Each inference stage, or inference engine, of the SAFE model has its own set of rules, or rule base, and combines certain input indicators into a composite output indicator.

The inference engines of SAFE uses product-sum algebra to compute the membership grades of the output indicator to the corresponding fuzzy sets. Products and sums correspond to the logical operations of conjunction (“and”) and disjunction (“or”). The operation “and” is involved in the rules and the operation “or” corresponds to an operation that aggregates all rules. Product-sum inference is described below by means of an example.

Each rule is assigned a firing strength which measures the degree to which the rule matches the inputs. Suppose, for example, that ECOS is A (Average) with membership grade 0.4 and G (Good) with grade 0.6, and HUMS is A with membership grade 0.9 and G with grade 0.1. Consider four rules of the rule base for OSUS:

a. R 1

if
	ECOS is A
	and HUMS is A
then
  	OSUS is I (Intermediate).

b. R 2

if
	ECOS is A
	and HUMS is G
then
  	OSUS is FH (Fairly High).

c. R 3

if
	ECOS is G
	and HUMS is A
then
  	OSUS is FH (Fairly High).

d. R 4

if
	ECOS is G
	and HUMS is G
then
  	OSUS is H (High)

The firing strength of a rule is given by the product of the input membership grades, and this value is passed to the membership grade of the output to the corresponding fuzzy set. Thus,

• firing strength of R₁ = 0.4 × 0.9 = 0.36 = membership grade of OSUS to the fuzzy set I
• firing strength of R₂ = 0.4 × 0.1 = 0.04 = membership grade of OSUS to the fuzzy set FH
• firing strength of R₃ = 0.6 × 0.9 = 0.54 = membership grade of OSUS to the fuzzy set FH
• firing strength of R₄ = 0.6 × 0.1 = 0.06 = membership grade of OSUS to the fuzzy set H.

If several rules assign the same fuzzy set to the output variable (here we have a disjunction or union of rules), then the overall membership grade of the output is the sum of the individual firing strengths. In the above example, both rules R₂ and R₃ assign the fuzzy FH to OSUS. Thus, the output of the inference engine is:

µ_I(OSUS) = 0.36, µ_FH(OSUS) = 0.04 + 0.54 = 0.58, µ_H(OSUS) = 0.06.