n this paper, general AND/OR graphs of a new type are defined on triangle norm. The backward heuristic search algorithm BHAO for general AND/OR graphs is presented, in terms of newly-defined heuristic function h(n,x) and the principle that every subtree of the optimum solution tree is also optimum solution one. The admissibility of algorithm BHAO is proved. Based on two newly - defined monotone restrictions for heuristic function h (n, x), the characteristic of monotone restrictions for algorithm BHAO is also investigated, and the comparison between two BHAO algorithms is also discussed.