A new method for solving interval and fuzzy equations: Linear case

A new approach to the solution of interval and fuzzy equations based on the generalized procedure of interval extension called “interval extended zero” method is proposed. The central for the proposed approach is the treatment of the interval zero as an interval centered around zero. It is shown that such proposition is not of heuristic nature, but is the direct consequence of the interval subtraction operation. Some methodological problems concerned with this definition of interval zero are discussed. It is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number. An important advantage of a new method is that it substantially decreases the excess width effect. On the other hand, we show that it can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them. The features of the method are illustrated by the example of the solution of the well known Leontief input–output problem in the interval setting.