4

Accounting for Modelling Errors in Fuzzy Models

4.1 An Introduction to Rule-Based Models

There are four basic types of fuzzy models: linguistic or Mamdani models, functional or T-S models, neurofuzzy models and fuzzy relational models. The first three types of models are described in this chapter. Fuzzy relational models are considered in Chapter 5.

4.2 Linguistic Fuzzy Models

This type of fuzzy model consists of IF-THEN rules where both the antecedent and the consequent are fuzzy propositions that can be interpreted linguistically.

The output of the model is derived using a fuzzy inferencing scheme. Fuzzy inferencing may generate a fuzzy output but, if necessary, a defuzzification scheme can be used to convert this into a crisp numerical value (see Section 4.6).

4.2.1 Fuzzy Rules

Fuzzy IF-THEN rules are of the form:

where each clause in the antecedent is a description of an input variable in terms of a fuzzy set and the consequent is a description of the output variable in terms of a fuzzy set.

4.2.2 Fuzzy Inferencing

Fuzzy inference is usually based on the use of generalized modus ponens. For example.

where B1 is similar to B2 if A1 is similar to A2.

Example 4.1

Consider fuzzy inference using the single rule,

where the fuzzy sets A and C have the following membership functions ...