Insert a membership function.

Description

Adds a membership function to a variable of a fis object.

Usage

addmf(fis, varType, varIndex, mfName, mfType, mfParams)

Arguments

Value

A fis structure with the new membership function added.

Examples

fis <- newfis('tipper')
fis <- addvar(fis, 'input', 'service', c(0, 10))
fis <- addmf(fis, 'input', 1, 'poor', 'gaussmf', c(1.5, 0))

Inserts a rule

Description

Adds a rule to a fis object.

Usage

addrule(fis, ruleList)

Arguments

Details

For example, if one has a fis with 2 input variables, and 1 output variable, each of which have 3 membership functions (the amount of membership functions need not be the same). The following rule: 1 3 2 1 2 will mean m = 2 (for 2 input variables), n = 1 (for 1 output variable), and the last 2 columns represent weight and fuzzy operator for the rule's antecedent respectively.

The first column refers to the first input variable's membership function at index 1.

The second column refers to the second input variable's membership function at index 3.

The third column refers to the first output variable's membership function at index 2.

The fourth column refers to the weight to be applied to the rule.

The fifth column refers to the fuzzy operator for the rule's antecedent (in this case it represents 'OR').

Value

A fis structure with the new rule added.

Examples

fis <- tipper()
ruleList <- rbind(c(1,1,1,1,2), c(2,0,2,1,1), c(3,2,3,1,2))
fis <- addrule(fis, ruleList)

Insert a variable

Description

Adds an input or output variable to a fis object.

Usage

addvar(
  fis,
  varType,
  varName,
  varBounds,
  method = NULL,
  params = NULL,
  firing.method = "tnorm.min.max"
)

Arguments

Value

A fis with the new variable added.

Examples

fis <- newfis('tipper')
fis <- addvar(fis, 'input', 'service', c(0, 10))
fis <- addvar(fis, 'input', 'service', c(0, 10), 'gauss', 0.5, 'tnorm.min.max')

The evaluator for nodes in Layer 1

Description

To evaluate the antecedent layer (L1) of anfis

Usage

anfis.L1.eval(anfis, output.LI, input.stack)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer 1

Author(s)

Chao Chen

The evaluator for nodes in Layer 2

Description

To evaluate the nodes in Layer 2 of the given ANFIS model

Usage

anfis.L2.eval(anfis, output.L1)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer 2

Author(s)

Chao Chen

L2.which

Description

To determin which output (w.lower, w.upper) to be used by the ekm algorithm

Usage

anfis.L2.which(anfis, output.L2, output.L4.mf)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

A list of matrix indicating which output (w.lower, w.upper) in layer 2 should be used by the ekm algorithm

Author(s)

Chao Chen

The evaluator for nodes in Layer 3

Description

To evaluate the nodes in Layer 3 of the given ANFIS model

Usage

anfis.L3.eval(anfis, output.L2, output.L2.which)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer 3

Author(s)

Chao Chen

The evaluator for nodes in Layer 4

Description

To evaluate the nodes in Layer 4

Usage

anfis.L4.eval(output.L3, output.L4.mf)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer 4

Author(s)

Chao Chen

The evaluator for membership functions of nodes in Layer 1

Description

To evaluate the membership functions of nodes in Layer 4

Usage

anfis.L4.mf.eval(anfis, input.stack)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The membership grades of the membership functions of nodes in Layer 4

Author(s)

Chao Chen

The evaluator for nodes in Layer 5

Description

To evaluate the nodes in Layer 5

Usage

anfis.L5.eval(output.L4)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer 5

Author(s)

Chao Chen

The evaluator for nodes in Layer I

Description

To evaluate the input Layer (LI) of anfis

Usage

anfis.LI.eval(anfis, input.stack)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning. See the source code of anfis.eval for usage.

Value

The output of nodes in Layer I

Author(s)

Chao Chen

ANFIS model builder

Description

To build an ANFIS model from an existing FIS model

Usage

anfis.builder(fis)

Arguments

Value

An ANFIS model

Author(s)

Chao Chen

References

[1] C. Chen, R. John, J. Twycross, and J. M. Garibaldi, “An extended ANFIS architecture and its learning properties for type-1 and interval type-2 models,” in Proceedings IEEE International Conference on Fuzzy Systems, 2016, pp. 602–609.
doi: 10.1109/FUZZ-IEEE.2016.7737742

[2] C. Chen, R. John, J. Twycross, and J. M. Garibaldi, “Type-1 and interval type-2 ANFIS: a comparison,” in Proceedings IEEE International Conference on Fuzzy Systems, 2017, pp. 1–6.
doi: 10.1109/FUZZ-IEEE.2017.8015555

Examples

fis <- anfis.tipper()
anfis <- anfis.builder(fis)

anfis.dE.dO1

Description

to calculate the derivatives of output error with respect to output.L1.

