Intelligent Systems II · M2 · read
Mamdani architecture: what every block does
2. Fuzzy logic, from meaning to full solutions
Definitions → membership graphs → operations → rules → defuzzification → complete controller.
Follow one measurement through the controller
A controller turns measurements into an action setting. Consider temperature 32°C and occupancy 7 people. The input numbers first become membership degrees. The rules then combine those degrees. Only the final defuzzification returns one fan-speed number.
| Stage | What goes in | Operation | What comes out |
|---|---|---|---|
| Fuzzifier | 32°C and 7 people | Use the supplied membership graphs | Temperature Medium=.3, High=.7; occupancy High=.5 |
| Knowledge base | Chosen labels and their shapes | Store graphs and IF–THEN rules | A reusable definition of how the controller works |
| Inference | Medium=.3 AND High=.5 | Rule strength=min(.3,.5)=.3 | “Fan High” fires at .3 |
| Aggregation | All clipped output sets | Take the largest output degree at each speed | One combined fuzzy output shape |
| Defuzzifier | Combined shape | Apply the specified MoM, centroid or representative method | One numerical speed |
The antecedent is the IF part (“temperature is Medium AND occupancy is High”). The consequent is the THEN part (“fan speed is High”). A rule strength of 0.3 is a membership height; it does not mean the fan runs at 30%.
Definition: a fuzzy inference system
A fuzzy inference system (FIS) maps inputs to an output by evaluating fuzzy IF–THEN rules. A Mamdani FIS uses fuzzy sets in the rule consequents, combines their inferred output sets, and defuzzifies the result.
Architecture: what each block contributes
| Block | What it stores or calculates | Concrete meaning |
|---|---|---|
| Fuzzifier | Membership values of the measured inputs | 32°C may be Medium to degree 0.3 and High to degree 0.7 |
| Knowledge base: database | Ranges and membership functions | Medium = Tri(15,25,35) |
| Knowledge base: rule base | IF–THEN rules | IF temperature High AND occupancy High THEN fan Very High |
| Inference engine | Combines conditions and applies consequents | min for AND; clips the output triangle at the rule strength |
| Aggregator | Combines all rule outputs | At every output location, take the maximum clipped membership |
| Defuzzifier | Converts the aggregate to one crisp value | Use centroid or mean of maxima, as requested |
Parts of an IF–THEN rule
In “IF temperature is High AND occupancy is High THEN fan speed is Very High”, the IF part is the antecedent (condition), and the THEN part is the consequent (output category). The input variable temperature, the label High, and the numerical membership μHigh(32) are different things.
Why a rule strength is not yet the fan speed
A strength such as 0.3 says how strongly a rule fires. It is on the membership scale 0–1. Fan speed might be on a 0–100% scale. Defuzzification is the step that produces a number on that output scale.
Explain the architecture of a Mamdani fuzzy inference system. [3 marks · Practice]
Answer
A Mamdani FIS contains a fuzzifier, knowledge base, inference engine and defuzzifier. The database specifies membership functions and the rule base stores IF–THEN rules. Crisp inputs are fuzzified. The inference engine calculates rule firing strengths and constructs output fuzzy sets. These sets are aggregated, then defuzzified into a crisp action. For a fan controller, temperature and occupancy are inputs and fan speed is the output.
Yaad rakho: Input ka degree → rule ka strength → output ka shape → final number.