Main technical features and functionalities
Fuzzy Logic Toolbox™ provides MATLAB® functions, apps, and a Simulink® block for analyzing, designing, and simulating systems based on fuzzy logic. The product guides you through the steps of designing fuzzy inference systems. Functions are provided for many common methods, including fuzzy clustering and adaptive neurofuzzy learning.
- The toolbox lets you model complex system behaviors using simple logic rules, and then implement these rules in a fuzzy inference system. You can use it as a stand-alone fuzzy inference engine. Alternatively, you can use fuzzy inference blocks in Simulink and simulate the fuzzy systems within a comprehensive model of the entire dynamic system.

Examples on how to use them to analyse Complex Systems
In Fuzzy logic, any non-linear cause and effect relationship is described by a Fuzzy Logic System (FLS).
The construction of an FLS requires three fundamental steps.
First, the granulation of all the variables in fuzzy sets. The number, position, and shape of the fuzzy sets are context-dependent.
Second, the graduation of all the variables. A word, often an adjective, labels every fuzzy set.
Third, the relationships between input and output fuzzy sets are described through syllogistic statements of the type “IF…, THEN….”, called fuzzy rules. The “IF…” part is the antecedent and involves the linguistic labels chosen for the input fuzzy sets. The “THEN…” part is the consequent and involves the linguistic labels chosen for the output fuzzy sets.
When we have multiple inputs, these are connected through the AND, OR, NOT operators.
Fuzzy rules may be provided by experts or can be extracted from numerical data.
The main elements of any Fuzzy Logic System are:
1) the Fuzzifier that transforms numerical inputs in degrees of membership to the input fuzzy sets.
2) The Fuzzy Inference Engine based on the Fuzzy rules, which activates output fuzzy sets.
3) The Defuzzifier that transforms the activated output fuzzy sets in crisp output values.
A FLS is a predictive tool or a decision support system for the particular phenomenon it describes.