include/a/mf.h

   1 /*!
   2  @file mf.h
   3  @brief membership function
   4 */
   5
   6 #ifndef LIBA_MF_H
   7 #define LIBA_MF_H
   8
   9 #include "a.h"
  10
  11 /*!
  12  @ingroup A
  13  @addtogroup A_MF membership function
  14  @{
  15 */
  16
  17 /*!
  18  @brief enumeration for membership function
  19 */
  20 enum
  21 {
  22     A_MF_NUL, //!< none
  23     A_MF_GAUSS, //!< gaussian membership function
  24     A_MF_GAUSS2, //!< gaussian combination membership function
  25     A_MF_GBELL, //!< generalized bell-shaped membership function
  26     A_MF_SIG, //!< sigmoidal membership function
  27     A_MF_DSIG, //!< difference between two sigmoidal membership functions
  28     A_MF_PSIG, //!< product of two sigmoidal membership functions
  29     A_MF_TRAP, //!< trapezoidal membership function
  30     A_MF_TRI, //!< triangular membership function
  31     A_MF_LINS, //!< linear s-shaped saturation membership function
  32     A_MF_LINZ, //!< linear z-shaped saturation membership function
  33     A_MF_S, //!< s-shaped membership function
  34     A_MF_Z, //!< z-shaped membership function
  35     A_MF_PI //!< pi-shaped membership function
  36 };
  37
  38 #if defined(__cplusplus)
  39 extern "C" {
  40 #endif /* __cplusplus */
  41
  42 /*!
  43  @brief gaussian membership function
  44  \f[
  45   f(x,\sigma,c)=e^{-\frac{(x-c)^2}{2\sigma^2}}
  46  \f]
  47  @param[in] x input value for which to compute membership value.
  48  @param[in] sigma is the standard deviation.
  49  @param[in] c is the mean.
  50  @return membership value.
  51 */
  52 A_EXTERN a_float a_mf_gauss(a_float x, a_float sigma, a_float c);
  53
  54 /*!
  55  @brief gaussian combination membership function
  56  \f[
  57   f(x,\sigma_1,c_1,\sigma_2,c_2)=\begin{cases}
  58   e^{-\frac{(x-c_1)^2}{2\sigma_1^2}} & x \lt c_1 \\
  59   1 & c_1 \le x \le c_2 \\
  60   e^{-\frac{(x-c_2)^2}{2\sigma_2^2}} & x \gt c_2 \\
  61   \end{cases}
  62  \f]
  63  @param[in] x input value for which to compute membership value.
  64  @param[in] sigma1 is the standard deviation of the left gaussian function.
  65  @param[in] c1 is the mean of the left gaussian function.
  66  @param[in] sigma2 is the standard deviation of the right gaussian function.
  67  @param[in] c2 is the mean of the right gaussian function.
  68  @return membership value.
  69 */
  70 A_EXTERN a_float a_mf_gauss2(a_float x, a_float sigma1, a_float c1, a_float sigma2, a_float c2);
  71
  72 /*!
  73  @brief generalized bell-shaped membership function
  74  \f[
  75   f(x,a,b,c)=\frac{1}{1+\left|\frac{x-c}{a}\right|^{2b}}
  76  \f]
  77  @param[in] x input value for which to compute membership value.
  78  @param[in] a defines the width of the membership function, where a larger value creates a wider membership function.
  79  @param[in] b defines the shape of the curve on either side of the central plateau, where a larger value creates a more steep transition.
  80  @param[in] c defines the center of the membership function.
  81  @return membership value.
  82 */
  83 A_EXTERN a_float a_mf_gbell(a_float x, a_float a, a_float b, a_float c);
  84
  85 /*!
  86  @brief sigmoidal membership function
  87  \f[
  88   f(x,a,c)=\frac{1}{1+e^{-a(x-c)}}
  89  \f]
  90  @param[in] x input value for which to compute membership value.
  91  @param[in] a defines the width of the transition area.
  92  @param[in] c defines the center of the transition area.
  93  @return membership value.
  94 */
  95 A_EXTERN a_float a_mf_sig(a_float x, a_float a, a_float c);
  96
  97 /*!
  98  @brief difference between two sigmoidal membership functions
  99  \f[
 100   f(x,a_1,c_1,a_2,c_2)=\frac{1}{1+e^{-a_1(x-c_1)}}-\frac{1}{1+e^{-a_2(x-c_2)}}
 101  \f]
 102  @param[in] x input value for which to compute membership value.
 103  @param[in] a1 defines the width of the first transition area.
 104  @param[in] c1 defines the center of the first transition area.
 105  @param[in] a2 defines the width of the second transition area.
 106  @param[in] c2 defines the center of the second transition area.
 107  @return membership value.
 108 */
 109 A_EXTERN a_float a_mf_dsig(a_float x, a_float a1, a_float c1, a_float a2, a_float c2);
 110
 111 /*!
 112  @brief product of two sigmoidal membership functions
 113  \f[
 114   f(x,a_1,c_1,a_2,c_2)=\frac{1}{1+e^{-a_1(x-c_1)}}\times\frac{1}{1+e^{-a_2(x-c_2)}}
 115  \f]
 116  @param[in] x input value for which to compute membership value.
 117  @param[in] a1 defines the width of the first transition area.
 118  @param[in] c1 defines the center of the first transition area.
 119  @param[in] a2 defines the width of the second transition area.
 120  @param[in] c2 defines the center of the second transition area.
 121  @return membership value.
 122 */
 123 A_EXTERN a_float a_mf_psig(a_float x, a_float a1, a_float c1, a_float a2, a_float c2);
 124
 125 /*!
