fuzzy math ip lpu

8/15/2019 Fuzzy math ip lpu

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Lovely Professional University, Punjab

Course Code Course Title Course Planner Lectures Tutorials Practicals Credits

MTH402 FUZZY MATHEMATICS 17146::Varun Joshi 3 0 0 3

Course Weightage ATT: 5 CA: 20 MTT: 25 ETT: 50 Exam Category: 13: Mid Term Exam: All MCQ – End Term Exam: MCQ +Subjective

Course Orientation KNOWLEDGE ENHANCEMENT, RESEARCH

TextBooks ( T )

Sr No Title Author Edition Year Publisher Name

T-1 FUZZY SETS AND FUZZY LOGICTHEORY AND APPLICATIONS

GEORGE J. KLIR ANDBO YUAN

2nd 2013 PHI Learning Pvt Ltd

Reference Books ( R )

Sr No Title Author Edition Year Publisher Name

R-1 FUZZY SET THEORY AND ITSAPPLICATIONS

H. J. ZIMMERMANN 4th 2001 SPRINGER

Other Reading ( OR )

Sr No Journals articles as Compulsary reading (specific articles, complete reference)

OR-1 http://fuzzy.cs.uni-magdeburg.de/ci/fs/fs_ch05_relations.pdf ,

OR-2 http://perso.telecom-paristech.fr/~bloch/papers/prDist99.pdf ,

Relevant Websites ( RW )

Sr No (Web address) (only if relevant to the course) Salient Features

RW-1 http://www.fuzzytech.com/ Provides reading materials, softwares, and data analysis relevent to thefuzzy mathematics

RW-2 http://reference.wolfram.com/applications/fuzzylogic/Manual/12.html Fuzzy clustering

RW-3 http://home.deib.polimi. it/matteucc/Clustering/tutorial_html/cmeans.html Fuzzy C-Means Clustering

Detailed Plan For Lectures

LTP week distribution: (LTP Weeks)

Weeks before MTE 7

Weeks After MTE 7

Spill Over (Lecture) 7

An instruction plan is a tentative plan only and a teacher may make some changes in his/her teaching plan. The students are advised to use syllabus for preparation of all examinations. The students are expected to keep themselvesupdated on the contemporary issues related to the course. Upto 20% of the questions in any examination/Academic tasks can be asked from such issues even if not explicitly mentioned in the instruction plan.


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WeekNumber

LectureNumber

Broad Topic(Sub Topic) Chapters/Sections ofText/referencebooks

Other Readings,Relevant Websites,Audio Visual Aids,software and VirtualLabs

Lecture Description Learning Outcomes Pedagogical ToolDemonstration/Case Study /Images /animation / pptetc. Planned

Live Examples

Week 1 Lecture 1 Fuzzy sets & fuzzy logic-Basic Definitions(Definition

f a fuzzy set)

T-1:1 RW-1 Lecture 1 should beconsidered as zerolecture and in lecture 2introduction to basicdefinitions should be

discussed

Students will be ableto understand aboutthe history of fuzzyset and its evolutionand need of the

subject.They will befamiliar with topicsand evaluationcomponents

Power Pointpresentation withwhite board andmarker.

Application offuzzy set inimagerecognition

Lecture 2 Fuzzy sets & fuzzy logic-Basic Definitions(Definition

f a fuzzy set)

T-1:1 RW-1 Lecture 1 should beconsidered as zerolecture and in lecture 2introduction to basicdefinitions should bediscussed

Students will be ableto understand aboutthe history of fuzzyset and its evolutionand need of thesubject.They will befamiliar with topicsand evaluation

components

Power Pointpresentation withwhite board andmarker.

Application offuzzy set inimagerecognition

Lecture 3 Fuzzy sets & fuzzy logic-Basic Definitions(Elements

f fuzzy logic)

T-1:1 Definition of fuzzy setand its elements, alphacut,strong alpha cut,Level set,Support andheight of fuzzy setConvex fuzzy set

Students will be ableto learn the definitionof fuzzy set and itsparameter like alphacut strong alpha cut

White board andPPT

The database of Cgpa and otherperformance of students andtheirclassification

Week 2 Lecture 4 Fuzzy sets & fuzzy logic-Basic Definitions(Elements

f fuzzy logic)

T-1:1 Definition of fuzzy setand its elements, alphacut,strong alpha cut,Level set,Support andheight of fuzzy set

