IF-THEN RULES AND FUZZY INFERENCE

Size: px
Start display at page:

Download "IF-THEN RULES AND FUZZY INFERENCE"

Transcription

1 Iferece IF-THEN RULES ND FUZZY INFERENE!! "! ##$" % "&% " Represetato of koledge % "" Represetato of koledge as rles s the most poplar form. f x s the y s here ad are lgstc ales defed by fzzy sets o erses of dscorse X ad Y. rle s also called a fzzy mplcato x s s called the atecedet or premse y s s called the coseqece or coclso Represetato of koledge Examples If pressre s hgh the olme s small. If the road s slppery the drg s dageros. If a apple s red the t s rpe. If the speed s hgh the apply the brake a lttle. http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ Koledge as Rles Ho do yo reaso? Yo at to play golf o Satrday or Sday ad yo do t at to get et he yo play. Use rles! If t ras yo get et! If yo get et yo ca t play golf If t ras o Satrday ad o t ra o Sday Yo play golf o Sday' *Fzzy ThkgThe e Scece of Fzzy Logc art Kosko Koledge as Rles Koledge s rles Rles are black-ad-hte lagage alet rles I has so far after oer 3 years of research ot prodced smart maches! ecase they ca t yet pt eogh rles the compter se - rles eed >k} Throg more rles at the problem *Fzzy ThkgThe e Scece of Fzzy Logc art Kosko

2 Forms of reasog Geeralzed Mods Poes Premse x s Implcato f x s the y s oseqece y s Where are fzzy sets ad x ad y are symbolc ames for objects. Forms of reasog Geeralzed Mods Toles Premse y s Implcato f x s the y s oseqece x s Where are fzzy sets ad x ad y are symbolc ames for objects. http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ Fzzy rle as a relato f x s the y s x s y s fzzy predcates x y f x the y ca be represeted as a relato Rxy x y here Rxy ca be cosdered a fzzy set th 2-dmetoal membershp fcto R xyf x y here f s fzzy mplcato fcto http//f.kast.ac.kr/lectre/cs67/textbook/ MIN fzzy mplcato Iterprets the fzzy mplcato as the mmm operato Mamda]. http//f.kast.ac.kr/lectre/cs67/textbook/ PRODUT fzzy mplcato Iterprets the fzzy mplcato as the prodct operato Larse]. EXMPLE OF FUZZY IMPLITION Fzzy rle If temperatre s hgh the hmdty s farly hgh Lets defe T erse of dscorse for temperatre H erse of dscorse for hmdty t T h H arables for temperatre ad hmdty Deote hgh as T Deote farly hgh as H The the rle becomes Rth f t s the h s or Rth Rt Rh http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ 2

3 EXMPLE OF FUZZY IMPLITION f e ko ad e ca fd Rth t h R t h t h / t h Mamda m mplcato EXMPLE OF FUZZY IMPLITION e ko R t h for fzzy rle If temperatre s hgh the hmdty s farly hgh ccordg to ths rle hat s the hmdty he temperatre s farly hgh or t s T? t http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ EXMPLE OF FUZZY IMPLITION We ca se composto of fzzy relatos to fd Rh! t Rt h R t h Rh Rt ο R t h OMPOSITIONL RULE OF INFERENE I order to dra coclsos from a set of rles rle base oe eeds a mechasm that ca prodce a otpt from a collecto of rles. Ths s doe sg the compostoal rle of ferece. osder a sgle fzzy rle ad ts ferece Rle f s the s Ipt s Reslt U W U ad. The fzzy rle s terpreted as a mplcato R or R Whe pt s ge to the ferece system the otpt ο R http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ OMPOSITIONL RULE OF INFERENE ο R ο s the composto operator. The ferece procedre s called compostoal rle of ferece. The ferece mechasm s determed by to factors. Implcato operators Mamda m Larse algebrac prodct 2. omposto operators Mamda max-m Larse max-prodct OMPOSITIONL RULE OF INFERENE ompostoal rle of ferece ca be represeted graphcally as a combato of cyldrcal exteso tersecto ad projecto of fzzy sets. ld a cyldrcal exteso of xy 2. Determe tersecto of Rxy ad xy 3. ld projecto of Rxyxy http//f.kast.ac.kr/lectre/cs67/textbook/ 3

4 * OMPOSITIONL RULE OF INFERENE INFERENE METHODS There are may methods to perform fzzy ferece. osder a fzzy rle R f s ad s the s Ipts ad ca be crsp pts. rsp pts ca be treated as fzzy sgletos fzzy sets ad http//f.kast.ac.kr/lectre/cs67/textbook/ MMDNI METHOD Ths method ses the mmm operato R as a fzzy mplcato ad the max-m operator for the composto. Sppose a rle base s ge the follog form R f s ad s the s 2 for U ad W. The R ad s defed by R ad MMDNI METHOD ase Ipts are crsp ad treated as fzzy sgletos. ad ] Iferece f the Reslt Example f temperatre s hgh ad hmdty s hgh the fa speed s hgh Ho to determe the fa speed for temperatre 85ºF ad hmdty 93%? http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ MMDNI METHOD Mamda method ses m operator as fzzy mplcato fcto here s called frg stregth matchg degree satsfacto degree http//f.kast.ac.kr/lectre/cs67/textbook/ "! # $% & '! + # *! $ $% "! # # -. $! $! MMDNI METHOD For mltple rles for example to rles R ad R 2 2 http//f.kast.ac.kr/lectre/cs67/textbook/ ] ] / 2 2 4

