  Conformally deformed special relativity is mathematically consistent example
of a theory with two observer independent scales. As compare with recent DSR
proposals, it is formulated starting from the position space. In this work we
propose interpretation of Lorentz boosts of the model as transformations among
accelerated observers. We point further that the model can be considered as
relativistic version of MOND program and thus may be interesting in context of
dark matter problem.
