Approximate nature of traditional fuzzy methodology naturally leads to complex-valued fuzzy degrees

In the traditional fuzzy logic, the experts´ degrees of confidence in their statements is described by numbers from the interval [0,1]. These degree have a clear intuitive meaning. Somewhat surprisingly, in some applications, it turns out to be useful to also consider different numerical degrees - e.g., complex-valued degrees. While these complex-valued degrees are helpful in solving practical problems, their intuitive meaning is not clear. In this paper, we provide a possible explanation for the success of complex-valued degrees which makes their use more intuitively understandable - namely, we show that these degrees naturally appear due to the approximate nature of the traditional fuzzy methodology.