Appendix H: Miscellaneous

See Figures H.1-H.4.

т£°*^Ен-³

~^Nor* gallery.

H.l Function Fuzzy Approximation 1

The function to approximate is: f (x) =sin(x).*cos(3*x)

The input domain is [-%pi %pi], the output domain is [-1 1] Press ENTER to start.

-->

The end See Figure H.5.

FIGURE H.5

Function fuzzy approximation 1.

H.2 Function Fuzzy Approximation 2

The function to approximate is:

f(X)=sin(X(:,1) . *COS(3*X( : , 1)

The input domain is [-%pi %pi]x[-%pi %pi], the output domain is [-1 1]

Press ENTER to start.

-->

The end

See Figures H.6-H.13.

-ssrs—

FIGURE H.7

FIS imported.

FIGURE H.8

Normalized PID.

FIGURE H.9

Box and Jenkins fuzzy approximation.

FIGURE H.10

Scicos 1.

FIGURE H.11

Scicos 2.

FIGURE H.12

C - means example.

FIGURE H.13

Subtractive clustering.

Index

Note: Bold page numbers refer to tables and italic page numbers refer to figures.

adaptive networkbased fuzzy inference system (ANIFS) 87

additive white Gaussian noise (AWGN) 86,87

air quality (AIR) 71 ambiguity 21-23 ambiguous logic systems 94 ambiguous mathematics 94 analysis of means (ANOM) 118 analysis of variance (ANOVA) 118 Andriantiatsaholiniaina, Luc A. 64, 66 ANIFS see adaptive networkbased fuzzy inference system (ANIFS)

application-specific integrated circuit (ASIC) 92

ARMA method see autoregressive moving-average (ARMA) method

AR method see autoregression (AR) method

artificial intelligence method 118 ASIC see application-specific integrated circuit (ASIC) association rule mining 53 asynchronous transmission system 91 Atanassov, Krassimir 111 ATM networks see automated teller machine (ATM) networks automated teller machine (ATM) networks 91

Connection Ticket Leasing in 92 connection ticket rental for 90-94 CAC visualization boundaries and results 93-94 extraction of knowledge for CAC 91-92

survey-based CAC using type 2 FLS 91

survey process 92-93

spirits parameters in 92 autoregression (AR) method 37 autoregressive integrated moving average (ARIMA) 38 model 51-52

autoregressive moving-average (ARMA) method 38

AWGN see additive white Gaussian noise (AWGN)

back-propagation (the steepest descent) method 49-50

Bayesian decision feedback equalizer (DFE) 86

Bayesian equalizer 86 bisecting defuzzifier 48 Boolean algebra 99 Boolean logic operations 18

CAC see connection admission control (CAC) camera parameters 78 camera's field of view (FoV) 77 CCA see cooling with cold compressed air (CCA)

CCI see co-channel interference (CCI) center type reduction algorithm 59 centroid defuzzifier 48 centroid method 107 CFs, elimination of 117 channel state 86-87 CL see cryogenic cooling (CL) classical logic, laws of 1 classic fuzzy approaches, Zadeh's and Mamdani 83

classic time series forecasting method 37

autoregression method 37 autoregressive integrated moving average 38

classic time series forecasting method (Cont.)

autoregressive moving-average method 38

Holt-Winter's Exponential Smoothing method 40 moving-average method 37-38 seasonal autoregressive integrated moving-average with exogenous regressors 39 seasonal autoregressive integrated moving stereotype 38 simple exponential smoothing method 40

vector autoregression method 39 vector autoregression moving- average with exogenous regressors 39-40 vector autoregressive moving- average method 39 clear logic 1

CNFF see compensatory neuro-fuzzy filter (CNFF)

co-channel interference (CCI) 86,87 Liaison system with ISI and 89-90 compensatory neuro-fuzzy filter (CNFF) 87

computation 105-107 computational complexity of type reduction algorithm 59-60 Computing With Words (CWW) 5,9 connection admission control (CAC) 90 extraction of knowledge for 91-92 model 92

survey-based CAC using type 2 FLS 91

visualization boundaries and results 93-94

Connection Ticket Leasing 90,92 in ATM networks 92 connection ticket rental for ATM networks 90-94

CAC visualization boundaries and results 93-94

extraction of knowledge for CAC 91-92

survey-based CAC using type 2 FLS 91

survey process 92-93 control system (CS) 51 cooling with cold compressed air (CCA) 117

crisp sets 9,12

vs. fuzzy sets 109,109 from fuzzy sets to 10-11 set-theoretic operations on 13 cryogenic cooling (CL) 117 CS see control system (CS)

