[Vuejs]-Vue.js – Buefy Modules (Radio btns/ Check Box)

you forget to add v-model to your radio group, try this and it should work

<div class="block">
  <b-radio-group v-model="permissionType">
      <b-radio v-model="permissionType" name="permission_type" native-value="basic">Basic Permission</b-radio>
      <b-radio v-model="permissionType" name="permission_type" native-value="crud">CRUD Permission</b-radio>
  </b-radio-group>