Usage

anfis.dE.dO1(anfis, output.L1, de.do2, do2.do1)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to output.L1.

Author(s)

Chao Chen

anfis.dE.dO2

Description

to calculate the derivatives of output error with respect to output.L2.

Usage

anfis.dE.dO2(de.do3, do3.do2)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to output.L2.

Author(s)

Chao Chen

anfis.dE.dO3

Description

to calculate the derivatives of output error with respect to output.L3.

Usage

anfis.dE.dO3(de.do4, do4.do3, output.L3)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to output.L3.

Author(s)

Chao Chen

anfis.dE.dO4

Description

to calculate the derivatives of output error with respect to output.L4.

Usage

anfis.dE.dO4(anfis, de.do5, do5.do4)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to output.L4.

Author(s)

Chao Chen

anfis.dE.dO5

Description

To calculate the derivatives of output error with respect to output.L5. NOTE: currently, only single output in L5 is supported

Usage

anfis.dE.dO5(output.L5, y)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to output.L5

Author(s)

Chao Chen

anfis.dE.dP1

Description

To calculate the derivatives of output error with respect to parameters in Layer 1.

Usage

anfis.dE.dP1(anfis, de.do1, input.stack)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to parameters in Layer 1.

Author(s)

Chao Chen

anfis.dE.dP1.gbellmf

Description

To calculate the derivatives of E versus mf.params.L1 for gbellmf: 1 / ( 1 + (((x - c)/a)^2)^b) NOTE: only singleton fuzzification is supported

Usage

anfis.dE.dP1.gbellmf(de.do1, x, mf.params)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Author(s)

Chao Chen

anfis.dE.dP1.it2gbellmf

Description

to calculate the derivatives of E versus mf.params.L1 for it2gbellmf NOTE: only singleton fuzzification is supported

Usage

anfis.dE.dP1.it2gbellmf(de.do1, x, mf.params)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Author(s)

Chao Chen

anfis.dE.dP4

Description

To calculate the derivatives of output error with respect to parameters in Layer 4.

Usage

anfis.dE.dP4(anfis, de.do4, output.L3, input.stack)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output error with respect to parameters in Layer 4.

Author(s)

Chao Chen

anfis.dMF.dP.gbellmf

Description

to calculate the derivatives of membership grades with respect to its parameters

Usage

anfis.dMF.dP.gbellmf(x, mf.params)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Author(s)

Chao Chen

anfis.dO2.dO1

Description

To calculate the derivatives of output.L2 with respect to output.L1.

Usage

anfis.dO2.dO1(anfis, output.L2, output.L1)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output.L2 with respect to output.L1. do2[j].do1[i] <- do2.do1[[i]][[which(fan.out==j)]]

Author(s)

Chao Chen

anfis.dO3.dO2

Description

To calculate the derivatives of output.L3 with respect to output.L2.

Usage

anfis.dO3.dO2(anfis, output.L2, output.L2.which)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output.L3 with respect to output.L2. do3.left[j].do2[i] <- do3.do2[[i]][[1]][[j]]

Author(s)

Chao Chen

anfis.dO4.dO3

Description

To calculate the derivatives of output.L4 with respect to output.L3.

Usage

anfis.dO4.dO3(output.L4, output.L4.mf)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output.L4 with respect to output.L3.

Author(s)

Chao Chen

anfis.dO5.dO4

Description

To calculate the derivatives of output.L5 with respect to output.L4. NOTE: currently, only single output in L5 is supported

Usage

anfis.dO5.dO4(output.L4)

Arguments

Details

This function is not recommended for external use, but can be used for debugging or learning.

Value

The derivatives of output.L5 with respect to output.L4.

Author(s)

Chao Chen

ANFIS evaluator

Description

To evaluate a ANFIS model with input data

Usage

anfis.eval(anfis, input.stack)

Arguments

Value

The output of the anfis for given input data.

