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Softcomputing for decision support-Intro.
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• Day one- Intro and fuzzy sets
• Day two- Fuzzy operators
• Day three- Computing with words
• Day four- Connectionist Models and evolutionary models
• Day five-Conclusions and evaluation
Course outline
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• Softcomputing
• Uncertainty
• Logic
• Bayes teorem
• Fuzzy sets
• Fuzzy relations and SNA (Big Data)
Outline
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• The principal constituents of soft computing (SC)
Softcomputing
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Soft
com
pu
tin
g fuzzy logic
neural network theory
probabilistic reasoning
evolutionary computing
• Soft computing is likely to play an especially important role in science and engineering, but eventually its influence may extend much farther.
• In many ways, soft computing represents a significant paradigm shift in the aims of computing - a shift which reflects the fact that the human mind, unlike present day computers, possesses a remarkable ability to store and process information which is pervasively imprecise, uncertain and lacking in categoricity.
Softcomputing
Recomendaciones
• 800mg-100mg, twice a day.
• About 120mg, 2-3 times a day.
• Likely to be 200mg twice a day.
• 30mg? or 80mg? twice a day (the number is hard to read).
• 200mg 4 times a day or 100mg once a day.
• 150mg.
Different types of uncertainty
Recomendaciones
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
• 800mg-100mg, twice a day-Interval number, vague statement
• About 120mg, 2-3 times a day-Fuzzy number.
• Likely to be 200mg twice a day-Statement of confidence.
• 30mg? or 80mg? twice a day (the number is hard to read)-Ambiguity.
• 200mg 4 times a day or 100mg once a day-Inconsistency.
• 150mg-incomplete information
Different types of uncertainty
Recomendaciones
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
• At least 100mg, twice a day.
• The usual dose for this drug is 100mg, twice a day.
• 1g twice a day.
• Google it.
• Never heard of that drug.
• 1313 Mokingbird Lane.
Different types of uncertainty
Recomendaciones
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
• At least 100mg, twice a day-Imprecise.
• The usual dose for this drug is 100mg twice a day-Too general statement.
• 1g twice a day-Anomalous statement.
• Google it –Incongruence.
• Never heard of that drug-Ignorant.
• 1313 Mokingbird Lane-Irrelevant .
Different types of uncertainty
Recomendaciones
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
Mathematical models of uncertainty
• Set Theory
• Probability Theory
• Logic
• Fuzzy set theory
• Rough set theory
• Neutrosophic logic
• Etc.
Uncertainty
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Set Theory
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• Euclides:
• Hamming
• Minkowski
Fuctions-Distances
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21
2
1*
)(),(
n
iii baBAF
)(),(1*
n
iii baBAF
1
1*
)(),(
n
iii baBAF
Symbol English
Not
And
Or
Implies
For all
There exists
Predicate logic
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A B
0 0 1 1 0 0
0 1 1 0 0 1
1 0 0 1 0 1
1 1 0 1 1 1
True table of logical connectives
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True≡1 , False ≡0
Bipolarity
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Aristotle is a man (Premise 1)
All men are mortal (premise 2)
Aristotle is mortal (conclusion)
Reasoning under uncertainty
Most firefighter are men
Most men have secure jobs
Most firefighter have secure jobs?
Logic
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Bayes Theorem
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Supervised Classification
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Fuzzy Sets
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Triangular:
Trapezoid:
Membership Functions
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S function:
Membership Functions
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Alpha-Cut
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Modifiers
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A linguistic variable is quintuple (H,T,U,G,M) :
• H is the name of the variable
• T is the set of linguistic names
• U is the universe of values
• G is a grammar that is used to specify the values allowed in T
• Meaning M(X) of a term X ∈ T, is specified as a fuzzy subset in U.
• Example :
Linguistic variable
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Fuzzy relations
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Big Data
Variety
Velocity Volume
Big Data
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Database model SNA
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Neo4j
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Cypher query language
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Example-SNA
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Far path Strength
Example-SNA
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Homework
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x A
a 0.1
b 1
a 0.5