5 2 MMDNI METHOD MMDNI METHOD I geeral ] max m 2 / 2 2 ase 2 Ipts are fzzy sets here mmax max ] & & http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ For mltple rles MMDNI METHOD & & http//f.kast.ac.kr/lectre/cs67/textbook/ ] U & & / EXMPLE OF MMDNI METHOD Let the fzzy rle base cosst of oe rle * + *-./+-/2 "33 Qesto What s the otpt f the pt s a crsp ale. 4 Qesto 2 What s the otpt f the pt s a fzzy set -.4 http//f.kast.ac.kr/lectre/cs67/textbook/ EXMPLE OF MMDNI METHOD Fzzy ferece th pt 3 4;6<9 3> ?9 Fzzy ferece th pt 2. LRSEN METHOD Ths method ses the prodct operato R P as a fzzy mplcato ad the max-prodct operator for the composto. Sppose a rle base s ge the follog form R f s ad s the s 2 for U ad W. The R ad s defed by R ad http//f.kast.ac.kr/lectre/cs67/textbook/ http//f.kast.ac.kr/lectre/cs67/textbook/ 5

6 6 LRSEN METHOD ase Ipts are crsp ad treated as fzzy sgletos. ` Iferece f the reslt For mltple rles ] ] here ad ] ] here ad http//f.kast.ac.kr/lectre/cs67/textbook/ U ] U ] LRSEN METHOD http//f.kast.ac.kr/lectre/cs67/textbook/ / 2 Graphcal represetato of Larse method th sgleto pt LRSEN METHOD ase 2 Ipts are fzzy sets For mltple rles max mmax here max mmax here http//f.kast.ac.kr/lectre/cs67/textbook/ U ] U ] LRSEN METHOD http//f.kast.ac.kr/lectre/cs67/textbook/ Graphcal represetato of Larse method th fzzy set pts / 2 EXMPLE OF LRSEN METHOD Let the fzzy rle base cosst of oe rle * + 5 *-./+-/25-/2 "33 Qesto What s the otpt f the pts are crsp ales. 6. /4 Qesto 2 What s the otpt f the pts are fzzy sets -.+7-/4 http//f.kast.ac.kr/lectre/cs67/textbook/ EXMPLE OF LRSEN METHOD http//f.kast.ac.kr/lectre/cs67/textbook/ Larse method th pt Larse method th pt

7 DEFUZZIFITION $8 33' "" 6" 633 6" "33 SUMMRY # " " 6% " " 33"9 6 % " *33" 33 " 33" 33 " "" SUMMRY $8 6 "33 " "' 33 " 33 7

Principle of Mathematical Induction

Principle of Mathematical Induction Secto. Prcple of Mthemtcl Iducto.. Defto Mthemtcl ducto s techque of proof used to check ssertos or clms bout processes tht occur repettvely ccordg to set ptter. It s oe of the stdrd techques of proof

More information

Recurrence Relations

Recurrence Relations CMPS Aalyss of Algorthms Summer 5 Recurrece Relatos Whe aalyzg the ru tme of recursve algorthms we are ofte led to cosder fuctos T ( whch are defed by recurrece relatos of a certa form A typcal example

More information

6.7 Network analysis. 6.7.1 Introduction. References - Network analysis. Topological analysis

6.7 Network analysis. 6.7.1 Introduction. References - Network analysis. Topological analysis 6.7 Network aalyss Le data that explctly store topologcal formato are called etwork data. Besdes spatal operatos, several methods of spatal aalyss are applcable to etwork data. Fgure: Network data Refereces

More information

Resource Management Model of Data Storage Systems Oriented on Cloud Computing

Resource Management Model of Data Storage Systems Oriented on Cloud Computing Resorce Maagemet Model of Data Storage Systems Oreted o Clod Comptg Elea Kaa, Yry Korolev Sat Petersbrg Electrotechcal Uversty "LETI" (ETU), Sat Petersbrg, Rssa {leaaa, yryg}@gmalcom Abstract Ths artcle

More information

An Approach to Evaluating the Computer Network Security with Hesitant Fuzzy Information

An Approach to Evaluating the Computer Network Security with Hesitant Fuzzy Information A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog, Frst ad Correspodg Author

More information

Fractal-Structured Karatsuba`s Algorithm for Binary Field Multiplication: FK

Fractal-Structured Karatsuba`s Algorithm for Binary Field Multiplication: FK Fractal-Structured Karatsuba`s Algorthm for Bary Feld Multplcato: FK *The authors are worg at the Isttute of Mathematcs The Academy of Sceces of DPR Korea. **Address : U Jog dstrct Kwahadog Number Pyogyag

More information

Questions? Ask Prof. Herz, herz@ucsd.edu. General Classification of adsorption

Questions? Ask Prof. Herz, herz@ucsd.edu. General Classification of adsorption Questos? Ask rof. Herz, herz@ucsd.edu Geeral Classfcato of adsorpto hyscal adsorpto - physsorpto - dsperso forces - Va der Waals forces - weak - oly get hgh fractoal coerage of surface at low temperatures

More information

ANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data

ANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data ANOVA Notes Page Aalss of Varace for a Oe-Wa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there

More information

A Study of Unrelated Parallel-Machine Scheduling with Deteriorating Maintenance Activities to Minimize the Total Completion Time

