What fuzzy interval operations should be hardware supported?

Abstract

An essential part of our knowledge is not formulated in well-defined mathematical terms. We humans have no problem processing this informal knowledge as long as there is a reasonably small amount of it. In many cases, there is a lot of such knowledge, and we need an automated way to process it. Such processing is called soft computing. In particular, when this knowledge is about numbers (e.g., about the temperature inside the reactor), then informal) means that we do not know the exact value. Instead, we have some ideas of what this number can be. For different values, we can have different degrees of belief that a particular value is possible. These degrees of belief can be represented as membership functions (fuzzy sets). The values of membership functions are not precisely known, so, to make this description more adequate, we must use membership function with interval values, i.e., interval fuzzy sets. Processing a function takes much longer than processing a number. How to make processing faster? A natural idea is to implement operations with fuzzy interval in hardware. At first glance, the solution is simple: take all the operations with real numbers that are hardware supported in the usual computers (they are all functions of one or two variables), and support similar fuzzy interval operations. In this paper, we prove that we also need hardware support of fuzzy interval operations with three (or maybe more) fuzzy operands. >