Effects of different effective nucleon-nucleon interactions on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay half-life and extracted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mm

Systematical calculations are performed to study the effects of different effective nucleon-nucleon ($NN$) interactions on $\ensuremath{\alpha}$-decay half-life and extracted $\ensuremath{\alpha}$-cluster preformation probability. Within the double-folding model, both the nonrelativistic M3Y-type and the relativistic R3Y-type $NN$ interactions are involved and different methods to include the medium effect into the interactions are also introduced. The differences of the effective $NN$ interactions as well as their corresponding nuclear potentials and total $\ensuremath{\alpha}$-core potentials are analyzed in detail, and then their impacts on the $\ensuremath{\alpha}$-decay half-lives are discussed. By fitting the experimental decay half-lives of $\ensuremath{\alpha}$ emitters throughout the nuclide chart, three kinds of common $\ensuremath{\alpha}$-cluster preformation probability for even-even, odd-$A$, and odd-odd parent nuclei are extracted within two usual strategies. The obtained values are consistent with previous results and the medium effect on the $\ensuremath{\alpha}$-cluster preformation probability is further discussed. Under the extracted preformation probability, the theoretical $\ensuremath{\alpha}$-decay half-lives are in good agreement with the experimental data.