Calculus for interval valued function on real space

In the classical optimization problem, parameters are generally estimated by using the probability theory or fuzzy theory. In the past few decades, such parameters are also assessed in the form of an interval, and correspondingly the interval optimization problem is imminent in existence. In this paper, the calculus for an interval-valued function is developed using partial ordering and non-standard difference to deal with such a situation. Further, the convexity for the interval-valued function is defined in terms of its mean and spread function; and several convexity results for the function are proved. All the developed concepts are illustrated through numerical examples.