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96 changes: 48 additions & 48 deletions doc/qfis.dox
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* using @c AND or @c OR logical connectives.
*
* Fuzzy inference works by sending any process's crisp input to the fuzzifier,
* which applies a fuzzy membership function and maps the actual readings into
* which applies a fuzzy membership function and maps the actual readings into
* fuzzy values. The inference engine applies fuzzy rules from the knowledge base
* and produces the fuzzy output. This output can not be used directly in any
* process or system. It needs to be mapped into the original domain. For this,
* the defuzzifier is used, which is the inverse process of fuzzification. It
* converts the fuzzy output into crisp output, which can be fed to the process.
*
* The FIS Fuzzy Inference System engine provides an API for building and
* evaluation of type-1 fuzzy logic inference systems.
*
* evaluation of type-1 fuzzy logic inference systems.
*
* The types of inferences supported by FIS are listed in the \ref qlibs::fis::type enum
* and are detailed below:
*
Expand All @@ -24,7 +24,7 @@
* In a Mamdani system, the output of each rule is a fuzzy set. Since Mamdani
* systems have more intuitive and easier to understand rule bases, they are
* well-suited to expert system applications where the rules are created
* from human expert knowledge.
* from human expert knowledge.
*
* The output of each rule is a fuzzy set derived from the output membership
* function and the implication method of the FIS. These output fuzzy sets are
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* function of the input values.
*
* and \f$w_i\f$, the rule firing strength, that is determined by the rule antecedent
*
*
* The output of each rule is the weighted output level, which is the product of
* \f$w_i\f$ and \f$u_i\f$.
*
*
* The final output of the system is the weighted average/sum over all rule outputs:
*
* <center> \f$out= \frac{ \sum_{i=1}^{N}w_{i}u_{i} }{ \sum_{i=1}^{N}w_{i}} \f$ </center>
*
*
* where \f$N\f$ is the number of rules.
*
* Because of the linear dependence of each rule on the input variables, the Sugeno
* method is ideal for acting as an interpolating supervisor of multiple linear
* controllers that are to be applied, respectively, to different operating
* Because of the linear dependence of each rule on the input variables, the Sugeno
* method is ideal for acting as an interpolating supervisor of multiple linear
* controllers that are to be applied, respectively, to different operating
* conditions of a dynamic nonlinear system.
*
* To specificy a FIS of this type, use the \ref qlibs::fis::Sugeno enum definition when
Expand All @@ -104,7 +104,7 @@
* In the Tsukamoto inference system, the consequent of each fuzzy if-then rule
* is represented by a fuzzy set with a monotonical membership function, As a result,
* the inferred output of each rule is defined as a crisp value induced by the
* rule's firing strength.
* rule's firing strength.
*
* The overall output is taken as the weighted average of each rule's output.
* Since each rule infers a crisp output, the Tsukamoto fuzzy model aggregates
Expand All @@ -131,22 +131,22 @@
* </center>
*
* @section qfis_defuzz Defuzzification Methods
*
*
* FIS supports five different methods, as listed in the \ref qlibs::fis::deFuzzMethod enum
* for computing a single crisp output value for such a fuzzy set.
*
* -# \ref qlibs::fis::centroid (default): this method applies only to \ref qlibs::fis::Mamdani
* systems and returns the center of gravity of the fuzzy set along the x-axis.
* If you think of the area as a plate with uniform thickness and density, the
* -# \ref qlibs::fis::centroid (default): this method applies only to \ref qlibs::fis::Mamdani
* systems and returns the center of gravity of the fuzzy set along the x-axis.
* If you think of the area as a plate with uniform thickness and density, the
* centroid is the point along the x-axis about which the fuzzy set would balance.
* The centroid is computed using the following formula, where \f$\mu(x)\f$ is
* The centroid is computed using the following formula, where \f$\mu(x)\f$ is
* the membership value for point \f$x_i\f$ in the universe of discourse.
*
*
* <center> \f$\text{centroid}= \frac{ \sum_{i=1}\mu(x_{i})x_{i} }{ \sum_{i=1}\mu(x_{i})} \f$ </center>
*
* -# \ref qlibs::fis::bisector : this method applies only for \ref qlibs::fis::Mamdani systems and finds the
* vertical line that divides the fuzzy set into two sub-regions of equal area.
