Towards Discrete Interval, Set, and Fuzzy Computations

In many applications, we know the function f (x₁,...,x_n), we know the intervals xi of possible values of each quantity x_i, and we are interested in the range of possible values of y = f(x₁,...,x_n), this problem is known as the problem of interval computations. In other applications, we know the function f(x₁,...,x_n), we know the fuzzy sets X_i that describe what we know about each quantity x_i, and we are interested in finding the fuzzy set Y corresponding to the quantity y = f(x₁,...,x_n), this problem is known as the problem of fuzzy computations. There are many efficient algorithms for solving these problems, however, most of these algorithms implicitly assume that each quantity x_i can take any real value within its range. In practice, some quantities are discrete: e.g., x_i can describe the number of people. In this paper, we provide feasible algorithms for interval, set, and fuzzy computations for such discrete inputs.