Cognitive radio sensor network (CRSN) is known as a distributed network of wireless cognitive radio sensor nodes. Such a system senses an event signal and ensures collaborative dynamic communication processes over the spectrum bands. Here the concept of dynamic spectrum access defines the method of reaching progressively to the unused range of spectrum band. As among the essential CRSN user types, the primary user (PU) has the license to access the spectrum band. On the other hand, the secondary user (SU) tries to access the unused spectrum efficiently, by not disturbing the PU. Considering that issue, this study introduces a fuzzy genetic based dynamic spectrum allocation (FGDSA) system for deciding spectrum allocation in cognitive radio sensor networks. In detail, the primary objective of the FGDSA system is to increase channel use without causing too much interference to the PU. In order to achieve that, some parameters such as signal interference noise ratio (SINR), bit error rate (BER), available channel bandwidth, SU transmission power, and the SU data rate are used as input variables for the fuzzy based inference mechanism taking place in the FGDSA. After development of the system, a performance analysis was done by comparing some metrics such as channel utilization, signal noise interference ratio, and the channel access delay for fuzzy based inference and the fuzzy genetic based inference that are both performing spectrum allocation. It was observed that the hybrid system of FGDSA outperforms fuzzy system by 2% in channel utilization, by also ensuring 16% less SINR, and 41% less channel access delay. The FGDSA was compared with also some existing spectrum allocation techniques such as edge coloring heuristic (ECH) and clique heuristic algorithm (CHA). It was seen that the FGDSA outperforms both ECH and CHA in average channel utilization, with the rates of 6% and 8%, respectively.