Summary: The probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives.