Fuzzy rule

Use `fisrule`

objects to represent fuzzy if-then rules that
relate input membership function conditions to corresponding output membership functions. The
*if* portion of a fuzzy rule is the *antecedent*,
which specifies the membership function for each input variable. The *then*
portion of a fuzzy rule is the *consequent*, which specifies the membership
function for each output variable. For more information on membership functions and fuzzy
rules, see Foundations of Fuzzy Logic.

To create fuzzy rule objects, use the `fisrule`

function. Using this
function, you can create a single fuzzy rule or a vector of multiple fuzzy rules.

`rule = fisrule`

`rule = fisrule(ruleText)`

`rule = fisrule(ruleValues,numInputs)`

`rule = fisrule`

creates a single fuzzy rule with the default
description `"input1==mf1 => output1=mf1"`

.

creates one or more fuzzy rules using the text descriptions in
`rule`

= fisrule(`ruleText`

)`ruleText`

.

creates one or more fuzzy rules using the numeric rule values in
`rule`

= fisrule(`ruleValues`

,`numInputs`

)`ruleValues`

. Specify the number of rule input variables using
`numInputs`

.

`ruleText`

— Text rule descriptionstring | character vector | string array | character array

Text rule description, specified as one of the following:

String or character vector specifying a single rule

rule = "If service is poor or food is rancid then tip is cheap";

String array, where each element corresponds to a rule. For example:

ruleList = ["If service is poor or food is rancid then tip is cheap"; "If service is good then tip is average"; "If service is excellent or food is delicious then tip is generous"];

Character array where each row corresponds to a rule. For example:

rule1 = 'If service is poor or food is rancid then tip is cheap'; rule2 = 'If service is good then tip is average'; rule3 = 'If service is excellent or food is delicious then tip is generous'; ruleList = char(rule1,rule2,rule3);

For each rule, use one of the following rule text formats:

Verbose — Linguistic expression in the following format, using the

`IF`

and`THEN`

keywords:"IF <antecedent> THEN <consequent> (<weight>)"

In

`<antecedent>`

, specify the membership function for each input variable using the`IS`

or`IS NOT`

keyword. Connect these conditions using the`AND`

or`OR`

keywords. If a rule does not use a given input variable, omit it from the antecedent.In

`<consequent>`

, specify the condition for each output variable using the`IS`

or`IS NOT`

keyword, and separate these conditions using commas. The`IS NOT`

keyword is not supported for Sugeno outputs. If a rule does not use a given output variable, omit it from the consequent.Specify the weight using a positive numerical value.

For example:

"IF A IS a AND B IS NOT b THEN X IS x, Y IS NOT y (1)"

Symbolic — Expression that uses the symbols in the following table instead of keywords. There is no symbol for the

`IF`

keyword.Symbol Keyword `==`

`IS`

(in rule antecedent)`~=`

`IS NOT`

`&`

`AND`

`|`

`OR`

`=>`

`THEN`

`=`

`IS`

(in rule consequent)For example, the following symbolic rule is equivalent to the previous verbose rule.

"A==a & B~=b => X=x, Y~=y (1)"

When you specify a rule using a text description, `fisrule`

sets the `Description`

, `Weight`

, and
`Connection`

properties of the rule based on the
description.

`ruleValues`

— Numeric rule descriptionrow vector | numeric array

Numeric rule description, specified as one of the following:

Row vector to specify a single fuzzy rule

Array, where each row of

`ruleValues`

specifies one rule

For each row, the numeric rule description has *M*+*N*+2 columns, where *M* is the number of input variables and *N* is the number of output variables. Each column contains the following information:

The first

*M*columns specify input membership function indices and correspond to the`Antecedent`

property of the rule. To indicate a`NOT`

condition, specify a negative value. If a rule does not use a given input, set the corresponding index to`0`

. For each rule, at least one input membership function index must be nonzero.The next

*N*columns specify output membership function indices and correspond to the`Consequent`

property of the rule. To indicate a`NOT`

condition for Mamdani systems, specify a negative value.`NOT`

conditions are not supported for Sugeno outputs. If a rule does not use a given output, set the corresponding index to`0`

. For each rule, at least one output membership function index must be nonzero.Column

*M*+*N*+1 specifies the rule weight and corresponds to the`Weight`

property of the rule.The final column specifies the antecedent fuzzy operator and corresponds to the

`Connection`

property of the rule.

When you specify a rule using `ruleVlaues`

,
`fisrule`

sets the `Description`

property
using default variable and membership function names.

`numInputs`

— Number of input variablespositive integer

Number of input variables for the rule, specified as a positive integer. If you
specify the rule description using `ruleValues`

, you must also
specify the number of input variables. `fisrule`

parses the rule
antecedent values into the membership function indices for the input and output
variables using `numInputs`

.

`Description`

— Text rule descriptionstring | character vector

Text rule description, specified as a string or character vector. The rule
description is stored as a symbolic expression no matter how you specify the rule. For
example, if you specify the following verbose rule using
`ruleText`

:

"IF A IS a AND B IS NOT b THEN X IS x, Y IS NOT y (1)"

The stored rule is:

"A==a & B~=b => X=x, Y~=y (1)"

For more information on the verbose and symbolic rule formats, see the
`ruleText`

input argument.

