Elasticsearch fuzzy intersection of two arrays

Question

I have an object in the Elasticsearch index that has a nested object which is a list of strings. I would like to do the intersection against this list in both exact and fuzzy ways. So for example I have browser names with versions in the index like:

{
  "browsers": [
    {
      "name": "Chrome 38"
    },
    {
      "name": "Firefox 32"
    },
    {
      "name": "Safari 5"
    }
  ]
}

the request could be:

[
  {
    "name": "Chrome 38"
  },
  {
    "name": "IE 10"
  }
]

then I have just 1 exact match.

or another example:

[
  {
    "name": "Chrome 39"
  },
  {
    "name": "Firefox 33"
  },
  {
    "name": "Safari 5"
  }
]

here I have 2 fuzzy-matches(Levenstein=2) and 1 exact match

How would you write this kind of query?