Author(s)

Chao Chen

Examples

fis <- anfis.tipper()
anfis <- anfis.builder(fis)
data.num <- 5
input.num <- length(fis$input)
input.stack <- matrix(rnorm(data.num*input.num), ncol=input.num)
y <- matrix(rnorm(data.num))
data.trn <- cbind(input.stack, y)
anfis.eval(anfis, input.stack)

ANFIS optimiser

Description

To optimise the performance of a given ANFIS model by learning the parameters in L1 and L4.

Usage

anfis.optimise(
  anfis,
  data.trn,
  data.chk = NULL,
  epoch.total = 100,
  stepsize = 0.1,
  rate.inc = 1.1,
  rate.dec = 0.9,
  method = c("gradient", "lse"),
  err.log = F,
  online = 0,
  lambda = 1,
  opt.by = "err.opt",
  err.trn.fix = T
)

Arguments

Value

The optimised ANFIS model.

Author(s)

Chao Chen

References

[1] C. Chen, R. John, J. Twycross, and J. M. Garibaldi, “An extended ANFIS architecture and its learning properties for type-1 and interval type-2 models,” in Proceedings IEEE International Conference on Fuzzy Systems, 2016, pp. 602–609.
doi: 10.1109/FUZZ-IEEE.2016.7737742

[2] C. Chen, R. John, J. Twycross, and J. M. Garibaldi, “Type-1 and interval type-2 ANFIS: a comparison,” in Proceedings IEEE International Conference on Fuzzy Systems, 2017, pp. 1–6.
doi: 10.1109/FUZZ-IEEE.2017.8015555

Examples

fis <- anfis.tipper()
anfis <- anfis.builder(fis)
data.num <- 5
input.num <- length(fis$input)
input.stack <- matrix(rnorm(data.num*input.num), ncol=input.num)
y <- matrix(rnorm(data.num))
data.trn <- cbind(input.stack, y)
anfis.eval(anfis, input.stack)
anfis.final <- anfis.optimise(anfis, data.trn, epoch.total=500,
                                 stepsize=0.01, rate.inc=1.1, rate.dec=0.9)

Plot membership functions for an ANFIS object

Description

Plots a 2D graph of all membership functions from the specified variable which must be part of an anfis object.

Usage

anfis.plotmf(
  anfis,
  varType,
  varIndex,
  xx = NULL,
  timelimit = 0,
  xlab = NULL,
  ylab = NULL,
  main = NULL
)

Arguments

Value

A two dimensional graph displaying all the membership functions of a given variable.

Examples

fis <- anfis.tipper()
anfis <- anfis.builder(fis)
data.num <- 5
input.num <- length(fis$input)
input.stack <- matrix(rnorm(data.num*input.num), ncol=input.num)
y <- matrix(rnorm(data.num))
data.trn <- cbind(input.stack, y)
anfis.eval(anfis, input.stack)
anfis.final <- anfis.optimise(anfis, data.trn, epoch.total=500,
                                 stepsize=0.01, rate.inc=1.1, rate.dec=0.9)
anfis.plotmf(anfis, 'input', 1)
anfis.plotmf(anfis.final, 'input', 1)

Produces an example fis object which can be used for ANFIS.

Description

A function used primarily for example purposes, it creates a fis with two input (service & food), output variables (tip) and their membership functions.

Usage

anfis.tipper()

Value

A fis is return

Examples

fis <- anfis.tipper()

Plot firing strength with different inference method

Description

Plots a 2D graph of the firing strength for a antecedent produced by different inference method

Usage

cmp.firing(
  IP,
  mfType,
  mfPara,
  fuzMethod,
  fuzPara,
  SFLS = TRUE,
  STD = TRUE,
  CEN = FALSE,
  SIM = FALSE,
  step = 100,
  fisRange = NULL
)

Arguments

Value

A two dimensional graph displaying all the firing strength produced by given method.

Author(s)

Yu Zhao

Examples

cmp.firing(1, 'gaussmf', c(1, 2.5, 1), 'gbell', c(0.4, 2), step=100)

Convert a fis

Description

Convert a fis object from one type to another (e.g. from singleton to non-singleton)

Usage

convertfis(fis, option = "s2n", ...)