* -# \ref qlibs::fis::bisector : this method applies only for \ref qlibs::fis::Mamdani systems and finds the
* vertical line that divides the fuzzy set into two sub-regions of equal area.
* It is sometimes, but not always, coincident with the centroid line.
*
* -# \ref qlibs::fis::mom : Middle of Maximum. Only for \ref qlibs::fis::Mamdani systems.
Expand All @@ -155,13 +155,13 @@
*
* -# \ref qlibs::fis::lom : Largest of Maximum. Only for \ref qlibs::fis::Mamdani systems.
*
* -# \ref qlibs::fis::wtaver (default): Weighted average of all rule outputs. This method applies only
* -# \ref qlibs::fis::wtaver (default): Weighted average of all rule outputs. This method applies only
* for \ref qlibs::fis::Sugeno and \ref qlibs::fis::Tsukamoto systems.
*
* -# \ref qlibs::fis::wtsum : Weighted sum of all rule outputs. This method applies only
* -# \ref qlibs::fis::wtsum : Weighted sum of all rule outputs. This method applies only
* for \ref qlibs::fis::Sugeno and \ref qlibs::fis::Tsukamoto systems.
*
* @note The defuzzification method is selected by default when setting up the
* @note The defuzzification method is selected by default when setting up the
* FIS instance with \ref qlibs::fis::instance::setup(). However, the user can later change the default
* method using the \ref qlibs::fis::instance::setDeFuzzMethod() function.
*
Expand All @@ -188,7 +188,7 @@
* -# <tt> IF the service IS excellent OR the food IS delicious, THEN the tip IS generous. </tt>
*
* This leads to a system with 2 inputs : @c service and @c food and 1 output: @c tip
*
*
* <center>
* @htmlonly
* <!DOCTYPE html>
Expand All @@ -213,7 +213,7 @@
* -# (food)rancid : A @a trapezoidal membership function with points located on <tt> [0 0 1 3] </tt>
* -# (food)delicious : A @a trapezoidal membership function with points located on <tt> [7 9 10 10] </tt>
*
* and 3 membership functions for the output
* and 3 membership functions for the output
*
* -# (tip)cheap : A @a triangular membership function with points located on <tt> [0 5 10] </tt>
* -# (tip)average : A @a triangular membership function with points located on <tt> [10 15 20] </tt>
Expand Down Expand Up @@ -257,13 +257,13 @@
* @endcode
*
* @attention
* Please note that all tag names are unique.
* Please note that all tag names are unique.
*
* Then, we will define the rules of
* Then, we will define the rules of
* the fuzzy system using the previously defined tags. Rules should be defined as
* an array of type \ref qlibs::fis::rules and the contents should be rules constructed
* with the provided statements:
*
* with the provided statements:
*
* - \ref #FIS_RULES_BEGIN to start the rules set
* - \ref #FIS_RULES_END to end the rules set
* - \ref #IF to start a rule sentence
Expand All @@ -275,7 +275,7 @@
* Let's apply some of these statements to build the rule set.
*
* @code{.c}
* static const fis::rules rules[] = {
* static const fis::rules rules[] = {
* FIS_RULES_BEGIN
* IF service IS service_poor OR food IS food_rancid THEN tip IS tip_cheap END
* IF service IS service_good THEN tip IS tip_average END
Expand All @@ -285,23 +285,23 @@
* @endcode
*
* Additionally, we also need to define a vector where the firing strength of each
* rule will be stored. The size of the vector will be the number of rules. In
* rule will be stored. The size of the vector will be the number of rules. In
* this particular case, there will be only three.
*
* @code{.c}
* static real_t rulesStrength[ 3 ];
* @endcode
*
* First step is to configure the instance that represents the fuzzy
* First step is to configure the instance that represents the fuzzy
* system using the \ref qlibs::fis::instance::setup() API:
*
* @code{.c}
* tipper.setup( fis::Mamdani, tipper_inputs, tipper_outputs, MFin, MFout, rules, rulesStrength );
* @endcode
*
* Then, we can proceed to the construction of the fuzzy system. First, we must
* configure the inputs and outputs by setting the ranges of each. For this, we
* will use the \ref qlibs::fis::instance::setupInput() and \ref qlibs::fis::instance::setupOutput()
* configure the inputs and outputs by setting the ranges of each. For this, we
* will use the \ref qlibs::fis::instance::setupInput() and \ref qlibs::fis::instance::setupOutput()
* methods as follows:
*
* @code{.c}
Expand All @@ -310,8 +310,8 @@
* tipper.setupOutput( tip, 0.0f, 30.0f );
* @endcode
*
* The next step is to configure the membership functions by relating I/O,
* tags, shape and parameters one by one by using the \ref qlibs::fis::instance::setupInputMF() and
* The next step is to configure the membership functions by relating I/O,
* tags, shape and parameters one by one by using the \ref qlibs::fis::instance::setupInputMF() and
* \ref qlibs::fis::instance::setupOutputMF() methods as follows:
* Then, let's define the parameters of all the membership functions:
*
Expand All @@ -331,23 +331,23 @@
*
* @section qfis_eval Evaluating a Fuzzy Inference System
*
* If we already have a fuzzy system configured with \ref qlibs::fis::instance::setup(), we can
* evaluate it by using \ref qlibs::fis::instance::fuzzify(), \ref qlibs::fis::instance::inference() and
* \ref qlibs::fis::instance::deFuzzify().
* Input values can be set with \ref qlibs::fis::instance::setInput() and output values can be
* If we already have a fuzzy system configured with \ref qlibs::fis::instance::setup(), we can
* evaluate it by using \ref qlibs::fis::instance::fuzzify(), \ref qlibs::fis::instance::inference() and
* \ref qlibs::fis::instance::deFuzzify().
* Input values can be set with \ref qlibs::fis::instance::setInput() and output values can be
* obtained with \ref qlibs::fis::instance::getOutput(). Also you can use the stream operator @c <<
* to set the inputs and the index operator [] to get the outputs of the FIS
* system (see example bellow).
*
* To show its use, first we are going to put everything together in a single
* code snippet and we are going to create two functions, @c tipper_init() and
* @c tipper_run() that will be in charge of setting up the fuzzy inference
* To show its use, first we are going to put everything together in a single
* code snippet and we are going to create two functions, @c tipper_init() and
* @c tipper_run() that will be in charge of setting up the fuzzy inference
* system and evaluating it respectively.
*
* @code{.c}
* #include "tipper_fis.h"
* #include "qfis.h"
*
* #include <qlibs.h>
*
* // I/O Names
* enum : fis::tag { service, food};
* enum : fis::tag { tip};
Expand All @@ -371,8 +371,8 @@
* };
* //Rule strengths
* real_t rStrength[ 3 ] = { 0.0f };
*
*
*
*
* void tipper_init( void )
* {
* tipper.setup( fis::Mamdani, tipper_inputs, tipper_outputs, MFin, MFout, rules, rStrength );
Expand All @@ -388,20 +388,20 @@
* tipper.setupOutputMF( tip, average, fis::trimf, (const real_t[]){ 10.0f, 15.0f, 20.0f } );
* tipper.setupOutputMF( tip, generous, fis::trimf, (const real_t[]){ 20.0f, 25.0f, 30.0f } );
* }
*
*
* void tipper_run( real_t *inputs, real_t *outputs )
* {
* // Set the crips inputs
* tipper << service << inputs[ service ] << food << inputs[ food ];
*
*
* tipper.fuzzify();
* if ( tipper.inference() ) {
* tipper.deFuzzify();
* }
* else {
* // Error!
* }
*
*
* // Get the crips outputs
* outputs[ tip ] = tipper[ tip ];
* }
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2 changes: 1 addition & 1 deletion doc/qltisys.dox
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* { 0.1f, 0.2f, 0.3f },
* { 1.0f, -0.85f, 0.02f },
* };
* continuousSystem gc( dtf );
* discreteSystem gc( dtf );
* real_t uk, yk;
*
* for( ;; ) {
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