Soft Computing and Its Applications, Volume One

400 Soft Computing and Its Applications

TABLE 2 Laws of fuzzy implication

Larsen

x

y = xy

Łukasiewicz

x

y = min { 1, 1 – x + y }

Mamdani

x y = min { x, y }

Standard Strict

x

y =

Gödel

x y =

Gaines

x

y =

Kleene-Dienes

x

y = max { 1 – x , y }

Kleene-Dienes – Łuk.

x y = 1 - x + xy

4.3 FUZZY MODIFIERS (HEDGES)

Fuzzy sets provide a basis for a systematic way for the manipulation of vague and

imprecise concepts. For instance, the statement “old” is a vague concept, which we

express as our perceptual representation of an individual’s age. Such perceptual repre-

sentation is not unique and its degree of imprecision depends on the environment (uni-

verse) ...