CWW see Computing With Words (CWW)

data dredging 41 data fishing 41

data mining (DM) 40,52-54, 75 data processing sequence 65 data snooping 41 data transformation 42 DCR see digital cellular radio (DCR)

decision feedback equalizer (DFE), Bayesian 86 decision-making 9 sustainable 67

defuzzification 10-11,47-48,107 defuzzifier 8,47,48,49, 59,102 bisecting 48 centroid 48

largest of maximum 48 midpoint of maximum 48 smallest maximum 49 weighted average 48 design parameters, optimization of rule 83

digital cellular radio (DCR) 86

digital signal processor (DSP) 93

dogberryism 24

dry machining 117

DSP see digital signal processor (DSP)

Dumbo rule 60,61

ecological footprint 66 ecological sustainability (ECOS) 64, 69,71

economic growth 63 ECOS see ecological sustainability (ECOS)

EKM algorithm see enhanced

Karnik-Mendel (EKM) algorithm

energy sustainability, sustainability by fuzzy assessment (SAFE) for 71 enhanced Karnik-Mendel (EKM) algorithm 56,57

environmental sustainability tabulate (ESI) 66

environments, healthy ecosystems and 72

epistemic uncertainty 21 equalization of time-varying nonlinear digital contacts 86-89 FAF design 87-88 Liaison system with ISI and CCI 89-90

preparation for equalization of water supply 86-87

simulation and conclusion 88-89 type 2 FAFs 87 equalizers 86 Bayesian 86, 88

fuzzy adaptive filter (FAF)-based water 87

linear fractional spacing equalizers (FSE) 86 nonlinear 86

vector constant state 86-87 ESI see environmental sustainability tabulate (ESI)

Euclidean distance 112,114 normalized 112

sample selection 112-113,113,114 EUT see Expected Utility Theory (EUT) exogenous regression variables, SARIMAX using 39 exogenous variables 39 Expected Utility Theory (EUT) 6

FCSs see fuzzy control systems (FCSs) field programmable gate array (FPGA) 92,93

filters, neurofuzzy 50

FIS see fuzzy inference system (FIS)

FIZ see fuzzy inference engine (FIZ)

FL see fuzzy logic (FL)

FLC see fuzzy logic control (FLC)

FLS see fuzzy logic system (FLS) footprint, ecological 66 footprint of uncertainty (FOU) 75,

102,103 on function 78 for IV FS 79

for measurement 79-80 Type 2 fuzzy set and increasing example of 28 forecasting 33

FOU see footprint of uncertainty (FOU) FPGA see field programmable gate array (FPGA)

fractional spacing equalizers (FSE), linear 86 Freilberger 4

function fuzzy approximation 1177, 178-182

function fuzzy approximation 2 177, 183-189

fuzzification 17,29

and effect on reasoning 46-47 fuzzification module 118 fuzzification operations 11 fuzzifier 47

fuzziness, permissiveness of 12 fuzzy adaptive filter (FAF) 87 based water equalizer 87 design 87-88 fuzzy assessment 67-68 fuzzy control systems (FCSs) 51 fuzzy events, higher-order 77 fuzzy expert system (ES) 89 fuzzy inference engine (FIZ) 46 fuzzy inference models 16 fuzzy inference system (FIS) 4,45 hierarchical 66 fuzzy logic (FL) 1-3,67,118 algorithm 8 computation 9 concept of 18 coverage 7-8

medical diagnosis by 109-114 multiple criteria and 66 process of 8

RBC's parameters 80-81 RBC test 83 techniques 4

fuzzy logic (FL) (Cent)

T-norm 98 traditional 50

fuzzy logic control (FLC) 17 fuzzy logic primer 16-17 crisp logic 17

from crisp logic to FL 17-18 fuzzy logic system (FLS) 45,49,58, 75 back-propagation (the steepest descent) method 49-50 flow of uncertainties 4-6 fundamental diamond requirement 4 new concepts and historical background 3-4 new direction for 2-3 optimized 117-160,119 problem with the use of FLS 76 repetitive diamond method 51 rule-based 1-2