Arguments

Details

• fuzzification.method, fuzzification.params, firing.method - see addvar

Usage:

1. convertfis(fis, option, mf.params, fuzzification.method, fuzzification.params)

2. convertfis(fis, option, mf.params, fuzzification.method, fuzzification.params, firing.method)

Value

Membership grade(s)

Author(s)

Chao Chen

Examples

fis <- tipper()
fis.ns.1 <- convertfis(fis, option='s2n', fuzzification.method='gauss', fuzzification.params=1)
fis.ns.2 <- convertfis(fis, option='s2n', fuzzification.method='gauss', fuzzification.params=1,
                         firing.method='tnorm.min.max')

Defuzzify a set of values.

Description

Defuzzifies a given set of values using a specified range and defuzzification type producing a crisp value.

Usage

defuzz(x, mf, type)

Arguments

Value

Returns a defuzzified crisp value (double).

Examples

Crisp_value = defuzz(1:10, c(1.5, 5), "centroid")

Evaluate a Fuzzy Inference System (fis)

Description

Returns an evaluated crisp value for a given fis structure.

Usage

evalfis(input_stack, fis, time = 1, point_n = 101, draw = FALSE)

Arguments

Value

Returns a matrix of evaluated values.

Examples

Input_data <- matrix((1:2),1,2)
fis <- tipper()
evalfis(Input_data, fis)

Evaluate fuzzy membership function

Description

To obtain the corresponding membership grade(s) for given crsip input(s) x

Usage

evalmf(...)

Arguments

Details

• x - the crisp input(s) on the universe of discourse for corresponding antecedent membership function
  

• mf.type - The type of fuzzy membership function
  

• mf.params - The parameters for the given type of membership function
  

• mf - the membership function generated by genmf

• fuzzification.method, fuzzification.params, firing.method and input.range - see addvar

Usage:

1. evalmf(x, mf.type, mf.params)

2. evalmf(x, mf)

3. evalmf(x, mf.type, mf.params, fuzzification.method, fuzzification.params, firing.method, input.range)

4. evalmf(x, mf, fuzzification.method, fuzzification.params, firing.method, input.range )

Value

Membership grade(s)

Author(s)

Chao Chen

Examples

evalmf(5, mf.type=gbellmf, mf.params=c(1,2,3))
evalmf(1:10, mf.type=gbellmf, mf.params=c(1,2,3))
evalmf(1:10, mf.type=gbellmf, mf.params=c(1,2,3), fuzzification.method='gauss',
         fuzzification.params=1, firing.method='tnorm.min.max', input.range=c(0,10))

mf <- genmf('gbellmf', c(1,2,3))
evalmf(5, mf)
evalmf(1:10, mf)
evalmf(1:10, mf, fuzzification.method='gauss', fuzzification.params=1,
         firing.method='tnorm.min.max', input.range=c(0,10))

Evaluate fuzzy membership function with membership function type and parameters

Description

To obtain the corresponding membership grade(s) for crisp input(s) x

Usage

evalmftype(x, mf.type, mf.params)

Arguments

Value

Membership grade(s)

Author(s)

Chao Chen

Examples

evalmftype(5, mf.type=gbellmf, mf.params=c(1,2,3))
evalmftype(1:10, mf.type=gbellmf, mf.params=c(1,2,3))

TSK FIS builder

Description

To build a one-output TSK FIS by automatically generating the input membership functions and the fuzzy rules

Usage

fis.builder(
  x.range,
  input.num,
  input.mf.num,
  input.mf.type,
  rule.num = prod(input.mf.num),
  rule.which = NULL,
  defuzzMethod = "default",
  params.ante,
  params.conse
)

Arguments

Author(s)

Chao Chen

Fuzzy rule firing

Description

To get the firing strength for the given input fuzzification membership function and the antecedent membership function in the domain of [lower, upper]

Usage

fuzzy.firing(operator, x.mf, ante.mf, lower, upper)

Arguments

Value

the rule firing strenth

Author(s)

Chao Chen

Examples

x.mf <- x.fuzzification(gbell.fuzzification, 3, c(1,2))
ante.mf <- genmf(gbellmf, c(1,2,6))
firing.strength <- fuzzy.firing(min, x.mf, ante.mf, lower=0, upper=10)
firing.strength

Fuzzy optimisation

Description

to get an approximation of the maximum membership grade for a given membership function in the domain of [lower, upper]

Usage

fuzzy.optimise(fuzzy.mf, lower, upper)

Arguments

Value

an approximation of the maximum membership grade in the given domain

Author(s)

Chao Chen

Examples

mf <- genmf(gbellmf, c(1,2,3))
x <- seq(4, 5, by=0.01)
max(evalmf(x, mf))
fuzzy.optimise(mf, 4, 5)

Fuzzy t-norm/t-conorm operation

Description

To conduct t-norm or t-conorm operation for given fuzzy member functions

Usage

fuzzy.t(operator, ...)