Convex fuzzy set

Students will be ableto learn the definitionof fuzzy set and itsparameter like alphacut strong alpha cut

White board andPPT

The database of Cgpa and otherperformance of students andtheir

classification

Lecture 5 peration on Fuzzy sets(Unions, Intersections,

omplements,sums,Products differences)

T-1:3 Fuzzy complement,Fuzzy intersections, tnorms, Fuzzy Union ort conorms. Yagerunion,intersection,complement. Boundedand AlgebraicSums,Products,Difference operations on a fuzzyset

Students will learnFuzzy set operationsas generalization of crisp set operations,Students will alsolearn about differentoperations on a Fuzzy

set as a subset of universal set.

White board andPPT along with thediscussion



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Week 2 Lecture 6 peration on Fuzzy sets(Unions, Intersections,

omplements,sums,Products differences)

T-1:3 Fuzzy complement,Fuzzy intersections, tnorms, Fuzzy Union ort conorms. Yagerunion,intersection,complement. Boundedand AlgebraicSums,Products,Difference operations on a fuzzyset

Students will learnFuzzy set operationsas generalization of crisp set operations,Students will alsolearn about differentoperations on a Fuzzy



Week 3 Lecture 7 peration on Fuzzy sets

(Unions, Intersections,omplements,

sums,Products differences)

T-1:3 Fuzzy complement,

Fuzzy intersections, tnorms, Fuzzy Union ort conorms. Yagerunion,intersection,complement. Boundedand AlgebraicSums,Products,Difference operations on a fuzzyset

Students will learn

Fuzzy set operationsas generalization of crisp set operations,Students will alsolearn about differentoperations on a Fuzzy


White board and

PPT along with thediscussion

Lecture 8 Fuzzy Relations(Join andomposition)

T-1:5R-1:6

Binary fuzzy relation,Join and Compositions(Max-min, Min-Max)

Students will able toconstruct the Joinsand Compositions for

relation matrix

White board andPPT along thediscussion

Fuzzy ternaryrelation by thegraph on CRISP

setLecture 9 Test1

Week 4 Lecture 10 Fuzzy Relations(Relationsincluding, Operations,Reflexivity, Symmetry and

ransitivity)

T-1:5R-1:6

OR-1OR-2

Relations including,Operations, Reflexivityon crisp and Fuzzy setSymmetric Fuzzyrelation on crisp andFuzzy set TransitiveFuzzy relation on crispand Fuzzy set

Students will learnhow thereflexive,symmetricand transitiverelations are used inthe object recognition

Discussion Simple fuzzyimage of alphabet andnumbers onFuzzy imagematrix

Lecture 11 Fuzzy Relations(Relations

including, Operations,Reflexivity, Symmetry andransitivity)

T-1:5

R-1:6

OR-1

OR-2

Relations including,

Operations, Reflexivityon crisp and Fuzzy setSymmetric Fuzzyrelation on crisp andFuzzy set TransitiveFuzzy relation on crispand Fuzzy set

Students will learn

how thereflexive,symmetricand transitiverelations are used inthe object recognition

Discussion Simple fuzzy

image of alphabet andnumbers onFuzzy imagematrix

Lecture 12 Fuzzy Relations(Patternlassification based on

fuzzy relations)

T-1:5 Pattern Classification onfuzzy relationscompatible relation.Fuzzy Orderingrelations



Imagerecognition(finger print,face imagematrix)



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Week 5 Lecture 13 Fuzzy Relations(Patternlassification based on

fuzzy relations)

T-1:5 Pattern Classification onfuzzy relationscompatible relation.Fuzzy Orderingrelations



Imagerecognition(finger print,face imagematrix)

Lecture 14 Fuzzy Analysis(Applicationsf Fuzzy sets)

T-1:15 Fuzzy linearprogramming solutionby lower bound andupper bound.Construction

of optimized Fuzzylinear programmingproblem. TriangularFuzzy linearprogramming problem

students will be ableto construct and solvethe problem of Fuzzylinear programming

White board andPPT

Theoptimization ofprofit and loss ofany industrialproblem by

Fuzzy linearprogramming

Lecture 15 Fuzzy Analysis(Applicationsf Fuzzy sets)