applicability outside of 8-9 SVD-QR method 50-51 type 1101

uncertainty at 22-23 Fuzzy Logic Toolbox 26 fuzzy neural network (NN) 3 fuzzy probability theory 76-77 fuzzy production rule 81 fuzzy reasoning system (FIS) 58,89 fuzzy rules 45-46,50,105-106 fuzzy set (FS) 3,45, 78,101,109 concept of 21

type 2 fuzzy set 27 vs. crisp sets 109,109 definition of 109-110 elements 17

interval type 2 center of 58 intervalued 110 intuitionistic 110-113 with linguistic values 68 membership features of 18 membership function 29 normal 110 primer on 9-16

crisp relations and compositions 14 expansion principle 16 from fuzzy sets to crisp sets 10-11 hedges 15-16

linguistic variables 11-12 membership functions 12 relations and compositions 14-15

set-theoretic operations for fuzzy sets 13

set-theoretic operations on crisp sets 13

terminology 13 set-theoretic operations for 13 subnormal 110 of type 2 110 type 2 fuzzy sets 6-7 type 2 fuzzy sets and related concepts 27-28

type 1 membership function for 27-29

fuzzy set-based approach 16 fuzzy set theory 10,12, 75,101 fuzzy system 3,36, 50, 51, 76,77, 80, 83, 84,118

components 118 IEEE transactions on 3 fuzzy techniques 12 fuzzy theory 5 fuzzy values 17,105-106

GA see genetic algorithms (GA) generalization center, for interval type 2 fuzzy set 57

general type 2 fuzzy sets (GT2FSs) 97

genetic algorithms (GA) 83 global warming 63 GOOD, membership features of 18 GPUs see graphics processing units (GPUs) graduality 21, 22 graphical user interface (GUI) environment 4

graphics processing units (GPUs) 92 green manufacturing 117 GT2FSs see general type 2 fuzzy sets (GT2FSs)

Hamlet, Zadeh 1

HaT2-FLS see hedge trigonometric type 2 fuzzy logic system (HaT2-FLS)

HaT2FS see type 2 fuzzy set-hedging

trigonometry type 2 fuzzy set (HaT2FS)

healthy ecosystems and environments 72

heart disease demo 161-162,162-163 hedge trigonometric type 2 fuzzy logic system (HaT2-FLS) 81 height type reduction algorithm 59 heteromorphs 23

hierarchical fuzzy inference system 66 higher membership function (UMF) 28-29

higher-order fuzzy events 77 high-frequency (HF) radar systems 93 high-pressure cooling (HPC) 117 Holt-Winter's Exponential Smoothing (HWES) method 40 homograph 23-24 homophones 23

HPC see high-pressure cooling (HPC) human-level components, of sustainability 64

human sustainability (HUMS) 69,71 human visual system 101 HWES method see Holt-Winter's Exponential Smoothing (HWES) method

IASCO see iterative algorithm with stop conditions (IASCO)

IFS see intuitionistic fuzzy sets (IFS) "IF-THEN" rules 13, 64, 66 ILC see iterative learning control (ILC) Indicator PR (BIOD) 65 International Union for the

Conservation of Nature (IUCN) 63, 66

inter-symbol interference (ISI) 86 Liaison system with ISI and CCI 89-90

Interval Tide Way 79 interval type 2 fuzzy logic system (IT2 FLS) 56,75

interval type 2 fuzzy set (IT2 FS)

58,97

generalization center for 57 interval type 2 symbolic logic systems (IT2 FLS) 97

intervalued fuzzy sets 110 intuitionistic fuzzy sets (IFS) 110-113 ISDN 90

ISI see inter-symbol interference (ISI) iterative algorithm with stop conditions (IASCO) 57

iterative learning control (ILC) 51 IT2 FLS see interval type 2 fuzzy logic system (IT2 FLS)

IT2 TSK approach 61

IUCN see International Union for the

Conservation of Nature (IUCN)

join, lattice-theoretic concept 99

Karnik-Mendel (KM) algorithm 56, 78-79

KDD see knowledge discovery in databases (KDD)

Keefe, Rosanna 22 Klaua, Dieter 110 knowledge-based systems 81 knowledge discovery in databases (KDD) 40,41 knowledge mining 40 methodology 42-42 using surveys 40-41 Kosko 4

Kouikoglou, Vassilis S. 66 Kouloumpis, Viktor D. 64,66 Kukrin 93 Kwakernaak, H. 76

