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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.