If the difference between the call and put is small, then, by the put-call parity, the forward and the strike are close. That is, the options are nearly the at-the-money options, which are assumed to be the most liquid and the most reliable.

Its not a big deal, just a way to determine which option is at the money

say the index is currently at 1798, while the nearest two strikes are 1795 and 1800, then you need to choose one to be the at the money.

CBOE use the standard you mentioned. But I also tried the alternative, both are ok. It is just a standard to avoid the chaos in calculation (maybe more reasonable and accurate).

best,

另一种解释是VIX的计算公式利用了ln(x)的Taylor近似，要求K和F要非常接近，再根据平价公式，所以要选择call-put最小的期权对应的执行价格

我想我悟到了答案，不过依然感谢。
VIX的设计真是精妙绝伦，背后的数学原理非常精彩，堪称金融指数界的欧拉公式

嗯，其实我更喜欢他的finance的交易方面的意义，他就是用option replicate 出SP 500的risk neutral density，然后得出log normal下对应的volatility。他应该也是参考了学术界的一些估计的理论。