Softcomputing for decision support

Softcomputing

PROFESSOR: PHD. MAIKEL LEYVA VÁZQUEZ MLEYVAZ@GMAIL.COM

Summer School, July-2014

• 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

• 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