How to filter multiple values (OR operation) in angularJS

You can use a controller function to filter.

function MoviesCtrl($scope) {

    $scope.movies = [{name:'Shrek', genre:'Comedy'},
                     {name:'Die Hard', genre:'Action'},
                     {name:'The Godfather', genre:'Drama'}];

    $scope.selectedGenres = ['Action','Drama'];

    $scope.filterByGenres = function(movie) {
        return ($scope.selectedGenres.indexOf(movie.genre) !== -1);
    };

}

HTML:

<div ng-controller="MoviesCtrl">
    <ul>
        <li ng-repeat="movie in movies | filter:filterByGenres">
            {{ movie.name }} {{ movie.genre }}
        </li>
    </ul>
</div>

Creating a custom filter might be overkill here, you can just pass in a custom comparator, if you have the multiples values like:

$scope.selectedGenres = "Action, Drama"; 

$scope.containsComparator = function(expected, actual){  
  return actual.indexOf(expected) > -1;
};

then in the filter:

filter:{name:selectedGenres}:containsComparator

Here is the implementation of custom filter, which will filter the data using array of values.It will support multiple key object with both array and single value of keys. As mentioned inangularJS API AngularJS filter Doc supports multiple key filter with single value, but below custom filter will support same feature as angularJS and also supports array of values and combination of both array and single value of keys.Please find the code snippet below,

myApp.filter('filterMultiple',['$filter',function ($filter) {
return function (items, keyObj) {
    var filterObj = {
        data:items,
        filteredData:[],
        applyFilter : function(obj,key){
            var fData = [];
            if (this.filteredData.length == 0)
                this.filteredData = this.data;
            if (obj){
                var fObj = {};
                if (!angular.isArray(obj)){
                    fObj[key] = obj;
                    fData = fData.concat($filter('filter')(this.filteredData,fObj));
                } else if (angular.isArray(obj)){
                    if (obj.length > 0){
                        for (var i=0;i<obj.length;i++){
                            if (angular.isDefined(obj[i])){
                                fObj[key] = obj[i];
                                fData = fData.concat($filter('filter')(this.filteredData,fObj));    
                            }
                        }

                    }
                }
                if (fData.length > 0){
                    this.filteredData = fData;
                }
            }
        }
    };
    if (keyObj){
        angular.forEach(keyObj,function(obj,key){
            filterObj.applyFilter(obj,key);
        });
    }
    return filterObj.filteredData;
}
}]);

Usage:

arrayOfObjectswithKeys | filterMultiple:{key1:['value1','value2','value3',...etc],key2:'value4',key3:[value5,value6,...etc]}

Here is a fiddle example with implementation of above "filterMutiple" custom filter. :::Fiddle Example:::

I would just create a custom filter. They are not that hard.

angular.module('myFilters', []).
  filter('bygenre', function() {
    return function(movies,genres) {
      var out = [];
      // Filter logic here, adding matches to the out var.
      return out;
    }
  });

template:

<h1>Movies</h1>

<div ng-init="movies = [
          {title:'Man on the Moon', genre:'action'},
          {title:'Meet the Robinsons', genre:'family'},
          {title:'Sphere', genre:'action'}
       ];" />
<input type="checkbox" ng-model="genrefilters.action" />Action
<br />
<input type="checkbox" ng-model="genrefilters.family" />Family
<br />{{genrefilters.action}}::{{genrefilters.family}}
<ul>
    <li ng-repeat="movie in movies | bygenre:genrefilters">{{movie.title}}: {{movie.genre}}</li>
</ul>

Edit here is the link: Creating Angular Filters

UPDATE: Here is a fiddle that has an exact demo of my suggestion.