Softcomputing
Summer School, July-2014
PROFESSOR: PHD. MAIKEL LEYVA VÁZQUEZ
[email protected]
Course outline • • • •
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
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Outline • • • • • •
Softcomputing Uncertainty Logic Bayes teorem Fuzzy sets Fuzzy relations and SNA (Big Data)
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Softcomputing
Softcomputing
• The principal constituents of soft computing (SC)
fuzzy logic Recomendaciones
neural network theory probabilistic reasoning evolutionary computing
Softcomputing • 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.
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Different types of uncertainty • • • •
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.
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
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Different types of uncertainty • 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 dayInconsistency. • 150mg-incomplete information Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
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Different types of uncertainty • 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.
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
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Different types of uncertainty • 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 .
Wierman, M.J., An Introduction to the Mathematics of Uncertainty. 2010: Center for Mathematics of Uncertainty, Inc.
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Uncertainty Mathematical models of uncertainty • Set Theory • Probability Theory • Logic • Fuzzy set theory • Rough set theory • Neutrosophic logic • Etc.
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Set Theory
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Fuctions-Distances • Euclides: 2
n
F ( A, B )
(
ai bi
1
)
2
i *1
• Hamming
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n
F ( A, B )
(
ai bi ) i *1
• Minkowski
n
F ( A, B )
(
1
ai bi i *1
)
Predicate logic Symbol
English Not And Or Implies For all There exists
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True table of logical connectives 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≡1 , False ≡0
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Bipolarity
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Logic Aristotle is a man (Premise 1) All men are mortal (premise 2) Aristotle is mortal (conclusion) Recomendaciones
Reasoning under uncertainty Most firefighter are men Most men have secure jobs Most firefighter have secure jobs?
Bayes Theorem
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Supervised Classification
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Fuzzy Sets
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Membership Functions Triangular:
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Trapezoid:
Membership Functions S function:
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Alpha-Cut
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Modifiers
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Linguistic variable 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 :
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Fuzzy relations
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Big Data
Volume Velocity Recomendaciones
Variety
Big Data
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
x
A
a
0.1
b
1
a
0.5
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