Hedge Functions

An important modifier for fuzzy systems is hedges , or modifiers of fuzzy memberships. These modifiers provide an additional linguistic construct to fuzzy logic and maintain mathematical consistency. Consider the hedge functions of VERY and NOT_VERY . Hedge functions are used in conjunction with membership functions and alter their value based upon the defined linguistic purpose. The hedge functions are defined below as Equations 9.4 and 9.5.

(9.4)  

(9.5)  

For example, consider their use with the m_high membership function as defined by Figure 9.2. Given a packet rate of 115, m_high would result in 0.75. If we applied the VERY hedge function to the membership function ( VERY(m_high(rate)) ), then the resulting value would be 0.5625 (in other words, it's high, but not very high). If the rate had been 119, m_high would result in 0.95. The VERY hedge function applied to this would then result in 0.903 (or, very high).