Langari, Reza 4 lattice-theoretic concept 99 join 99 meet 99 negation 99 laws of classical logic 1 Liaison system with ISI and CCI 89-90

linear fractional spacing equalizers (FSE)86

linear tip demo 166,167 linguistic variables 11-12 Liu, Xinwang 56-57,66 LMF see lower membership function (LMF)

logic systems, rule-based fuzzy 1-2

lower membership function (LMF) 28-29

lower MF (LMF) 78-80 Lukasiewicz 12

machine learning methods 37 Mamdani's classic fuzzy approaches 83 Mamdani fuzzy inference system

(SMFI) simulation module 89 Mamdani tip demo 165,167,168-170 MA method see moving-average (MA) method MATLAB 4

MCDM see multi-criteria decisionmaking (MCDM)

McNeill 4

medical diagnosis by fuzzy logic 109-114

meet, lattice-theoretic concept 99 member function (MF) 55 membership function (MF) 12,25, 78, 110

back to the language label 29 fuzzy set 29

type 1 membership function for 27-29 types 110

and uncertainty 25-30 membership probability density function (Mpdf) 77 Mendel, Jerry M. 55-59, 80 MF see membership function (MF) midpoint of maximum defuzzifier 48 minimum quantity lubrication (MQL) 117

minimum quantity lubrication and cooling (MQLC) 117 mining 75

association rule 53 data 40, 52-54,75 mining, knowledge methodology 42-42 using surveys 40-41 moving-average (MA) method 34,37-38 moving stereotype (MA) models 38 Mpdf see membership probability density function (Mpdf)

MQL see minimum quantity lubrication (MQL)

MQLC see minimum quantity

lubrication and cooling (MQLC)

multi-criteria decision-making (MCDM) 66

multiple criteria and fuzzy logic 66 multi-strategy methodology 41 multivariate time series 39

near-dry machining (NDM) 117 neural networks (NNs) 2 fuzzy 3 RBF87

self-learning skills of 94 neurofuzzy filters 50 NNs see neural networks (NNs) 2 nonlinear equalizers non-singleton fuzzy logic system (NSFLS)

normal fuzzy sets 110 NSFLS see non-singleton fuzzy logic system (NSFLS) 45

optimization of rule design parameters 83 Organization for Economic Cooperation 65, 66 overall sustainability (OSUS)

64, 69-71

ozone depletion, stratospheric 63

particle cluster optimization (PSO) 83 Phased Mission System (PMS) 18-19 Phillis, Yannis A. 64,66 power-spectrum-based neuralnet CAC (PNCAC) method 94 pressure state response (PSR) 66

qualitative prediction techniques 33 quality of service (QoS) 90 quantitative forecasting methods 33 quantitative research 31

radar 93

radial basis function (RBF) 87 neural networks 87 random fluctuations, in time series 34 RBC's parameters, FL 80-81 RBC test, FL 83

RBF see radial basis function (RBF) recurrent multilayer perceptron (RMLP) 50

repetitive diamond method 51 representation theorem (RT), of type 2 fuzzy set (T2 FS) 56 research methodology 111 RMLP see recurrent multilayer perceptron (RMLP) rule-based fuzzy logic systems 1-2 applicability outside of 8-9 rule-based nomenclature for video traffic 77-86 calculation formula

for type 1 FL RBC 81-82 for type 2 FL RBC 82-83 FL RBC's parameters 80-81 FL RBC test 83 FOU for measurement 79-80 FOU on function 78 optimization of rule design parameters 83

results and conclusions 84-86 rules 78-79

selected function 77-78 rule evaluation results 106 rule mining, association 53

SAFE see sustainability by fuzzy assessment (SAFE) sample research methods 31 accumulative method 32 advantages 32-33 disadvantages 33 exploratory 32 illustrative 31 key cases 32

SARIMA see seasonal autoregressive integrated moving stereotype (SARIMA)

seasonal autoregressive integrated moving-average with exogenous regressors (SARIMAX) 39 using exogenous regression variables 39

seasonal autoregressive integrated moving stereotype (SARIMA) 38

self-learning skills, of neural networks 94

sensitivity analysis 69-70 sensitivity test 69 sensitivity wringer 69 SES method see simple exponential smoothing (SES) method set center type reduction algorithm 59 set-theoretic operations on crisp sets 13 for fuzzy sets 13

