Based on the Computerized Parkinson's Law "work expands so as to fill the time available for its completion" (Thimbleby, 1993) it can be deduced that regardless of the size of the memory, there will always be programs to completely fill, or even overload that memory. Thus intelligent/sensible memory allocation process is crucial to system's performance. However, due to the constant increase of processing power and the growth and spread of distributed systems, such as grid and cloud computing, memory allocation becomes a great challenge in the area of memory management today. Making allocation intelligent, so that the memory fragmentation and response time are reduced would be great, and in this research, this was attempted. The research presents Fuzzy Allocator, memory allocator based on fuzzy inference system. The allocator manages to sort the incoming memory requests according to their size and the size of free memory slot (hole). The output of the fuzzy allocator is the order in which the allocation of memory will be performed on the incoming memory requests. It reorders the incoming memory request queue so that the response time is reduced, and fragmentation is minimized.