## 1 Introduction
Third, they cannot adapt to the dynamic changing of the network conditions, _i.e._, when theconstraint or the topology changes, the routing algorithm needs to be redesigned [27], which is not flexible in the mobile wireless network. Fourth, all these two types of routing algorithms are concentrated on the specific aspect of the network performance (such as the congestion, the energy consumption, or the throughput), so they cannot achieve the balanced performance of the network. Motivated by this, in this paper, we propose a new fuzzy logic-based routing algorithm, named the Balanced Cross-layer Fuzzy Logic (BCFL) routing algorithm  
To the best of our knowledge, BCFL is the first that introduces the dispersion into the fuzzy logic-based routing algorithm instead of the absolute cross-layer parameter values as the fuzzy logic inference system inputs (which is different with the traditional fuzzy logic-based routing algorithm, such as the routing algorithms discussed in [19, 20, 21], _etc._), the first in setting every cross-layer parameter a dynamic weight, and also the first that proposes the dispersion formula. Based on these innovations, the BCFL will achieve better performance than the traditional routing algorithms mentioned above. We learn the properties of BCFL and compare the performance of BCFL with the traditional fuzzy logic-based routing algorithm (the algorithm used in [19, 20]) and the optimization-based routing algorithm (the algorithm used in [9]). The simulation results also show that the BCFL has better performance on selecting the next hop relay node than the other two algorithms. Moreover, the complexity of BCFL is much less than the other two algorithms. Finally, we apply the BCFL in a multiple constraints scenario; the result shows that the BCFL can deal with the multiple constraints perfectly. The advantages of BCFL are:  
* the number of if-then rules will keep constant when the number of cross layer parameters increase;
* the BCFL has the capability to handle multiple constraints without increasing the complexity of the algorithm;
* we give each parameter a dynamic weight, which can dynamically change according to the network conditions;
* as we use the dispersion of each cross-layer parameter as the input, when the network condition changes, the if-then rules will remain stable; therefore, we do not need redesign the if-then rules;
* in BCFL, the large dispersion parameter has a small weight and the small dispersion parameter has a large weight, which can decrease the influence of the parameters whose dispersion are large and obtain a more balanced solution. The rest of this paper assignment is as follows. In Section 2, we introduce the related works about the fuzzy logic-based cross layer routing algorithms. In Section 3, we will state the problem and introduce the notations and the definitions that we will use in this paper. In Section 4, we introduce the principle of the Balanced Cross-layer Fuzzy Logic routing algorithm. In Section 5, we compare the performance of the BCFL with the optimization-based algorithm and fuzzy logic-based routing algorithm, and talk about the performance in a multiple constraints scenario. In Section 6, we will discuss the conclusion and talk about the future development of BCFL.