Softcomputing for decision support-Intro.

1. Softcomputing
PROFESSOR:
PHD. MAIKEL LEYVA VÁZQUEZ
MLEYVAZ@GMAIL.COM
Summer School, July-2014

2. • 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
Recomendaciones

3. • Softcomputing
• Uncertainty
• Logic
• Bayes teorem
• Fuzzy sets
• Fuzzy relations and SNA (Big Data)
Outline
Recomendaciones

4. • The principal constituents of soft computing (SC)
Softcomputing
Recomendaciones
Softcomputing fuzzy logic
neural network
theory
probabilistic
reasoning
evolutionary
computing

5. • 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

6. • 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.

7. • 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.

8. • 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.

9. • 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.

10. Mathematical models of uncertainty
• Set Theory
• Probability Theory
• Logic
• Fuzzy set theory
• Rough set theory
• Neutrosophic logic
• Etc.
Uncertainty
Recomendaciones

11. Set Theory
Recomendaciones

12. • Euclides:
• Hamming
• Minkowski
Fuctions-Distances
Recomendaciones
2
1
2
1*
)(),(
n
i
ii baBAF
)(),(
1*
n
i
ii baBAF
1
1*
)(),(
n
i
ii baBAF

13. Symbol English
Not
And
Or
Implies
For all
There exists
Predicate logic
Recomendaciones

14. 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
Recomendaciones
True≡1 , False ≡0

15. Bipolarity
Recomendaciones

16. 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
Recomendaciones

17. Bayes Theorem
Recomendaciones

18. Supervised Classification
Recomendaciones

19. Fuzzy Sets
Recomendaciones

20. Triangular:
Trapezoid:
Membership Functions
Recomendaciones

21. S function:
Membership Functions
Recomendaciones

22. Alpha-Cut
Recomendaciones

23. Modifiers
Recomendaciones

24. 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
Recomendaciones

25. Fuzzy relations
Recomendaciones

26. Big Data
Variety
Velocity
Volume
Big Data
Recomendaciones

27. Database model SNA
Recomendaciones

28. Neo4j
Recomendaciones

29. Cypher query language
Recomendaciones

30. Example-SNA
Recomendaciones
Far path Strength

31. Example-SNA
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32. Homework
Recomendaciones
x A
a 0.1
b 1
a 0.5