A Study of Unrelated Parallel-Machine Scheduling with Deteriorating Maintenance Activities to Minimize the Total Completion Time Joural of Na Ka, Vol. 0, No., pp.5-9 (20) 5 A Study of Urelated Parallel-Mache Schedulg wth Deteroratg Mateace Actvtes to Mze the Total Copleto Te Suh-Jeq Yag, Ja-Yuar Guo, Hs-Tao Lee Departet of Idustral

More information

Information technology, organizational design, and transfer pricing*

Information technology, organizational design, and transfer pricing* Iformato techology, orgazatoal desg, ad trasfer prcg* Shae S Doll The Uversty of Texas at Ast McCombs School of Bsess CBA 4M0 Ast, TX 787-0 USA Igor Vaysma** INSEAD Accotg ad Cotrol Bolevard de Costace,

More information

Chapter 11 Systematic Sampling

Chapter 11 Systematic Sampling Chapter Sstematc Samplg The sstematc samplg techue s operatoall more coveet tha the smple radom samplg. It also esures at the same tme that each ut has eual probablt of cluso the sample. I ths method of

More information

Measures of Dispersion, Skew, & Kurtosis (based on Kirk, Ch. 4) {to be used in conjunction with Measures of Dispersion Chart }

Measures of Dispersion, Skew, & Kurtosis (based on Kirk, Ch. 4) {to be used in conjunction with Measures of Dispersion Chart } Percetles Psych 54, 9/8/05 p. /6 Measures of Dsperso, kew, & Kurtoss (based o Krk, Ch. 4) {to be used cojucto wth Measures of Dsperso Chart } percetle (P % ): a score below whch a specfed percetage of

More information

Elementary Theory of Russian Roulette

Elementary Theory of Russian Roulette Elemetary Theory of Russia Roulette -iterestig patters of fractios- Satoshi Hashiba Daisuke Miematsu Ryohei Miyadera Itroductio. Today we are goig to study mathematical theory of Russia roulette. If some

More information

2 2 Matrices. Scalar multiplication for matrices. A2 2matrix(pronounced 2-by-2matrix )isasquareblockof4numbers. For example,

2 2 Matrices. Scalar multiplication for matrices. A2 2matrix(pronounced 2-by-2matrix )isasquareblockof4numbers. For example, 2 2 Matrices A2 2matrix(prononced 2-by-2matrix )isasqareblockofnmbers. For example, is a 2 2matrix. It scalleda2 2 matrix becase it has 2 rows 2 colmns. The for nmbers in a 2 2matrixarecalledtheentries

More information

The Digital Signature Scheme MQQ-SIG

The Digital Signature Scheme MQQ-SIG The Dgtal Sgature Scheme MQQ-SIG Itellectual Property Statemet ad Techcal Descrpto Frst publshed: 10 October 2010, Last update: 20 December 2010 Dalo Glgorosk 1 ad Rue Stesmo Ødegård 2 ad Rue Erled Jese

More information

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ  1 STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ

More information

Fuzzy Reliability of a Marine Power Plant Using Interval Valued Vague Sets

Fuzzy Reliability of a Marine Power Plant Using Interval Valued Vague Sets Iteratoal Joural of Appled Scece ad Egeerg 006. 4 : 7-8 uzzy Relablty of a Mare Power Plat Usg Iterval alued ague Sets Amt Kumar a Shv Prasad Yadav a * ad Suredra Kumar b a Departmet of Mathematcs Ida

More information

A Bayesian Approach to Information Fusion for Evaluating the Measurement Uncertainty

A Bayesian Approach to Information Fusion for Evaluating the Measurement Uncertainty 006 IEEE Iteratoal Coferece o Mltsesor Fso ad Iterato for Itellet Sstems September 3-6, 006, Hedelber, Germa WeB0. A Baesa Approach to Iformato Fso for Evalat the Measremet Ucertat Klas-Deter Sommer, Olaf

More information

Sequences and Series

Sequences and Series Secto 9. Sequeces d Seres You c thk of sequece s fucto whose dom s the set of postve tegers. f ( ), f (), f (),... f ( ),... Defto of Sequece A fte sequece s fucto whose dom s the set of postve tegers.

More information

Online Appendix: Measured Aggregate Gains from International Trade

Online Appendix: Measured Aggregate Gains from International Trade Ole Appedx: Measured Aggregate Gas from Iteratoal Trade Arel Burste UCLA ad NBER Javer Cravo Uversty of Mchga March 3, 2014 I ths ole appedx we derve addtoal results dscussed the paper. I the frst secto,

More information

Chapter Eight. f : R R

Chapter Eight. f : R R Chapter Eght f : R R 8. Itroducto We shall ow tur our atteto to the very mportat specal case of fuctos that are real, or scalar, valued. These are sometmes called scalar felds. I the very, but mportat,

More information

MEASURES OF CENTRAL TENDENCY

MEASURES OF CENTRAL TENDENCY MODULE - 6 Statstcs Measures of Cetral Tedecy 25 MEASURES OF CENTRAL TENDENCY I the prevous lesso, we have leart that the data could be summarsed to some extet by presetg t the form of a frequecy table.

More information

Preprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)-size data structure that enables O(log n) query time.

Preprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)-size data structure that enables O(log n) query time. Computatoal Geometry Chapter 6 Pot Locato 1 Problem Defto Preprocess a plaar map S. Gve a query pot p, report the face of S cotag p. S Goal: O()-sze data structure that eables O(log ) query tme. C p E

More information

Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity

Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity Computer Aded Geometrc Desg 19 (2002 365 377 wwwelsevercom/locate/comad Optmal mult-degree reducto of Bézer curves wth costrats of edpots cotuty Guo-Dog Che, Guo-J Wag State Key Laboratory of CAD&CG, Isttute

More information

Derive the material derivative

Derive the material derivative Fld Mechncs: Dertons & Proofs Dere the mterl derte No, f: Then: (,,, t) ρ (.) δρ ρ ρ δt δ (.) t Dde (.) bδ t, nd te lmt: δρ lm δt 0 δt ρ δ lm t δt 0 δt (.) No: lm δ δt 0 δt t (.4) We defne the LH of (.)

