The uncertainties of grid sites security are main hurdle to make the job scheduling secure, reliable and fault-tolerant. Most existing scheduling algorithms use fixed-number job replications to provide fault tolerant ability and high scheduling success rate, which consume excessive resources or can not provide sufficient fault tolerant functions when grid security conditions change. In this paper a fuzzy-logic-based self-adaptive replication scheduling (FSARS) algorithm is proposed to handle the fuzziness or uncertainties of job replication number which is highly related to trust factors behind grid sites and user jobs. Remote sens-ing-based soil moisture extraction (RSBSME) workload experiments in real grid environment are performed to evaluate the proposed approach and the results show that high scheduling success rate of up to 95% and less grid resource utilization can be achieved through FSARS. Extensive experiments show that FSARS scales well when user jobs and grid sites increase.