Arguments

Value

A membership function, which is the t-norm/t-conorm of membership functions

Author(s)

Chao Chen

Examples

mf1 <- genmf(gbellmf, c(1,2,3))
mf2 <- genmf(gbellmf, c(4,5,6))
mf3 <- fuzzy.t(max, mf1, mf2)
tmp1 <- evalmf(1:10, mf1)
tmp2 <- evalmf(1:10, mf2)
tmp3 <- evalmf(1:10, mf3)
identical(tmp3, pmax(tmp1, tmp2))
tmp3

Fuzzy t-conorm

Description

To conduct t-conorm operation for given fuzzy member functions

Usage

fuzzy.tconorm(operator, ...)

Arguments

Value

A membership function, which is the t-conorm of membership functions

Author(s)

Chao Chen

Examples

mf1 <- genmf(gbellmf, c(1,2,3))
mf2 <- genmf(gbellmf, c(4,5,6))
mf3 <- fuzzy.tconorm(max, mf1, mf2)
tmp1 <- evalmf(1:10, mf1)
tmp2 <- evalmf(1:10, mf2)
tmp3 <- evalmf(1:10, mf3)
identical(tmp3, pmax(tmp1, tmp2))
tmp3

Fuzzy tnorm

Description

To conduct t-norm operation for given fuzzy member functions

Usage

fuzzy.tnorm(operator, ...)

Arguments

Value

A membership function, which is the t-norm of membership functions

Author(s)

Chao Chen

Examples

mf1 <- genmf(gbellmf, c(1,2,3))
mf2 <- genmf(gbellmf, c(4,5,6))
mf3 <- fuzzy.tnorm(prod, mf1, mf2)
tmp1 <- evalmf(1:10, mf1)
tmp2 <- evalmf(1:10, mf2)
tmp3 <- evalmf(1:10, mf3)
identical(tmp3, tmp1*tmp2)
tmp3

Fuzzy Accuracy

Description

This function is to provide performance indicators by using eight different accuracy measures including a new measure UMBRAE.

Usage

fuzzyr.accuracy(f, y, f.ref = 0, scale.mase = NULL)

Arguments

Value

A vector of results by each measure.

Author(s)

Chao Chen

References

[1] C. Chen, J. Twycross, and J. M. Garibaldi, “A new accuracy measure based on bounded relative error for time series forecasting,” PLOS ONE, vol. 12, no. 3, pp. 1–23, 2017.
doi: 10.1371/journal.pone.0174202

Examples

f <- rnorm(10)
y <- rnorm(10)
fuzzyr.accuracy(f, y)

fuzzyr.match.fun

Description

This is a modification of the original match.fun, where parent.frame(2) is changed to parent.env(environment()).

Usage

fuzzyr.match.fun(FUN, descend = TRUE)

Arguments

Details

See match.fun.

Generalised bell fuzzification

Description

To generate a fuzzy membership function based on generalised bell fuzzification for the given crisp input x

Usage

gbell.fuzzification(x, mf.params)

Arguments

Value

The gbell MF centred at the crisp point x

Author(s)

Chao Chen

Examples

mf <- gbell.fuzzification(3, c(1,2))
# This is the same as:
mf <- genmf('gbellmf', c(1,2,3))

evalmf(1:10, mf)

Generalised bell membership function

Description

To specify a generalised bell membership function with a pair of particular parameters

Usage

gbellmf(mf.params)

Arguments

Details

This is not an external function. It should be used through genmf.

Value

The generalised bell membership function of x for a given pair of parameters, where x is a generic element of U, which is the universe of discourse of a fuzzy set X

Author(s)

Chao Chen

Examples

mf <- gbellmf(c(1,2,3))
# This is the same as:
mf <- genmf('gbellmf', c(1,2,3))

evalmf(5, mf)

Fuzzy membership function generator

Description

To generate the corresponding membership function f(x), also called fuzzy set, according to type and parameters

Usage

genmf(mf.type, mf.params)

Arguments

Details

Built-in membership function types are: 'gbellmf', 'it2gbellmf', 'singletonmf', 'linearmf', 'gaussmf', 'trapmf', 'trimf'.

mf.params for

• 'gbellmf' is c(a, b, c), where a denotes the width, b is usually positive and c locates the center of the curve.
  