More information

The analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0

The analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0 Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may

More information

Automated Event Registration System in Corporation

Automated Event Registration System in Corporation teratoal Joural of Advaces Computer Scece ad Techology JACST), Vol., No., Pages : 0-0 0) Specal ssue of CACST 0 - Held durg 09-0 May, 0 Malaysa Automated Evet Regstrato System Corporato Zafer Al-Makhadmee

More information

1. The Time Value of Money

1. The Time Value of Money Corporate Face [00-0345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg

More information

Bayesian Network Representation

Bayesian Network Representation Readgs: K&F 3., 3.2, 3.3, 3.4. Bayesa Network Represetato Lecture 2 Mar 30, 20 CSE 55, Statstcal Methods, Sprg 20 Istructor: Su-I Lee Uversty of Washgto, Seattle Last tme & today Last tme Probablty theory

More information

Models for Selecting an ERP System with Intuitionistic Trapezoidal Fuzzy Information

Models for Selecting an ERP System with Intuitionistic Trapezoidal Fuzzy Information JOURNAL OF SOFWARE, VOL 5, NO 3, MARCH 00 75 Models for Selectg a ERP System wth Itutostc rapezodal Fuzzy Iformato Guwu We, Ru L Departmet of Ecoomcs ad Maagemet, Chogqg Uversty of Arts ad Sceces, Yogchua,

More information

Plastic Number: Construction and Applications

Plastic Number: Construction and Applications Scet f c 0 Advaced Advaced Scetfc 0 December,.. 0 Plastc Number: Costructo ad Applcatos Lua Marohć Polytechc of Zagreb, 0000 Zagreb, Croata lua.marohc@tvz.hr Thaa Strmeč Polytechc of Zagreb, 0000 Zagreb,

More information

Credibility Premium Calculation in Motor Third-Party Liability Insurance

Credibility Premium Calculation in Motor Third-Party Liability Insurance Advaces Mathematcal ad Computatoal Methods Credblty remum Calculato Motor Thrd-arty Lablty Isurace BOHA LIA, JAA KUBAOVÁ epartmet of Mathematcs ad Quattatve Methods Uversty of ardubce Studetská 95, 53

More information

Future Value of an Annuity

Future Value of an Annuity Future Value of a Auty After payg all your blls, you have $200 left each payday (at the ed of each moth) that you wll put to savgs order to save up a dow paymet for a house. If you vest ths moey at 5%

More information

Abraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract

Abraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected

More information

Chapter 9: Correlation and Regression: Solutions

Chapter 9: Correlation and Regression: Solutions Chapter 9: Correlatio ad Regressio: Solutios 9.1 Correlatio I this sectio, we aim to aswer the questio: Is there a relatioship betwee A ad B? Is there a relatioship betwee the umber of emploee traiig hours

More information

Applications of Support Vector Machine Based on Boolean Kernel to Spam Filtering

Applications of Support Vector Machine Based on Boolean Kernel to Spam Filtering Moder Appled Scece October, 2009 Applcatos of Support Vector Mache Based o Boolea Kerel to Spam Flterg Shugag Lu & Keb Cu School of Computer scece ad techology, North Cha Electrc Power Uversty Hebe 071003,

More information

Load Balancing Control for Parallel Systems

Load Balancing Control for Parallel Systems Proc IEEE Med Symposum o New drectos Cotrol ad Automato, Chaa (Grèce),994, pp66-73 Load Balacg Cotrol for Parallel Systems Jea-Claude Heet LAAS-CNRS, 7 aveue du Coloel Roche, 3077 Toulouse, Frace E-mal

More information

Analysis of Multi-product Break-even with Uncertain Information*

Analysis of Multi-product Break-even with Uncertain Information* Aalyss o Mult-product Break-eve wth Ucerta Iormato* Lazzar Lusa L. - Morñgo María Slva Facultad de Cecas Ecoómcas Uversdad de Bueos Ares 222 Córdoba Ave. 2 d loor C20AAQ Bueos Ares - Argeta lazzar@eco.uba.ar

More information

South East of Process Main Building / 1F. North East of Process Main Building / 1F. At 14:05 April 16, 2011. Sample not collected

South East of Process Main Building / 1F. North East of Process Main Building / 1F. At 14:05 April 16, 2011. Sample not collected At 14:05 April 16, 2011 At 13:55 April 16, 2011 At 14:20 April 16, 2011 ND ND 3.6E-01 ND ND 3.6E-01 1.3E-01 9.1E-02 5.0E-01 ND 3.7E-02 4.5E-01 ND ND 2.2E-02 ND 3.3E-02 4.5E-01 At 11:37 April 17, 2011 At

More information

European Exotic Options

European Exotic Options Hado # for B9.38 rg lecre dae: 4/3/ * Rsk-Neral Valao Eroea Exoc Oos e. Prce rocess of he derlyg secry. e. Payoff of he dervave. e 3. Execao of dscoed ayoff der RNPM.. Chooser Oo oo o oo A me : rchase