SFLS see singleton fuzzy logic system (SFLS)

sharp set elements 17 signal-to-interference-noise-ratio (SINR) signal-to-noise (S/N) ratio 118 simple exponential smoothing (SES) method 40

singleton fuzzy logic system (SFLS) 45 singular value decomposition (SVD) 51 SINR see signal-to-interference-noise- ratio (SINR)

smallest maximum defuzzifier 49 Smith 22

smoothing method (stable series) 34 social environmental systems, dynamics of 67

soil quality (LAND) 71 sparse rule 60 spirits parameters, in ATM networks 92

SSI see sustainable society table (SSI) stratospheric ozone depletion 63 subnormal fuzzy sets 110 sugeno tip demo 167,171-173, 173-175 support vector machine (SVM) 83 surveillance system, video-based 77 survey-based CAC using type 2 FLS 91 surveys, knowledge mining using 40-41

sustainability 63-64 defined 72

ecological sustainability 64 human-level components of 64 indicator of 66 measurement 65-67 modeling of 63-72 overall sustainability (OSUS) 64 SAFE model 64-65

sustainability by fuzzy assessment (SAFE) 64

for energy sustainability 71 model 64-65, 69, 70

advantages and disadvantages 70-71

sustainable decision-making 67 sustainable development key indicators of 65 strategy 117

sustainable society table (SSI) 67 SVD see singular value decomposition (SVD)

SVD-QR method 50-51

SVM see support vector machine (SVM)

Taguchi method 118 Takagi-Sugeno fuzzy nomenclature system (T-S FCS) 83 T2 FLS theory 56 T2 FS see type 2 fuzzy set (T2 FS) Thomson-CSF communications 89 time series

components of 34 method 33 multivariate 39 random fluctuations in 34 time series prediction (TSP) 33-36,

75,76

classic time series forecasting method 37

autoregression method 37 autoregressive integrated moving average 38

autoregressive moving-average method 38

vector autoregression method 39

vector autoregression moving- average with exogenous regressors 39-40 vector autoregressive moving- average method 39 extracting rules from data 36-37 sample study 51-52 T-norm fuzzy logics 98 trace theory 5 traditional fuzzy logic 50 traditional IT2 TSK approach 61 transmission system, asynchronous 91 T-S FCS see Takagi-Sugeno fuzzy

nomenclature system (T-S FCS) TSP see time series prediction (TSP) type 1 FL RBC, calculation formula for 81-82

type 2 FL RBC, calculation formula for 82-83 type 2 FLS

application for 76-77 survey-based CAC using 91 vs. type 1 fuzzy logic system (T1 FLS) 75

type 2 fuzzy adaptive filter (FAF)-based water equalizer 87 type 1 fuzzy logic system (T1 FLS)

75,101

vs. type 2 FLS 75 type 1 fuzzy set (T1 FS) 101-102 type 2 fuzzy set (T2 FS) 55-56,75,80, 102-103 concept of 27 deepening of 58 existing literature on 6-7 and increasing example of FOU 28 non-repetitive type reduction of 56 and related concepts 27-28 representation theorem (RT) of 56 type 1 purge set represented by 29 0 and 1 membership of 29 type 2 fuzzy set-hedging trigonometry type 2 fuzzy set (HaT2FS) 81 type 1 membership function, for fuzzy set 27-29

type reduction algorithm 58-59 center type reduction 59

computational complexity of type reduction 59-60 height type reduction 59 set center type reduction 59

uncertainty 21-22 epistemic 21 at FLS 22-23

membership function and 25-30 unspecified consequences for center 7 upper MF (LMF) 78-80

VC see virtual channel (VC) vector autoregression (VAR) method 39 vector autoregression moving-average with exogenous regressors (VARMAX) 39-40

vector autoregressive moving-average (VARMA) method 39 video-based surveillance systems 77 video traffic, rule-based nomenclature for 77-86

calculation formula

for type 1 FL RBC 81-82 for type 2 FL RBC 82-83 FL RBC's parameters 80-81 FL RBC test 83 FOU for measurement 79-80

FOU on function 78 optimization of rule design parameters 83

results and conclusions 84-86 rules 78-79

selected function 77-78 virtual channel (VC) 91 virtual path identifiers (VPIs) 91 visualization-making problems 9 VPIs see virtual path identifiers (VPIs)

Wang, Liang 4 warming, global 63 water supply, preparation for equalization of 86-87 weighted average defuzzifier 48 Widrow's least-medium-squares (LMS) algorithm 50

Yen, John 4

Zadeh, Lotfi Asker 3,12,15-18,

22, 23,28, 75, 77,97,101,
102,110

classic fuzzy approaches 83 extension principle 7 rule 16

zmf function 26