• 'it2gbellmf' is c(a.lower, a.upper, b, c), where a.upper > a.lower when b > 0 and a.upper < a.lower when b < 0
  

• 'singletonmf' is c(c), where c is the location where the membership grade is 1.
  

• 'linearmf' is c(...), which are the coefficients of the linear membership function.
  

• 'gaussmf' is c(sig, c), which are the parameters for exp(-(x - c)^2/(2 * sig^2)).
  

• 'trapmf' is c(a, b, c, d), where a and d locate the "feet" of the trapezoid and b and c locate the "shoulders".
  

• 'trimf' is c(a, b, c), where a and c locate the "feet" of the triangle and b locates the peak.

Note that users are able to define their own membership functions.

Value

The desired type of membership function f(x), where x is a generic element of U, which is the universe of discourse for a fuzzy set

Author(s)

Chao Chen

Examples

mf <- genmf('gbellmf', c(1,2,3))
evalmf(1:10, mf)

Produce a graphical evaluated fuzzy inference system.

Description

Produces a three dimensional graphical view of a specific fis object. This function is only works for FIS structures with 3 variables. It will only work for 2 inputs, and 1 output.

Usage

gensurf(fis, ix1 = 1, ix2 = 2, ox1 = 1)

Arguments

Value

A three dimensional graphical model generated from the fis and other optional parameters.

Examples

fis <- tipper()
gensurf(fis)

Produces an example it2fis object for Waiter-Tipping.

Description

A function used primarily for example purposes, it creates a it2 fis with two input (service & food), output variables (tip) and their membership functions.

Usage

it2tipper()

Value

A fis object

Examples

it2fis <- it2tipper()

km.da

Description

A Direct Approach for Determining the Switch Points in the Karnik-Mendel Algorithm.

Usage

km.da(wl, wr, f, maximum = F, w.which = F, sorted = F, k.which = F)

Arguments

Value

w.which=T, a two-column matrix indicating which membership grades to be used; w.which=F and k.which=T, a vector of the centroid and the switch point; w.which=F and k.which=F, a single value of the centroid.

Author(s)

Chao Chen

References

[1] C. Chen, R. John, J. Twycross, and J. M. Garibaldi, “A Direct Approach for Determining the Switch Points in the Karnik–Mendel Algorithm,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 1079–1085, Apr. 2018.
doi: 10.1109/TFUZZ.2017.2699168

[2] C. Chen, D. Wu, J. M. Garibaldi, R. John, J. Twycross, and J. M. Mendel, “A Comment on ‘A Direct Approach for Determining the Switch Points in the Karnik-Mendel Algorithm,’” IEEE Transactions on Fuzzy Systems, vol. 26, no. 6, pp. 3905–3907, 2018.
doi: 10.1109/TFUZZ.2018.2865134

Examples

wr <- runif(100, 0, 1)
wl <- wr * runif(100, 0, 1)
f <- abs(runif(100, 0, 1))
f <- sort(f)
km.da(wl, wr, f)

Linear membership function

Description

To specify a 1st order linear membership function with given parameters

Usage

linearmf(mf.params)

Arguments

Value

A linear membership function

Author(s)

Chao Chen

Create a fis using newfis function

Description

Creates a fis object.

Usage

newfis(
  fisName,
  fisType = "mamdani",
  mfType = "t1",
  andMethod = "min",
  orMethod = "max",
  impMethod = "min",
  aggMethod = "max",
  defuzzMethod = "centroid"
)

Arguments

Value

A new fis structure.

Examples

fis <- newfis("fisName")

Plots a 2D graph of all membership functions in a variable.

Description

Plots a 2D graph of all membership functions from the specified variable which must be part of a fis object.

Usage

plotmf(
  fis,
  varType,
  varIndex,
  xx = NULL,
  timelimit = 0,
  xlab = NULL,
  ylab = NULL,
  main = NULL
)

Arguments

Value

A two dimensional graph displaying all the membership functions of a given variable.