More information

Chapter 14 Nonparametric Statistics

Chapter 14 Nonparametric Statistics Chapter 14 Noparametric Statistics A.K.A. distributio-free statistics! Does ot deped o the populatio fittig ay particular type of distributio (e.g, ormal). Sice these methods make fewer assumptios, they

More information

Fuzzy Based Diagnostics System for Identifying Network Traffic Flow Anomalies

Fuzzy Based Diagnostics System for Identifying Network Traffic Flow Anomalies Fuzz Based Dagostcs Sstem for Idetfg Network Traffc Flow omales Gobthasa Rudrusam, zrud hmad, Rahmat Budarto, zma Samsud, Sureswara Ramadass Network Research Group, School of Computer Sceces Uverst Sas

More information

Research on the Evaluation of Information Security Management under Intuitionisitc Fuzzy Environment

Research on the Evaluation of Information Security Management under Intuitionisitc Fuzzy Environment Iteratoal Joural of Securty ad Its Applcatos, pp. 43-54 http://dx.do.org/10.14257/sa.2015.9.5.04 Research o the Evaluato of Iformato Securty Maagemet uder Itutostc Fuzzy Evromet LI Feg-Qua College of techology,

More information

The simple linear Regression Model

The simple linear Regression Model The smple lear Regresso Model Correlato coeffcet s o-parametrc ad just dcates that two varables are assocated wth oe aother, but t does ot gve a deas of the kd of relatoshp. Regresso models help vestgatg

More information

Study on Trust Evolution and Simulation Oriented to Cloud Services

Study on Trust Evolution and Simulation Oriented to Cloud Services Joral of Advaced Maagemet Scece Vol., No., Je 014 Stdy o Trst Evolto ad Smlato Oreted to Clod Servces Zho Ye School of Maagemet ad Egeerg, Nag Uversty, Nag, Cha yzho@.ed.c I ths paper, trst stdy s focsed

More information

Velocity of Ultrasonic Waves in liquid by the Debye- Sears Effect

Velocity of Ultrasonic Waves in liquid by the Debye- Sears Effect elocity of Ultrasonic Waves in liqid by the Debye- Sears Effect Introdction: Acostic waves in liqids case density changes with spacing determined by the freqency and the speed of the sond wave. For ltrasonic

More information

Chapter 14. Three-by-Three Matrices and Determinants. A 3 3 matrix looks like a 11 a 12 a 13 A = a 21 a 22 a 23

Chapter 14. Three-by-Three Matrices and Determinants. A 3 3 matrix looks like a 11 a 12 a 13 A = a 21 a 22 a 23 1 Chapter 14. Three-by-Three Matrices and Determinants A 3 3 matrix looks like a 11 a 12 a 13 A = a 21 a 22 a 23 = [a ij ] a 31 a 32 a 33 The nmber a ij is the entry in ro i and colmn j of A. Note that

More information

DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT

DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT ESTYLF08, Cuecas Meras (Meres - Lagreo), 7-9 de Septembre de 2008 DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT José M. Mergó Aa M. Gl-Lafuete Departmet of Busess Admstrato, Uversty of Barceloa

More information

Fuzzy Task Assignment Model of Web Services Supplier in Collaborative Development Environment

Fuzzy Task Assignment Model of Web Services Supplier in Collaborative Development Environment , pp.199-210 http://dx.do.org/10.14257/uesst.2015.8.6.19 Fuzzy Task Assget Model of Web Servces Suppler Collaboratve Developet Evroet Su Ja 1,2, Peg Xu-ya 1, *, Xu Yg 1,3, Wag Pe-e 2 ad Ma Na- 4,2 1. College

More information

APPENDIX III THE ENVELOPE PROPERTY

APPENDIX III THE ENVELOPE PROPERTY Apped III APPENDIX III THE ENVELOPE PROPERTY Optmzato mposes a very strog structure o the problem cosdered Ths s the reaso why eoclasscal ecoomcs whch assumes optmzg behavour has bee the most successful

More information

RUSSIAN ROULETTE AND PARTICLE SPLITTING

RUSSIAN ROULETTE AND PARTICLE SPLITTING RUSSAN ROULETTE AND PARTCLE SPLTTNG M. Ragheb 3/7/203 NTRODUCTON To stuatos are ecoutered partcle trasport smulatos:. a multplyg medum, a partcle such as a eutro a cosmc ray partcle or a photo may geerate

More information

Curve Fitting and Solution of Equation

Curve Fitting and Solution of Equation UNIT V Curve Fttg ad Soluto of Equato 5. CURVE FITTING I ma braches of appled mathematcs ad egeerg sceces we come across epermets ad problems, whch volve two varables. For eample, t s kow that the speed

More information

hp calculators HP 12C Platinum Statistics - correlation coefficient The correlation coefficient HP12C Platinum correlation coefficient

hp calculators HP 12C Platinum Statistics - correlation coefficient The correlation coefficient HP12C Platinum correlation coefficient HP 1C Platium Statistics - correlatio coefficiet The correlatio coefficiet HP1C Platium correlatio coefficiet Practice fidig correlatio coefficiets ad forecastig HP 1C Platium Statistics - correlatio coefficiet

More information

Lecture 4. Materials Covered: Chapter 7 Suggested Exercises: 7.1, 7.5, 7.7, 7.10, 7.11, 7.19, 7.20, 7.23, 7.44, 7.45, 7.47.

