In this paper, compensatory granular reasoning methods are proposed based on fuzzy logic, neural networks, genetic algorithms, compensatory computing and granular computing. The compensatory operation can be reduced to the relevant general compensatory AND operations which replace the traditional AND operations in the compensatory granular reasoning. Different compensatory AND operations such as fuzzy compensatory AND, neural compensatory AND, genetic compensatory AND, linear compensatory AND, and exponential compensatory AND are defined. The compensatory granular reasoning methods can be used to make more reliable decisions. For example, the compensatory granular reasoning methods can make more fault-tolerant fuzzy moves in a fuzzy game if a player carefully chooses a reasonable compensatory operation. In the future, different compensatory granular reasoning methods will be used in different decision-making applications.