This document discusses fuzzy genetic algorithms (FGAs), which combine fuzzy logic and genetic algorithms. It provides definitions of fuzzy logic and genetic algorithms. Fuzzy logic handles imprecise variables between 0 and 1, while genetic algorithms use techniques like selection, crossover and mutation to evolve solutions. The document notes that FGAs use fuzzy logic techniques to improve genetic algorithm behavior and components. It describes different FGA approaches and lists application sectors like engineering and economics.

1. Fuzzy Genetic
Algorithm
A Solution to The Problem
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2. 
Introduction

Fuzzy logic

Genetic Algorithm

Fuzzy Genetic Algorithm

Different FGA Approach

Application Sector
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3. 
After scientists became disillusioned with classical and neoclassical attempts at modeling intelligence, they looked in
other directions.

Two prominent fields arose, connectionism (neural networking,
parallel processing) and evolutionary computing.

It is the latter that this essay deals with - genetic algorithms
and genetic programming.

Fuzzy logic is a form of many-valued logic

A Fuzzy Genetic Algorithm (FGA) is considered as a GA that
uses fuzzy logic based techniques
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4. 
Definition of fuzzy


Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
A form of knowledge representation suitable for
notions that cannot be defined precisely, but which
depend upon their contexts.
 Compared to traditional binary sets fuzzy logic
variables may have a truth value that ranges in
degree between 0 and 1
Membership Function


The membership function represents the
degree of truth as an extension of valuation.
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5.  The term "fuzzy logic" was introduced with
the 1965 proposal of fuzzy set theory by
Lotfi A. Zadeh.
 Fuzzy logic has been applied to many fields,
from control theory to artificial intelligence.
 Fuzzy logics however had been studied
since the 1920s as infinite-valued logics
notably by Łukasiewicz and Tarski.
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6.  A point on that scale has three "truth values"—one for each of the
three functions.
 red arrow points to zero, this temperature may be interpreted as
"not hot“
 The orange arrow (pointing at 0.2) may describe it as "slightly
warm“
 The blue arrow (pointing at 0.8) "fairly cold"
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7. 
A genetic algorithm (or GA) is a search technique used in
computing to find true or approximate solutions to
optimization and search problems.

Genetic algorithms are categorized as global search heuristics.

Genetic algorithms are a particular class of evolutionary
algorithms that use techniques inspired by evolutionary
biology such as inheritance, mutation, selection, and
crossover (also called recombination).
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8. 
The new population is then used in the next iteration of the
algorithm.

Commonly, the algorithm terminates when either a maximum
number of generations has been produced, or a satisfactory
fitness level has been reached for the population.

If the algorithm has terminated due to a maximum number of
generations, a satisfactory solution may or may not have been
reached.
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9. Initial Population
Selection
• The evolution usually starts from a
population of randomly generated
individuals
Mating
• Individual solutions are selected through
a fitness-based process
Crossover
Mutation
• This generational process is repeated
until a termination condition has been
reached.
• improve the solution through repetitive
Terminate
application of the mutation, crossover,
inversion and selection operators
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10.  The use of FL based techniques for either improving GA behaviour and
modeling GA components, the results obtained have been called fuzzy
genetic algorithms (FGAs),
 The application of GAs in various optimization and search problems
involving fuzzy systems.
 An FGA may be defined as an ordering sequence of instructions in which
some of the instructions or algorithm components may be designed with
fuzzy logic based tools
 A fuzzy fitness finding mechanism guides the GA through the search
space by combining the contributions of various criteria/features that
have been identified as the governing factors for the formation of the
clusters.
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11. A single objective optimization model cannot serve the purpose of a fitness
measuring index because we are looking at multiple criteria that could be
responsible for stringing together data items into clusters. This is true; not
only for the clustering problem but for any problem solving using GA that
involves multiple criteria. In multi-criteria optimization, the notion of
optimality is not clearly defined. A solution may be best w.r.t. one criterion
but not so w.r.t. the other criteria. Pareto optimality offers a set of nondominated solutions called the P-optimal set where the integrity of each of
the criteria is respected.
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12. The algorithm has two computational elements that work together.
i) The Genetic Algorithm (GA) and
ii) The Fuzzy Fitness Finder (FFF).
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13. Cossover is a genetic operator used
to vary the programming of a
chromosome or chromosomes from
one generation to the next. It is
analogous to reproduction and
biological crossover, upon which
genetic algorithms are based. Cross
over is a process of taking more than
one parent solutions and producing a
child solution from them.
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14.  Mutation is a genetic operator used to maintain genetic diversity
from one generation of a population of genetic algorithm
chromosomes to the next.
 It is analogous to biological mutation. Mutation alters one or
more gene values in a chromosome from its initial state.
 In mutation, the solution may change entirely from the previous
solution. Hence GA can come to better solution by using
mutation.
 Mutation occurs during evolution according to a user-definable
mutation probability.
 This probability should be set low. If it is set too high, the search
will turn into a primitive random search.
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16. FGA
Fuzzy
GA
· A genetic representation for
potential solutions to the problem.
While the population of the genetic
algorithm undergoes evolution at
every generation, the relatively
‘good’ solutions reproduce while the
relatively ‘bad’ solutions die.
· Method to create an initial
population of potential solutions
To distinguish between solutions, an
objective (evaluation) function is
used. In the simple cases, there is
only one criterion for optimization
for example, maximization of profit
or minimization of cost.
· Selection of individuals for the next
generation
But in many real-world decision
making problems, there is a need for
simultaneous optimization of
multiple objectives.
· An evaluation function to rate
solutions in terms of their “fitness”
· Genetic operators that alter the
composition of the children
In order to make a successful run of a
GA, the values for the parameters of
the GA have to be defined like the
population size, parameters for the
genetic operators and the terminating
condition.
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17. • The Fuzzy Fitness Finder
• Input and Output Criteria
• Fuzzification of Inputs
• Fuzzy Inference Engine
• Defuzzification of Output
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18. Pittsburgh Approach
Iterative Rule Learning Approach
Michigan Approach
The Nagoya Approach
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19. Electrical Engg.
Mechanical Engg.
Economics
Artificial Intelligence
Approx. in all sectors of life.
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