Lecture 4. Materials Covered: Chapter 7 Suggested Exercises: 7.1, 7.5, 7.7, 7.10, 7.11, 7.19, 7.20, 7.23, 7.44, 7.45, 7.47. TT 430, ummer 006 Lecture 4 Materals Covered: Chapter 7 uggested Exercses: 7., 7.5, 7.7, 7.0, 7., 7.9, 7.0, 7.3, 7.44, 7.45, 7.47.. Deftos. () Parameter: A umercal summary about the populato. For example:

More information

α 2 α 1 β 1 ANTISYMMETRIC WAVEFUNCTIONS: SLATER DETERMINANTS (08/24/14)

α 2 α 1 β 1 ANTISYMMETRIC WAVEFUNCTIONS: SLATER DETERMINANTS (08/24/14) ANTISYMMETRI WAVEFUNTIONS: SLATER DETERMINANTS (08/4/4) Wavefuctos that descrbe more tha oe electro must have two characterstc propertes. Frst, scll electros are detcal partcles, the electros coordates

More information

Constrained Cubic Spline Interpolation for Chemical Engineering Applications

Constrained Cubic Spline Interpolation for Chemical Engineering Applications Costraed Cubc Sple Iterpolato or Chemcal Egeerg Applcatos b CJC Kruger Summar Cubc sple terpolato s a useul techque to terpolate betwee kow data pots due to ts stable ad smooth characterstcs. Uortuatel

More information

Ben - Daya. ; Ouyang Chang [12 ] ; Ouy2 ang [13-14 ] Lee [15 ] Chu [ 16 ] , Hall [1 ] Schonberger [ 2 ] J IT. , Ouyang [17 ]

Ben - Daya. ; Ouyang Chang [12 ] ; Ouy2 ang [13-14 ] Lee [15 ] Chu [ 16 ] , Hall [1 ] Schonberger [ 2 ] J IT. , Ouyang [17 ] 15 3 2007 6 Chese Joural of Maagemet Scece :1003-207 (2007) 03-0068 - 07 15, No. 3 Vol. J u., 2007 (, 210094) :,,,,,, :;; : F830 :A 1, Hall [1 ] Schoberger [ 2 ] J IT,J IT ; Mode Toyota [9 ] [10-11 ] ;

More information

Lesson 12. Sequences and Series

Lesson 12. Sequences and Series Retur to List of Lessos Lesso. Sequeces ad Series A ifiite sequece { a, a, a,... a,...} ca be thought of as a list of umbers writte i defiite order ad certai patter. It is usually deoted by { a } =, or

More information

Adder Based Residue to Binary Number Converters for (2 n 1, 2 n,2 n + 1) Yuke Wang, Xiaoyu Song, Mostapha Aboulhamid, Hong Shen.

Adder Based Residue to Binary Number Converters for (2 n 1, 2 n,2 n + 1) Yuke Wang, Xiaoyu Song, Mostapha Aboulhamid, Hong Shen. Adder Based Resdue to Bary Number Coverters for (,, + ) Yuke Wag, aoyu Sog, Mostapha Aboulhamd, Hog She Abstract Based o a algorthm derved from the New Chese Remader Theorem I, we preset three ew resdue-to-bary

More information

Notes Inflation and Interest Rates in the Medium Run

Notes Inflation and Interest Rates in the Medium Run Notes Inflation and Interest Rates in the Medim Rn Point of the class Math maniplating an eqation algebraically maniplating graphs Model bilding Using previos models to develop insight Economic concepts

More information

Multiple Regression Analysis

Multiple Regression Analysis Extesio of Bi-variate Statistics Y~ radom variables where ~ vectors of radom variables [ ] Y ~ a sigle radom variable c Pogsa Porchaiwisesul Faculty of Ecoomics ultiple Regressio Aalysis Focus o the depedecy

More information

Reliability Investigation of Series-Parallel and Components of Power System using Interval Type-2 Fuzzy Set Theory

Reliability Investigation of Series-Parallel and Components of Power System using Interval Type-2 Fuzzy Set Theory Iteratoal Joural of Iovatve Research Scece, Egeerg ad Techology (A ISO 3297: 2007 Certfed Orgazato) Relablty Ivestgato of Seres-Parallel ad Compoets of Power System usg Iterval Type-2 Fuzzy Set Theory

More information

Chapter 3. 2. Consider an economy described by the following equations: Y = 5,000 G = 1,000

Chapter 3. 2. Consider an economy described by the following equations: Y = 5,000 G = 1,000 Chapter C evel Qestions. Imagine that the prodction of fishing lres is governed by the prodction fnction: y.7 where y represents the nmber of lres created per hor and represents the nmber of workers employed

More information

Knauf, Rainer; Sakurai, Yoshitaka; Tsuruta, Setsuo ; Takada, Kouhei; Dohi, Shinichi

Knauf, Rainer; Sakurai, Yoshitaka; Tsuruta, Setsuo ; Takada, Kouhei; Dohi, Shinichi Kauf, Raer; Sakura, Yoshtaka; Tsuruta, Setsuo ; Takada, Kouhe; Doh, Shch Persoalzed currculum composto by learer profle drve data mg Zuerst erschee : IEEE Iteratoal Coferece o Systems, Ma ad Cyberetcs

More information

On Error Detection with Block Codes

On Error Detection with Block Codes BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 9, No 3 Sofa 2009 O Error Detecto wth Block Codes Rostza Doduekova Chalmers Uversty of Techology ad the Uversty of Gotheburg,