T-1:15 Fuzzy linearprogramming solutionby lower bound andupper bound.Constructionof optimized Fuzzylinear programming

problem. TriangularFuzzy linearprogramming problem


White board andPPT

Theoptimization ofprofit and loss ofany industrialproblem byFuzzy linearprogramming

Week 6 Lecture 16 Fuzzy Analysis(Applicationsf Fuzzy sets)

T-1:15 Fuzzy linearprogramming solutionby lower bound andupper bound.Constructionof optimized Fuzzylinear programmingproblem. TriangularFuzzy linear

programming problem


White board andPPT

Theoptimization ofprofit and loss ofany industrialproblem byFuzzy linearprogramming

Lecture 17 Test2

Lecture 18 Fuzzy Analysis(Distancesetween Fuzzy Sets)

T-1:1 Hamming, EuclideanPseudo metric andMalinowski Distancesbetween two fuzzy set

Students will able todetermine thedistance between twofuzzy sets


The comparisonof image and itsquality fuzzymatrix by thedistances

Week 7 Lecture 19 xtensions, Projections(Cylindrical extensions andlosure , types ofrojections)

T-1:5 Ternary Fuzzy relationand its projections, Cylindrical extensionsand closure

Students will able tofind Closers andExtensions fromternary relation




5/10

SPILL OVERWeek 7 Lecture 20 Spill Over

Lecture 21 Spill Over

MID-TERMWeek 8 Lecture 22 luster Analysis and its

pplication in modellinginformation system(Clustering method, Fuzzy

-mean clusteringmethod,Fuzzy C-meanslgorithm,Clustering methodased upon Fuzzyquivalence relations)

T-1:13 RW-2RW-3

Construction of clusterby Fuzzy compatiblerelation, fuzzyequivalence relation.

Fuzzy Cmean clustering

Students will be ableto differentiate thefuzzy compatible andequivalence relation

and also determinethe C-mean andequivalenceclustering


Lecture 23 luster Analysis and itspplication in modelling

information system(Clustering method, Fuzzy

-mean clusteringmethod,Fuzzy C-meanslgorithm,Clustering method

ased upon Fuzzyquivalence relations)

T-1:13 RW-2RW-3

Construction of clusterby Fuzzy compatiblerelation, fuzzyequivalence relation.Fuzzy Cmean clustering

Students will be ableto differentiate thefuzzy compatible andequivalence relationand also determinethe C-mean andequivalence

clustering


Lecture 24 luster Analysis and itspplication in modelling



T-1:13 RW-2RW-3


Students will be ableto differentiate thefuzzy compatible andequivalence relationand also determinethe C-mean andequivalenceclustering


Week 9 Lecture 25 luster Analysis and its

pplication in modellinginformation system(Clustering method, Fuzzy


T-1:13 RW-2

RW-3

Construction of cluster

by Fuzzy compatiblerelation, fuzzyequivalence relation.Fuzzy Cmean clustering

Students will be able

to differentiate thefuzzy compatible andequivalence relationand also determinethe C-mean andequivalenceclustering

White board and

PPT along thediscussion



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Week 9 Lecture 26 luster Analysis and itspplication in modelling



T-1:13 RW-2RW-3


Students will be ableto differentiate thefuzzy compatible andequivalence relationand also determinethe C-mean andequivalenceclustering


Lecture 27 Applications of fuzzy sets.(Fuzzy graphs and

onnectivity,Fuzzypplication in Databaseheory, Applications to

Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph from

relation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MUlength, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from one

point to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevantdocuments

White board andPPT along with the

discussion

Week 10 Lecture 28 Applications of fuzzy sets.(Fuzzy graphs andonnectivity,Fuzzypplication in Databaseheory, Applications to

Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph fromrelation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-

cycle,Strength MUlength, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from onepoint to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex terms

and a set of relevantdocuments




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Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph fromrelation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MU

length, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from onepoint to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevant

documents


Lecture 30 Applications of fuzzy sets.(Fuzzy graphs andonnectivity,Fuzzypplication in Databaseheory, Applications to

Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph fromrelation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MUlength, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from onepoint to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevantdocuments


Week 11 Lecture 31 Applications of fuzzy sets.(Fuzzy graphs and

onnectivity,Fuzzypplication in Databaseheory, Applications to

Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph from

relation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MUlength, MU distance.Lecture 31-32:Fuzzydata base.

Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from one

point to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevantdocuments


discussion



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Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph fromrelation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MU

length, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from onepoint to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevant

documents


Lecture 33 Applications of fuzzy sets.(Fuzzy graphs andonnectivity,Fuzzypplication in Databaseheory, Applications to

Neural Networks)

T-1:12R-1:6

Lecture 27-fuzzy graphand sub graph fromrelation.Lecture 28-CompleteFuzzy graph,Pathlength.Lecture 29-Spanninggraph,Connected fuzzygraph, Connectivity.Lecture 30-cycle,Strength MUlength, MU distance.Lecture 31-32:Fuzzydata base.Lecture 33-Applicationto Fuzzy NeuralNetworks

Understanding of readability from onepoint to other in afuzzy graphand understanding of fuzzy database andfuzzy informationretrieval with the helpof set of recognizedindex termsand a set of relevantdocuments


Week 12 Lecture 34 Test3

Lecture 35 Fuzzy Regression(Fuzzyegression)

T-1:17 Linear regression basicidea with crisp data

Students will be ableto understand thefuzzy regression andconstruct thetransitive relationfrom compatiblematrix for perfectpartitionclassification.


The reduction oerror in imageecognition byequivalenceelation



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Week 12 Lecture 35 Fuzzy Regression(Linearegression basic idea withrisp data)


Students will be ableto understand thefuzzy regression andconstruct thetransitive relationfrom compatiblematrix for perfectpartitionclassification.



Lecture 36 Fuzzy Regression(Linearegression basic idea with

risp data)


Students will be ableto understand the

fuzzy regression andconstruct thetransitive relationfrom compatiblematrix for perfectpartitionclassification.


discussion

The reduction oerror in image

ecognition byequivalenceelation

Fuzzy Regression(Fuzzyegression)


Students will be ableto understand thefuzzy regression andconstruct thetransitive relation

from compatiblematrix for perfectpartitionclassification.



Week 13 Lecture 37 Fuzzy Regression(LinearRegression with Fuzzy

arameters)

T-1:17 Linear regression withFuzzy parameters

Student will learnlinear regression withFuzzy parameters



Lecture 38 Fuzzy Regression(LinearRegression with Fuzzy

arameters)

T-1:17 Linear regression withFuzzy parameters

Student will learnlinear regression withFuzzy parameters


The reduction oerror in imageecognition by

equivalenceelation

Lecture 39 Fuzzy Regression(LinearRegression with Fuzzy Data)

T-1:17 Linear regression withFuzzy data

Student will learnlinear regression withFuzzy data


Week 14 Lecture 40 Fuzzy Regression(LinearRegression with Fuzzy Data)

T-1:17 Linear regression withFuzzy data

Student will learnlinear regression withFuzzy data


SPILL OVERWeek 14 Lecture 41 Spill Over




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Week 15 Lecture 43 Spill Over



Scheme for CA:

Component Frequency Out Of Each Marks Total Marks

Test 2 3 30 60

Total :- 30 60

Details of Academic Task(s)

AT No. Objective Topic of the Academic Task Nature of Academic Task(group/individuals/field

work

Evaluation Mode Allottment /submission Week

Test1 To check theunderstanding oftopics fuzzy set,elements of fuzzy

logic, relationsincluding, operationsetc.

Definition of a fuzzy set, Elements of fuzzy logic, Relationsincluding, Operations, Reflexivity, Symmetry and Transitivity.

Individual A test of 30 markswill be conducted.Each question willbe of 5 marks or in

multiple of 5. Allquestions will becompulsary

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Test2 To check thekonwladge ofstudents in Fuzzyanalysis andextention principle

Distances between Fuzzy Sets, Height, Width of Fuzzy Subsets,Continuity and Integrals. Applications of Fuzzy sets extensions,Projections ,Cylindrical extensions and closure , types of projections

Individual A test of 30 markswill be conducted.Each question willbe of 5 marks or inmultiple of 5. Allquestions will becompulsary

5 / 6

Test3 To test theunderstanding ofApplications offuzzy sets and FuzzyAlgebra.

Paths and Connectedness, Clusters including Cluster Analysis andModelling Information Systems, bApplications, Connectivity inFuzzy Graphs,Application in Database Theory, Applications toNeural Networks

Individual A test of 30 markswill be conducted.Each question willbe of 5 marks or inmultiple of 5. Allquestions will becompulsary

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fuzzy math ip lpu

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