When you specify a rule using `ruleVlaues`

,
`fisrule`

sets the `Description`

property using
default variable and membership function names. Before using the rule in a fuzzy system,
you must update the description to use the variable and membership function names from
that fuzzy system using the `update`

function.

`Antecedent`

— Rule antecedentnumeric vector

Rule antecedent, specified as a numeric vector of length *M*, where
*M* is the number of input variables. Each element of
`Antecedent`

contains one of the following values:

Positive integer — The index of an input membership function, which represents an

`IS`

conditionNegative integer — The negative of an input membership function, which represents an

`IS NOT`

condition`0`

— A*don't care*condition, which means that the rule does not use the corresponding input variable

This value is set when you create a fuzzy rule using
`ruleValues`

. If you create a fuzzy rule using
`ruleText`

, before using the rule in a fuzzy system, you must
populate the `Antecedent`

property using the `update`

function.

If you update the indices in the rule antecedent using dot notation, the
`Description`

property is not updated to reflect the changes. To
update the rule description, use the `update`

function.

`Consequent`

— Rule consequentnumeric vector

Rule consequent, specified as a numeric vector of length *N*, where
*N* is the number of output variables. Each element of
`Consequent`

contains one of the following values:

Positive integer — The index of an output membership function, which represents an

`IS`

conditionNegative integer — The negative of an output membership function, which represents an

`IS NOT`

condition`0`

— A*don't care*condition, which means that the rule does not use the corresponding output variable

This value is set when you create a fuzzy rule using
`ruleValues`

. If you create a fuzzy rule using
`ruleText`

, before using the rule in a fuzzy system, you must
populate the `Consequent`

property using the `update`

function.

If you update the indices in the rule consequent using dot notation, the
`Description`

property is not updated to reflect the changes. To
update the rule description, use the `update`

function.

`Weight`

— Rule weight`1`

(default) | positive numeric scalarRule weight, specified as a positive numeric scalar in the range
[`0`

`1`

].

If you update the rule weight using dot notation, the weight value in the
`Description`

property text is also updated.

`Connection`

— Rule antecedent connection`1`

| `2`

Rule antecedent connection, specified as one of the following:

`1`

— Evaluate rule antecedents using the AND operator.`2`

— Evaluate rule antecedents using the OR operator.

If you update the rule connection using dot notation, the antecedent operators in
the `Description`

property text are also updated.

`update` | Update fuzzy rule using fuzzy inference system |

Create a default fuzzy rule.

rule = fisrule

rule = fisrule with properties: Description: "input1==mf1 => output1=mf1 (1)" Antecedent: 1 Consequent: 1 Weight: 1 Connection: 1

To modify the rule properties, use dot notation. For example, specify a rule weight of `0.5`

.

rule.Weight = 0.5;

Create a fuzzy rule using a verbose text description.

`rule = fisrule("if service is poor and food is delicious then tip is average (1)");`

Alternatively, you can specify the same rule using a symbolic text description.

`rule = fisrule("service==poor & food==delicious => tip=average")`

rule = fisrule with properties: Description: "service==poor & food==delicious => tip=average (1)" Antecedent: [] Consequent: [] Weight: 1 Connection: 1

Before using `rule`

with a fuzzy system, update the rule `Antecedent`

and` Consequent`

properties using the `update`

function.

```
fis = readfis("tipper");
rule = update(rule,fis)
```

rule = fisrule with properties: Description: "service==poor & food==delicious => tip=average (1)" Antecedent: [1 2] Consequent: 2 Weight: 1 Connection: 1

Create a fuzzy rule using a numeric description. Specify that the rule has two input variables.

rule = fisrule([1 2 2 0.5 1],2)

rule = fisrule with properties: Description: "input1==mf1 & input2==mf2 => output1=mf2 (0.5)" Antecedent: [1 2] Consequent: 2 Weight: 0.5000 Connection: 1

Before using `rule`

with a fuzzy system, update the rule `Description`

property using the `update`

function.

```
fis = readfis("tipper");
rule = update(rule,fis)
```

rule = fisrule with properties: Description: "service==poor & food==delicious => tip=average (0.5)" Antecedent: [1 2] Consequent: 2 Weight: 0.5000 Connection: 1

Create a string array of text rule descriptions.

rules1 = ["if service is poor or food is rancid then tip is cheap (0.5)"... "if service is excellent and food is not rancid then tip is generous (0.75)"];

Create an array of fuzzy rules using these descriptions.

fuzzyRules1 = fisrule(rules1)

fuzzyRules1 = 1x2 fisrule array with properties: Description Antecedent Consequent Weight Connection Details: Description __________________________________________________________ 1 "service==poor | food==rancid => tip=cheap (0.5)" 2 "service==excellent & food~=rancid => tip=generous (0.75)"

Alternatively, you can specify multiple rules using an array of numeric rule descriptions.

rules2 = [1 1 1 0.5 2; 2 -1 3 0.75 1]; fuzzyRules2 = fisrule(rules2,2)

fuzzyRules2 = 1x2 fisrule array with properties: Description Antecedent Consequent Weight Connection Details: Description _________________________________________________ 1 "input1==mf1 | input2==mf1 => output1=mf1 (0.5)" 2 "input1==mf2 & input2~=mf1 => output1=mf3 (0.75)"

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