Constructing membership function systems using the middle hedge operator

Abstract

Here, we present an operator-dependent, analytic membership function family that is derived from two soft inequalities by using the so-called middle hedge operator. This operator is defined over a pair of a strictly increasing and a strictly decreasing parametric membership functions that represent two soft inequalities. The middle hedge operator can also be treated as a membership function of an interval on a bounded or unbounded domain. Owing to its construction, the values of this membership function at the end points of the interval, which it represents, are equal to a given parameter value. This parameter may be interpreted as an intersection parameter. That is, if a fuzzy partition of a bounded or unbounded interval is created by using middle hedge operators with a fixed value of the intersection parameter, then each two successive membership functions in the fuzzy partition intersect at the same level. Here, we demonstrate that this new membership function family is very flexible and it can be readily used for constructing a membership function system in a fuzzy control system.