2. A. Artificial neural network
Introduction
“Neural networks are parallel computing devices, which is basically an attempt to make a
computer model of the brain. The main objective is to develop a system to perform various
computational tasks faster than the traditional systems. These tasks include pattern
recognition and classification, approximation, optimization, and data clustering.”
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3. What is Artificial Neural Network?
It is a computational system inspired by the
Structure
Processing Method
Learning Ability of a biological brain
A large number of very simple processing neuron-like processing elements A large number
of weighted connections between the elements Distributed representation of knowledge
over the connections Knowledge is acquired by network through a learning process
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6. B. Fuzzy logic
Introduction
Fuzzy concepts first introduced by Zadeh in the 1960s and 70s
Traditional computational logic and set theory is all about :-
true or false
zero or one
in or out (in terms of set membership)
black or white (no grey)
Not the case with fuzzy logic and fuzzy sets!
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7. Formal Fuzzy Logic
Fuzzy logic can be seen as an extension of ordinary logic, where the main difference is that
we use fuzzy sets for the membership of a variable
We can have fuzzy propositional logic and fuzzy predicate logic
Fuzzy logic can have many advantages over ordinary logic in areas like artificial
intelligence where a simple true/false statement is insufficient
Simple Fuzzy Operators
o As described by Zadeh (1973).NOT X = 1 - µX (y). e.g. 0.8 cold → (1 – 0.8) = 0.2 NOT
cold
o X OR Y (union) = max(µX (y), µY (y)). e.g. 0.8 cold, 0.5 rainy → 0.8 cold OR rainy
o X AND Y (intersection) = min(µX (y), µY (y)). e.g. 0.9 hot, 0.7 humid → 0.7 hot AND
humid
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8. Fuzzy System Overview
When making inferences, we want to clump the continuous numerical values into sets
Unlike Boolean logic, fuzzy logic uses fuzzy sets rather than crisp sets to determine the
membership of a variable
This allows values to have a degree of membership with a set, which denotes the extent to
which a proposition is true
The membership function may be triangular, trapezoidal, Gaussian or any other shape
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9. Application
Structural analysis and Design for structural optimization and optimum Design of
structures.
The field of Hydrology & Water Resource engineering.
Traffic engineering.
Reliability of structures.
Metal structures.
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11. C. Genetic algorithm
Introduction
“Growing specialization and diversification have brought a host of monographs and textbooks
on increasingly specialized topics. However, the “tree” of knowledge of mathematics and
related fields does not grow only by putting forth new branches. It also happens, quite often
in fact, that branches which were thought to be completely disparate are suddenly seen to
be related”
Michiel Hazewinkel
Applying mathematics to a problem of the real world mostly means, at first, modeling the
problem mathematically, maybe with hard restrictions, idealizations, or simplifications,
then solving the mathematical problem, and finally drawing conclusions about the real
problem based on the solutions of the mathematical problem.
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12. Components, Structure, & Terminology
Since genetic algorithms are designed to simulate a biological process, much of the
relevant terminology is borrowed from biology. However, the entities that this terminology
refers to in genetic algorithms are much simpler than their biological counterparts.
The basic components common to almost all genetic algorithms are:
a fitness function for optimization
a population of chromosomes
selection of which chromosomes will reproduce
crossover to produce next generation of chromosomes
random mutation of chromosomes in new generation
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13. Application
1) Resource Leveling.
2) Scheduling Of Large Projects.
3) Resource Constraints.
4) A Solution To The Scheduling Problem.
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