Examples

fis <- tipper()
plotmf(fis, "input", 1)

Read a fis object from a .fis file.

Description

Reads a fis object from a file with the .fis extension, and converts it into a data structure to be used within the environment.

Usage

readfis(fileName)

Arguments

Value

A fis structure with its values generated from that of the files.

Show a Graphic User Interface of fis object

Description

Show a Graphic User Interface to display membership function plots for input and output, rules and evaluate the fis.

Usage

showGUI(fis, advancedGUI = FALSE)

Arguments

Details

This function is purposed to display all the membership plots and rules of fis object in Graphic User Interface (GUI). It also provide a function to evaluate the fis object.

showGUI(fis) will display the GUI of fis object.

Value

Return the GUI to display membership function for input and output together with rules.

Author(s)

Tajul Razak

Examples

fis <- tipper()
fis <- showGUI(fis)

Show a fis object.

Description

Shows a fis and all its data in an ordered format on the console.

Usage

showfis(fis)

Arguments

Value

Returned the organised text regarding the fis is output to console.

Examples

fis <- tipper()
showfis(fis)

Showing rule from fis object

Description

All the rule is showing from fis object

Usage

showrule(fis)

Arguments

Value

Show the total of rules inside fis object

Examples

fis <- tipper()
ruleList <- rbind(c(1,1,1,1,2), c(2,0,2,1,1), c(3,2,3,1,2))
fis <- addrule(fis, ruleList)
showrule(fis)

Singleton Fuzzification

Description

To generate a fuzzy membership function based on singleton fuzzification for the given crisp input x

Usage

singleton.fuzzification(x, mf.params = NULL)

Arguments

Value

The singleton MF at the crisp point x

Author(s)

Chao Chen

Examples

mf <- singleton.fuzzification(3)
evalmf(1:10, mf)

Singleton membership function

Description

To specify a singleton membership function at the particular point

Usage

singletonmf(mf.params)

Arguments

Details

This is not an external function. It should be used through genmf.

Value

The singleton membership function of x at the particular point, where x is a generic element of U, which is the universe of discourse of a fuzzy set X

Author(s)

Chao Chen

Examples

mf <- singletonmf(3)
# This is the same as:
mf <- genmf('singletonmf', 3)

evalmf(1:10, mf)

Produces an example fis object for Waiter-Tipping.

Description

A function used primarily for example purposes, it creates a fis with two input (service & food), output variables (tip) and their membership functions.

Usage

tipper()

Value

A fis is return

Examples

fis <- tipper()

Produces an example non-singleton fis object for Waiter-Tipping.

Description

A function used primarily for example purposes, it creates a nsfis with two input (service & food), output variables (tip) and their membership functions.

Usage

tipper.ns()

Value

A non-singleton fis object

Author(s)

Yu Zhao

Examples

fis <- tipper.ns()

Produces an example fis object (TSK type), which can also be optimised by ANFIS.

Description

A function used primarily for example purposes, it creates a fis with two input (service & food), output variables (tip) and their membership functions.

Usage

tipper.tsk()

Value

A fis is return

Examples

fis <- tipper.tsk()

Graphic User Interface for Waiter-Tipping

Description

Graphic User Interface for Waiter-Tipping to display the membership function (input & output) and rules.

Usage

tipperGUI()

Value

Return graphic user interface for Waiter-Tipping

Author(s)

Tajul Razak

Examples

fis <- tipperGUI()

Graphic User Interface for Waiter-Tipping (another style)

Description

Another style of Graphic User Interface for Waiter-Tipping to display the membership function (input & output) and rules.

Usage

tipperGUI2()

Value

Return graphic user interface for Waiter-Tipping

Author(s)

Tajul Razak

Examples

fis <- tipperGUI2()

Write a fis object to a .fis file.

Description

Write a fis object to a file with the .fis extension.

Usage

writefis(fis, fileName = "fuzzy.fis")

Arguments

Fuzzification

Description

To convert the crisp input x to a fuzzy membership function with specified fuzzification method

Usage

x.fuzzification(fuzzification.method, x, mf.params)

Arguments

Value

The corresponding fuzzy membership function

Author(s)

Chao Chen

Examples

x <- 3
mf <- x.fuzzification(gbell.fuzzification, x, c(1,2))
# This is the same as:
mf <- genmf(gbellmf, c(1,2,x))

evalmf(1:10, mf)