things (IoT) applications. This work focuses on optimizing the objective function of Routing Protocol for Low-power and Lossy Networks (RPL) in mobile applications. RPL routing is the most common standard routing protocol designed for IoT applications. We optimized RPL objective function by combining several RPL parameters, such as (i) Expected Transmission Count (ETX), (ii) number of hops, and (iii) average Received Signal Strength Indicator (RSSI) as inputs in a fuzzy logic model. These parameters are more influenced in mobile applications. We applied the fuzzy decision to the mRPL (a hand-off enabled RPL mechanism). We fine-tuned the weighting scheme by running extensive simulations to achieve reliable data communication. We found that the fuzzy-based hand-off approach provides high reliability by successfully delivering nearly 100% of data packets, while achieving a very short hand-off delay.