可以通过使用 Fragment 来解决 BottomNavigationView 不能保存 UI 状态的问题。具体实现方法如下：

1.创建三个 Fragment，并在 MainActivity 中添加 BottomNavigationView：

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);

    BottomNavigationView navigation = (BottomNavigationView) findViewById(R.id.navigation);
    navigation.setOnNavigationItemSelectedListener(mOnNavigationItemSelectedListener);

    FragmentManager fragmentManager = getSupportFragmentManager();
    fragmentManager.beginTransaction().replace(R.id.content, HomeFragment.newInstance()).commit();
}

private BottomNavigationView.OnNavigationItemSelectedListener mOnNavigationItemSelectedListener
        = new BottomNavigationView.OnNavigationItemSelectedListener() {

    @Override
    public boolean onNavigationItemSelected(@NonNull MenuItem item) {

        switch (item.getItemId()) {
            case R.id.navigation_home:
                FragmentManager fm = getSupportFragmentManager();
                fm.beginTransaction().replace(R.id.content, HomeFragment.newInstance()).commit();
                return true;
            case R.id.navigation_dashboard:
                FragmentManager fm1 = getSupportFragmentManager();
                fm1.beginTransaction().replace(R.id.content, DashboardFragment.newInstance()).commit();
                return true;
            case R.id.navigation_notifications:
                FragmentManager fm2 = getSupportFragmentManager();
                fm2.beginTransaction().replace(R.id.content, NotificationFragment.newInstance()).commit();
                return true;
        }
        return false;
    }
};

2.在各个 Fragment 中保存自己的 UI 状态：

@Override
public void onSaveInstanceState(Bundle outState) {
    super.onSaveInstanceState(outState);
    outState.putInt("scroll_position", mRecyclerView.getScrollY());
}

@Override
public void onViewStateRestored(@Nullable Bundle savedInstanceState) {
    super.onViewStateRestored(savedInstanceState);
    if (savedInstanceState != null) {
        scrollToPosition(savedInstanceState.getInt("scroll_position"));
    }
}

这样，每个 Fragment 在被销毁和重建时都可以保存自己的 UI 状态，从而实现 BottomNavigationView 保存 UI 状态的效果。