# Soft Computing
#### Andrea Bonarini
##### 5 October 2015

#### What is Soft Computing?

The term was introduced by Lotfi Zadeh, the father of fuzzy sets,
to denote programming techniques not related to *traditional* programming languages:
- Fuzzy systems
- Neural networks
- Stochastic systems

##### definition
A set of techniques to model systems (input-output mapping) by approximating them.

##### Modelling technique: generalization
Considers a small sample of the entity to make an approximate model,


#### Model

- Is a *representation* of some entity, defined for a *specific purpose*.

- Is limited to aspects of the entity represented which are *relevant for the purpose*

- A model is different to the represented entity ex: map vs land

- Models lead to *approximation, uncertainty, imprecision*.

##### Approximation
The model features are similar to the real ones but not the same.
##### Uncertainty
We are not sure that the features of the model are the same of the entity.
##### Imprecision
The model features values are not precise.

#### Techniques

- ##### Fuzzy sets:
    Correct model in a finite number of points, smooth transistion (approximation) among them.

    ex: in a thermal control system we fix the normal working point and the critical one, and the system approximates the behaviour between.

- ##### Neural networks
    input-output samples, learning algorithms to define output values for unknown values.

- ##### Genetic algorithms
    Optimal solution, obtained by evaluating populations of tentative solutions and combining their parts (sort of copying from nature).

#### Applications:

From washing machines to helicopters, to rice cookers

### Fuzzy Sets

Were created in 1965 by Lotfi Zadeh

The principle is to make computation with words.

#### What is a fuzzy set?
Is a set whose membership function can range on the interval [0,1].

On contrary to __crisp sets__ that admit only {0,1}

###### A membership function defines a set
###### Defines the degree of membership of an element to the set
μ: U -> [0,1]

#### How to define membership functions
- select a variable
    - distance
- define a range of the variable
    - [0..10]
- identify labels
    - close, medium, far
- for each label identify the charachteristic points
    - 0, max, middle values, where MF=1, ...
- identify function shapes
    - linear
- check

#####Membership functions can also overlap,
and this quality is useful for example in classification of a noisy input,
in fact with overlapping MF we have a *smooth transition* from a label to another

#### MF and concepts

__MFs__ define __fuzzy sets__

__Labels__ denote __fuzzy sets__

__Fuzzy sets__ can be considered as conceptual representations

#### Symbol grounding
Reason in terms of concepts and grounds them to reality.