A formalization of constraint interval: A precussor to fuzzy interval analysis

This presentation outlines some aspects of interval analysis from the constraint interval point of view, focusing on some issues associated with mathematical analysis, especially those that are fundamental to fuzzy mathematical analysis. We begin by reviewing interval representations from the standard interval point of view and the study of intervals as functions of parameters varying in hypercubes, called constraint interval representation (CI). These concepts are used to define arithmetic operations between intervals, as well, interval-valued and interval functions for rational and transcedental functions. Issues of semantics as they apply to interval analysis and fuzzy interval analysis are discussed. The definition of constrained interval function extension is used to prove that each CI arithmetic operation is an isotonic inclusion.