Interval Type-2 Fuzzy logic vs Perceptual Computing

8/9/2019 Interval Type-2 Fuzzy logic vs Perceptual Computing

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Interval Type-2 Fuzzy Logic

System versus Perceptual

Computer: Similarities and

Differences

Jerry M. Mendel

University of Southern California

Los Angeles, CA





IT2 FLS vs Per-C: Issues

•Inputs

•Fuzzifier

•Rules

•

Inference•Output Processing

•Outputs



IT2 FLS vs Per-C: Issues

•Inputs

•Fuzzifier

•Rules

•

Inference•Output Processing

•Outputs

•Inputs

•Encoder

•CWW Engine

•

Output of CWW Engine•Decoder

•Recommendation + Data



IT2 FLS vs Per-C: Applications

•“Function Approximation”

•Fuzzy logic control

•Signal processing

•

Rule-based classification



IT2 FLS vs Per-C: Applications

•“Computing With Words”

•Investment advising

•Social judgments

•

Decision making

•“Function Approximation”

•Fuzzy logic control

•Signal processing

•

Rule-based classification



IT2 FLS vs Per-C

•Inputs

•Numbers first, then

the Membership

Functions (MFs)

•Doesn’t matter whatyou call the fuzzy

sets



•Inputs

•Words first, then

the MFs

•Words that

mean somethingto end-user label

the fuzzy sets

IT2 FLS vs Per-C

•Inputs

•Numbers first, then

the Membership

Functions (MFs)

•Doesn’t matter whatyou call the fuzzy

sets



•Fuzzifier—Different

kinds (choices)•Singleton

•T1 FS—a fuzzy

number • IT2 FS—a fuzzy-fuzzy

number

IT2 FLS vs Per-C



•Encoder

•Words mean different things

to different people

• IT2 FS—No choice

•

Data from group of subjects• IA maps data into an FOU

• Three canonical FOUs

• Codebook {Wi, FOU(Wi)}

IT2 FLS vs Per-C

•Fuzzifier—Different

kinds (choices)•Singleton

•T1 FS—a fuzzy

number

• IT2 FS—a fuzzy-fuzzy

number



•Rules—IF-THEN

•From experts

•From data

• Independent of kind of

FSs used

•Words in antecedents

and consequents

modeled as IT2 FSs

IT2 FLS vs Per-C



•Rules—IF-THEN

•From experts

•From data

• Independent of kind of

FSs used

•Words in antecedents

and consequents

modeled as IT2 FSs

•CWW Engine

• IF-THEN rules

•LWA

•Others under development

• All words used by the CWW

Engine must be in a

Codebook

IT2 FLS vs Per-C



•Inference

•Mamdani

• Extended sup-star composition:

firing interval

• Computations only involve

LMFs and UMFs

• Fired rule outputs may be

combined or not, depending on

kind of output processing

IT2 FLS vs Per-C



•Inference

•TSK

• Firing interval

• Computations only involve

LMFs and UMFs

• Fired rule outputs combined

using TSK formula

IT2 FLS vs Per-C



•Inference

•Mamdani

•TSK

IT2 FLS vs Per-C

•Output of CWW Engine

• IF-THEN rules

• Similarity used to compute firing

level

• Perceptual Reasoning used to

aggregate fired rules

• Resulting output IT2 FS

resembles word FOUs—new

requirement for CWW



•Perceptual Reasoning

IT2 FLS vs Per-C


• IF-THEN rules

• Similarity used to compute firing

level

• Perceptual Reasoning used to

aggregate fired rules

• Resulting output IT2 FS

resembles word FOUs—new

requirement for CWW

Y PR =

f iGii=1

M

f j j =1

M

=

f i

f j j =1

M

Gii=1

M




•LWA (words, T1 FSs,intervals and numbers)

• Extension Principle

• Alpha-cuts function

decomposition theorem

• Two FWAs

• IWAs

• FOU(LWA) resembles word

FOUs

IT2 FLS vs Per-C

•Inference

•Mamdani

•TSK




•LWA (words, T1 FSs,intervals and numbers)

• Extension Principle

• Alpha-cuts function

decomposition theorem

• Two FWAs

• IWAs

• FOU(LWA) resembles word

FOUs

IT2 FLS vs Per-C

•LWA

Y LWA =

X iW ii=1

M

W j j =1

M



•Output Processing

•Type-reduction

• Different kinds

• KM algorithms

• TR set is an IVFS—uncertainty

measure

•Defuzzification

• Average of TR FS

IT2 FLS vs Per-C





•Outputs

• Crisp outputs that are used in anaction

• TR IVFS that can be used as a

measure of uncertainties that have

flowed through the IT2FLS

(analogous to a confidence interval)

IT2 FLS vs Per-C



•Outputs

• Crisp outputs that are used in anaction

• TR IVFS that can be used as a

measure of uncertainties that have

flowed through the IT2FLS

(analogous to a confidence interval)

•Recommendation + Data

• People want to know “Why?”

• Linguistic and numerical outputs

• Centroid and ranking bands can be

used as measures of uncertainties

that have flowed through the Per-C

IT2 FLS vs Per-C



•Words before FSs

•

Words mean different things to different people•Words mean similar things to different people

•Words or a mixture of words and numbers always excite the Per-C

•CWW Engines are constrained so that their outputs resemble the

FOUs in the Codebook

•Computations developed for IT2 FLSs are used in Perceptual

Computing

•Similarity, rank and subsethood are important in Per-C

IT2 FLS vs Per-C:

Recapitulation



Conclusions

•There are many differences between anIT2 FLS and a Perceptual Computer

• By comparing their architectures, block-

by-block, it is easy to enumerate thosedifferences

•

They are used for very different kinds of problems



IT2 FLS vs Per-C

•One Reference

J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems:

Introduction and New Directions,

Prentice-Hall, 2001

•There are now a multitude of references for IT2 FLSs



IT2 FLS vs Per-C

•Reference

J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems:

Introduction and New Directions,

Prentice-Hall, 2001

•There are now a multitude ofreferences for IT2 FLSs

•Reference

J. M. Mendel and D. Wu,Perceptual Computing: Aiding

People in Making Subjective

Judgments, Wiley and IEEE Press,

2010•There is not yet a multitude of

references for Perceptual

Computing



Thanks

Documents

Interval Type-2 Fuzzy logic vs Perceptual Computing