Several studies have been achieved to construct a finite automaton that recognizes the set of words that are at a bounded distance from some word of a given language. In this paper, we introduce a new family of regular operators based on a generalization of the notion of distance and we define a new family of expressions, the
approximate regular expressions
. We compute Brzozowski derivatives and Antimirov derivatives of such operators, which allows us to provide two recognizers for the language denoted by any approximate regular expression.