Fuzzy Inference Methods

After learning Fuzzy Inference System Overview, let's go towards the learning of Fuzzy Inference Methods.

If you haven't gone through it, just click below for that.

Click here to get an overview of FIS:  " Fuzzy Rule-Based System "

Methods of FIS:

1. Mamdani Fuzzy Inference System
2. Takagi - Sugeno Fuzzy Model (TS Method) 

Mamdani Inference System

This System proposed by Ebhasim Mamdani in 1975. It was anticipated to control a steam engine and boiler combination by synthesizing a set of fuzzy rules obtained from people working on the system.

Mamdani Fuzzy Inference System 

Steps need to be followed for computing output of the FIS:

1. Determining a set of fuzzy rules
2. Fuzzifying the inputs using the input membership functions
3. Combining the fuzzified inputs according to the fuzzy rules to establish a rule strength
4. Finding the consequence of the rule by combining the rule strength and the output membership function
5. Combining the consequences to get an output distribution 
6. Defuzzifying the output distribution (this step is only if a crisp output (class) is needed)

Takagi - Sugeno Fuzzy Model (TS Method)

This model was proposed by Takagi, Sugeno, and Kang in 1985. Format of this rule is given as -

IF x is A and y is B THEN z = f(x,y)

here, A, B are fuzzy sets in antecedents, and z = f(x,y) is a crisp function in the consequent.

Steps need to be followed for TS Method:

1. Fuzzyfying the inputs - the inputs of the system are made fuzzy.
2. Applying the fuzzy operator - In this step, the operator must be applied to get the output.

Rule format of the Sugeno form:

If x=7 and y=9 Then the output is z=ax+by+c

Comparison between Mamdani's FIS and TS Method:

• Output Membership Function : In Sugeno Model, output membership functions are either linear or constant.
• Aggregation and defuzzification procedure : Consequence of fuzzy rules and due to the same their aggregation and defuzzification procedure differs.
• Mathematical Rules : More mathematical rules exist for Sugeno rule than Mamdani rule. 
• Adjustable Parameters : The Sugeno controller has more adjustable parameters than the Mamdani controller.

Advantages of Sugeno and Mamdani Method:

The Sugeno Method:

• It is computationally efficient. 
• It works well with linear techniques (e.g., PID control).
• It works well with optimization and adaptive techniques.
• It has guaranteed continuity of the output surface.
• It is well suited to mathematical analysis.

The Mamdani Method:

• It is intuitive.
• It has widespread acceptance.
• It is well suited to human input.

Thanks & Keep Learning