More information

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics

More information

Measuring the Quality of Credit Scoring Models

Measuring the Quality of Credit Scoring Models Measur the Qualty of Credt cor Models Mart Řezáč Dept. of Matheatcs ad tatstcs, Faculty of cece, Masaryk Uversty CCC XI, Edurh Auust 009 Cotet. Itroducto 3. Good/ad clet defto 4 3. Measur the qualty 6

More information

Puck Possession Report

Puck Possession Report - -- : at Umeå Arena Group No. Game No. -- :: - - (-, -, -) Start time: End time: : : Ended st period Possession By :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. : :. :

More information

Gas Behavior - Chapter 11. Behavior of Gases. Importance of Gases. The States of Matter. General Properties of Gases

Gas Behavior - Chapter 11. Behavior of Gases. Importance of Gases. The States of Matter. General Properties of Gases Pae Behavior of Gases Chapter Gases and Their Properties Jeffrey ack California State University, Sacramento Importance of Gases Hot Air Balloons How Do They Work? Airbas fill with N as in an accident

More information

Lecture 9: Heteroskedasticity and Robust Estimators

Lecture 9: Heteroskedasticity and Robust Estimators Takashi Yamao Fall Semester 9 Lectre Notes o Advaced coometrics Lectre 9: Heteroskedasticity ad Robst stimators I this lectre, we stdy heteroskedasticity ad how to deal with it Remember that we did ot

More information

Clase 4: Detector de Clases Multiples

Clase 4: Detector de Clases Multiples Aprededo y reooedo ategoras de objetos Clase 4: Detetor de Clases Multples Jua Wahs Computer ee Departmet & MOVE Isttute Naal Postgraduate hool Moterey CA Courtesy o Atoo Torralba Aprededo y reooedo ategoras

More information

Bonds with Embedded Options and Options on Bonds

Bonds with Embedded Options and Options on Bonds FIXED-INCOME SECURITIES Chapter 14 Bonds with Embedded Options and Options on Bonds Callable and Ptable Bonds Instittional Aspects Valation Convertible Bonds Instittional Aspects Valation Options on Bonds

More information

Chapter 3 3-1. Chapter Goals. Summary Measures. Chapter Topics. Measures of Center and Location. Notation Conventions

Chapter 3 3-1. Chapter Goals. Summary Measures. Chapter Topics. Measures of Center and Location. Notation Conventions Chapter 3 3- Chapter Goals Chapter 3 umercal Descrptve Measures After completg ths chapter, you should be able to: Compute ad terpret the mea, meda, ad mode for a set of data Fd the rage, varace, ad stadard

More information

THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE

THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE JAVIER CILLERUELO Abstract. We obtai, for ay irreducible quadratic olyomial f(x = ax 2 + bx + c, the asymtotic estimate log l.c.m. {f(1,..., f(} log. Whe

More information

Overview. Eingebettete Systeme. Model of periodic tasks. Model of periodic tasks. Echtzeitverhalten und Betriebssysteme

Overview. Eingebettete Systeme. Model of periodic tasks. Model of periodic tasks. Echtzeitverhalten und Betriebssysteme Overvew Egebettete Systeme able of some kow preemptve schedulg algorthms for perodc tasks: Echtzetverhalte ud Betrebssysteme 5. Perodsche asks statc prorty dyamc prorty Deadle equals perod Deadle smaller

More information

10.5 Future Value and Present Value of a General Annuity Due

10.5 Future Value and Present Value of a General Annuity Due Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the

More information

Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study. Normal and t Distributions. Density Plot. Normal Distributions Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

More information

(I) NSC E

(I) NSC E (I) NSC9-3--8-07- 9 08 0 9 07 3 9 0 7 (I) A Iterval Arthmetc Approach or WA based uzzy MCDM Model ad Its Applcato to Mauacturg Capablty valuato (I) * -mal: mrchu@mal.stut.edu.tw Abstract 9/08/0~9/07/3

More information

Building Trust How Banks are Attracting and Retaining Business Clients With Institutional Money Fund Portals

Building Trust How Banks are Attracting and Retaining Business Clients With Institutional Money Fund Portals Bilding Trst How Banks are Attracting and Retaining Bsiness Clients With Instittional Money Fnd Portals By George Hagerman, Fonder and CEO, CacheMatrix Holdings, LLC C ompetitive pressres are driving innovation

More information

Maintenance Scheduling of Distribution System with Optimal Economy and Reliability

Maintenance Scheduling of Distribution System with Optimal Economy and Reliability Egeerg, 203, 5, 4-8 http://dx.do.org/0.4236/eg.203.59b003 Publshed Ole September 203 (http://www.scrp.org/joural/eg) Mateace Schedulg of Dstrbuto System wth Optmal Ecoomy ad Relablty Syua Hog, Hafeg L,

More information

Searching Algorithm Efficiencies

Searching Algorithm Efficiencies Efficiecy of Liear Search Searchig Algorithm Efficiecies Havig implemeted the liear search algorithm, how would you measure its efficiecy? A useful measure (or metric) should be geeral, applicable to ay

More information

when n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on.

when n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on. Geometric eries Before we defie what is meat by a series, we eed to itroduce a related topic, that of sequeces. Formally, a sequece is a fuctio that computes a ordered list. uppose that o day 1, you have

More information

CHAPTER 2. Time Value of Money 6-1

CHAPTER 2. Time Value of Money 6-1 CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show

More information

Candidate: Suzanne Maxwell. Date: 09/19/2012

Candidate: Suzanne Maxwell. Date: 09/19/2012 Medical Coder / Billing Clerk Assessment Report Szanne Maxwell 09/19/2012 www.resorceassociates.com Szanne Maxwell 09/19/2012 Prepared For: NAME Prepared by: John Lonsbry, Ph.D. & Lcy Gibson, Ph.D., Licensed

