Self-affine multiplicity fluctuation is investigated by using the two-dimensional factorial moment methodology and the concept of the tturst exponent (H). Investigation on the experimental data of compound particles and target fragments emitted in 84Kr-AgBr interactions at 1.7 A GeV reveals that the best power law behaviours are exhibited at H=0.7 and 0.6 respectively, and the data for shower particles produced in 84Kr-emulsion interactions at 1.7 A GeV indicate that the best power law behaviour occurs at H=0.6, all of which show the self-affine multiplicity fluctuation pattes. The multifractality and the non-thermal phase transition occurring during producing the compound particles, the target fragments, and the shower particles in the 84Kr-AgBr interaction and the 84Kr-emulsion interaction are also discussed. The multifractality is observed during producing compound particles, target fragments, and showcr particles. In the target fragment production, an evidence of non-thermal phase transition is observed, but in the shower particle production and the compound particle production, no evidence of non-thermal phase transition is observed.