Soft Computing and Its Applications, Volume One

Fuzzy Logic 283

The answer provided by the extension principle may be expressed as the inference

rule:

X is A

is

where the membership function of is dened by:

(3.56)

subject to the condition

, .

In particular, if the function is 1:1, then Equation (3.56) simplies to:

where is the inverse of v.

Example 3.50

and

.

As in the case of the entailment rule, the dispositional version of the extension

principle has the simple form:

Remark 3.18 The dispositional extension principle plays an important role in in-

ference from commonsense knowledge.

284 Soft Computing and Its Applications

FIGURE 9 Principal facets of fuzzy logic (FL). The core of ...