More information

Load and Resistance Factor Design (LRFD)

Load and Resistance Factor Design (LRFD) 53:134 Structural Desg II Load ad Resstace Factor Desg (LRFD) Specfcatos ad Buldg Codes: Structural steel desg of buldgs the US s prcpally based o the specfcatos of the Amerca Isttute of Steel Costructo

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Section 7.2 Confidence Interval for a Proportion

Section 7.2 Confidence Interval for a Proportion Sectio 7.2 Cofidece Iterval for a Proportio Before ay ifereces ca be made about a proportio, certai coditios must be satisfied: 1. The sample must be a SRS from the populatio of iterest. 2. The populatio

More information

Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =

Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R = Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are

More information

OPTIMAL KNOWLEDGE FLOW ON THE INTERNET

OPTIMAL KNOWLEDGE FLOW ON THE INTERNET İstabul Tcaret Üverstes Fe Blmler Dergs Yıl: 5 Sayı:0 Güz 006/ s. - OPTIMAL KNOWLEDGE FLOW ON THE INTERNET Bura ORDİN *, Urfat NURİYEV ** ABSTRACT The flow roblem ad the mmum sag tree roblem are both fudametal

More information

Preparing your heavy vehicle for brake test

Preparing your heavy vehicle for brake test GUIDE Preparing yor heavy vehicle for brake test A best practice gide Saving lives, safer roads, ctting crime, protecting the environment Breaking the braking myth Some people believe that a locked wheel

More information

A New Bayesian Network Method for Computing Bottom Event's Structural Importance Degree using Jointree

A New Bayesian Network Method for Computing Bottom Event's Structural Importance Degree using Jointree , pp.277-288 http://dx.do.org/10.14257/juesst.2015.8.1.25 A New Bayesa Network Method for Computg Bottom Evet's Structural Importace Degree usg Jotree Wag Yao ad Su Q School of Aeroautcs, Northwester Polytechcal

More information

Using Phase Swapping to Solve Load Phase Balancing by ADSCHNN in LV Distribution Network

Using Phase Swapping to Solve Load Phase Balancing by ADSCHNN in LV Distribution Network Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204), pp.-4 http://dx.do.org/0.4257/jca.204.7.7.0 Usg Phase Swappg to Solve Load Phase Balacg by ADSCHNN LV Dstrbuto Network Chu-guo Fe ad Ru Wag College

More information

A Fast Algorithm for Computing the Deceptive Degree of an Objective Function

A Fast Algorithm for Computing the Deceptive Degree of an Objective Function IJCSNS Iteratoal Joural of Computer See ad Networ Seurty, VOL6 No3B, Marh 6 A Fast Algorthm for Computg the Deeptve Degree of a Objetve Futo LI Yu-qag Eletro Tehque Isttute, Zhegzhou Iformato Egeerg Uversty,

More information

Session 4: Descriptive statistics and exporting Stata results

Session 4: Descriptive statistics and exporting Stata results Itrduct t Stata Jrd Muñz (UAB) Sess 4: Descrptve statstcs ad exprtg Stata results I ths sess we are gg t wrk wth descrptve statstcs Stata. Frst, we preset a shrt trduct t the very basc statstcal ctets

More information

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity) Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of

More information

START Selected Topics in Assurance

START Selected Topics in Assurance SAR Selected opcs Assurace Related echologes able of Cotets Itroducto Relablty of Seres Systems of Idetcal ad Idepedet Compoets Numercal Examples he Case of Dfferet Compoet Relabltes Relablty of Parallel

More information

CSSE463: Image Recognition Day 27

CSSE463: Image Recognition Day 27 CSSE463: Image Recogto Da 27 Ths week Toda: Alcatos of PCA Suda ght: roject las ad relm work due Questos? Prcal Comoets Aalss weght grth c ( )( ) ( )( ( )( ) ) heght sze Gve a set of samles, fd the drecto(s)

More information

Projection model for Computer Network Security Evaluation with interval-valued intuitionistic fuzzy information. Qingxiang Li

Projection model for Computer Network Security Evaluation with interval-valued intuitionistic fuzzy information. Qingxiang Li Iteratoal Joural of Scece Vol No7 05 ISSN: 83-4890 Proecto model for Computer Network Securty Evaluato wth terval-valued tutostc fuzzy formato Qgxag L School of Software Egeerg Chogqg Uversty of rts ad

More information

Dynamic Service and Data Migration in the Clouds

Dynamic Service and Data Migration in the Clouds 2009 33rd Aual IEEE Iteratoal Computer Software ad Applcatos Coferece Dyamc Servce ad Data Mgrato the Clouds We Hao Departmet of Computer Scece Norther Ketucky Uversty haow1@ku.edu Abstract Cloud computg

More information

CH. V ME256 STATICS Center of Gravity, Centroid, and Moment of Inertia CENTER OF GRAVITY AND CENTROID

CH. V ME256 STATICS Center of Gravity, Centroid, and Moment of Inertia CENTER OF GRAVITY AND CENTROID CH. ME56 STTICS Ceter of Gravt, Cetrod, ad Momet of Ierta CENTE OF GITY ND CENTOID 5. CENTE OF GITY ND CENTE OF MSS FO SYSTEM OF PTICES Ceter of Gravt. The ceter of gravt G s a pot whch locates the resultat

More information