The Role Genetic algorithm And Fuzzy Logic

Posted By on March 25, 2016

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Rough Set Approach

The idea of genetic algorithm is derived from natural evolution. In genetic algorithm, first of all, the initial population is created. This initial population consists of randomly generated rules. We can represent each rule by a string of bits.

For example, in a given training set, the samples are described by two Boolean attributes such as A1 and A2. And this given training set contains two classes such as C1 and C2.

We can encode the rule IF A1 AND NOT A2 THEN C2 into a bit string 100. In this bit representation, the two leftmost bits represent the attribute A1 and A2, respectively.

Likewise, the rule IF NOT A1 AND NOT A2 THEN C1 can be encoded as 001.

Note − If the attribute has K values where K>2, then we can use the K bits to encode the attribute values. The classes are also encoded in the same manner.

Points to remember −

  • Based on the notion of the survival of the fittest, a new population is formed that consists of the fittest rules in the current population and offspring values of these rules as well.
  • The fitness of a rule is assessed by its classification accuracy on a set of training samples.
  • The genetic operators such as crossover and mutation are applied to create offspring.
  • In crossover, the substring from pair of rules are swapped to form a new pair of rules.
  • In mutation, randomly selected bits in a rule’s string are inverted

Fuzzy Set Approaches:

Fuzzy Set Theory is also called Possibility Theory. This theory was proposed by Lotfi Zadeh in 1965 as an alternative the two-value logic and probability theory. This theory allows us to work at a high level of abstraction. It also provides us the means for dealing with imprecise measurement of data.

The fuzzy set theory also allows us to deal with vague or inexact facts. For example, being a member of a set of high incomes is in exact (e.g. if $50,000 is high then what about $49,000 and $48,000). Unlike the traditional CRISP set where the element either belong to S or its complement but in fuzzy set theory the element can belong to more than one fuzzy set.

For example, the income value $49,000 belongs to both the medium and high fuzzy sets but to differing degrees. Fuzzy set notation for this income value is as follows −

mmedium_income($49k)=0.15 and mhigh_income($49k)=0.96

where ‘m’ is the membership function that operates on the fuzzy sets of medium_income and high_income respectively. This notation can be shown diagrammatically as follows −


Rough Set Approach

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Posted by Virat Fichadiya