Infer

The Infer option of the FIS menu graphically shows the inference mechanism. The input values are entered directly or by moving a cursor within each variable range. The inferred output value is displayed, together with several intermediate values, which allow to understand the different stages of the fuzzy reasoning:

For each rule:

• membership degree of each input value to each MF that appears in the rule premise. It is shown as a filled area ratio.
• rule firing strength, or matching degree.

  The matching degree is, in our particular case, equal to the input membership degree, as the system has a single input. In more complex cases, it is obtained by combining the MFs present in the rule premise.

  It is shown as a numerical value if the output is crisp, or as a filled area ratio if the output is fuzzy.

Figure 5: Fuzzy inference in FisPro

For each output:

• The inferred value is displayed on top, at the right, 480 here.

The Price output being crisp, with a Sugeno defuzzification and a sum aggregation, the inferred value is simply a weighted average of the rule conclusions, where the weights are the rule matching degrees.

For any degree in the Degree input range, between 9 and 14, we get the corresponding price.

The price progression is smooth, due to the interpolating capacities of the FIS.