 126  @brief trapezoidal membership function
 127  \f[
 128   f(x,a,b,c,d)=\begin{cases}
 129   0 & x \le a \\
 130   \frac{x-a}{b-a} & a \le x \le b \\
 131   1 & b \le x \le c \\
 132   \frac{d-x}{d-c} & c \le x \le d \\
 133   0 & x \ge d \\
 134   \end{cases}
 135  \f]
 136  @param[in] x input value for which to compute membership value.
 137  @param[in] a defines its left foot.
 138  @param[in] b defines its left shoulder.
 139  @param[in] c defines its right shoulder.
 140  @param[in] d defines its right foot.
 141  @return membership value.
 142 */
 143 A_EXTERN a_float a_mf_trap(a_float x, a_float a, a_float b, a_float c, a_float d);
 144
 145 /*!
 146  @brief triangular membership function
 147  \f[
 148   f(x,a,b)=\begin{cases}
 149   0 & x \le a \\
 150   \frac{x-a}{b-a} & a \le x \le b \\
 151   \frac{c-x}{c-b} & b \le x \le c \\
 152   0 & x \ge c \\
 153   \end{cases}
 154  \f]
 155  @param[in] x input value for which to compute membership value.
 156  @param[in] a defines its left foot.
 157  @param[in] b defines its peak.
 158  @param[in] c defines its right foot.
 159  @return membership value.
 160 */
 161 A_EXTERN a_float a_mf_tri(a_float x, a_float a, a_float b, a_float c);
 162
 163 /*!
 164  @brief linear s-shaped saturation membership function
 165  \f[
 166   f(x,a,b)=\begin{cases}
 167   0 & x \lt a \\
 168   \frac{x-a}{b-a} & a \le x \le b \\
 169   1 & x \gt b \\
 170   \end{cases}
 171  \f]
 172  @param[in] x input value for which to compute membership value.
 173  @param[in] a defines its foot.
 174  @param[in] b defines its shoulder.
 175  @return membership value.
 176 */
 177 A_EXTERN a_float a_mf_lins(a_float x, a_float a, a_float b);
 178
 179 /*!
 180  @brief linear z-shaped saturation membership function
 181  \f[
 182   f(x,a,b)=\begin{cases}
 183   1 & x \lt a \\
 184   \frac{b-x}{b-a} & a \le x \le b \\
 185   0 & x \gt b \\
 186   \end{cases}
 187  \f]
 188  @param[in] x input value for which to compute membership value.
 189  @param[in] a defines its shoulder.
 190  @param[in] b defines its foot.
 191  @return membership value.
 192 */
 193 A_EXTERN a_float a_mf_linz(a_float x, a_float a, a_float b);
 194
 195 /*!
 196  @brief s-shaped membership function
 197  \f[
 198   f(x,a,b)=\begin{cases}
 199   0 & x \le a \\
 200   2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\
 201   1-2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\
 202   1 & x \ge b \\
 203   \end{cases}
 204  \f]
 205  @param[in] x input value for which to compute membership value.
 206  @param[in] a defines its foot.
 207  @param[in] b defines its shoulder.
 208  @return membership value.
 209 */
 210 A_EXTERN a_float a_mf_s(a_float x, a_float a, a_float b);
 211
 212 /*!
 213  @brief z-shaped membership function
 214  \f[
 215   f(x,a,b)=\begin{cases}
 216   1 & x \le a \\
 217   1-2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\
 218   2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\
 219   0 & x \ge b \\
 220   \end{cases}
 221  \f]
 222  @param[in] x input value for which to compute membership value.
 223  @param[in] a defines its shoulder.
 224  @param[in] b defines its foot.
 225  @return membership value.
 226 */
 227 A_EXTERN a_float a_mf_z(a_float x, a_float a, a_float b);
 228
 229 /*!
 230  @brief pi-shaped membership function
 231  \f[
 232   f(x,a,b,c,d)=\begin{cases}
 233   0 & x \le a \\
 234   2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\
 235   1-2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\
 236   1 & b \le x \le c \\
 237   1-2(\frac{x-c}{d-c})^2 & c \le x \le \frac{c+d}{2} \\
 238   2(\frac{d-x}{d-c})^2 & \frac{c+d}{2} \le x \le d \\
 239   1 & x \ge d \\
 240   \end{cases}
 241  \f]
 242  @param[in] x input value for which to compute membership value.
 243  @param[in] a defines its left foot.
 244  @param[in] b defines its left shoulder.
 245  @param[in] c defines its right shoulder.
 246  @param[in] d defines its right foot.
 247  @return membership value.
 248 */
 249 A_EXTERN a_float a_mf_pi(a_float x, a_float a, a_float b, a_float c, a_float d);
 250
 251 /*!
 252  @brief membership function
 253  @param[in] e enumeration for membership function
 254  |                   |                                        |
 255  | :---------------- | -------------------------------------- |
 256  | \ref A_MF_GAUSS   | a_mf_gauss(x, sigma, c)                |
 257  | \ref A_MF_GAUSS2  | a_mf_gauss2(x, sigma1, c1, sigma2, c2) |
 258  | \ref A_MF_GBELL   | a_mf_gbell(x, a, b, c)                 |
 259  | \ref A_MF_SIG     | a_mf_sig(x, a, c)                      |
 260  | \ref A_MF_DSIG    | a_mf_dsig(x, a1, c1, a2, c2)           |
 261  | \ref A_MF_PSIG    | a_mf_psig(x, a1, c1, a2, c2)           |
 262  | \ref A_MF_TRAP    | a_mf_trap(x, a, b, c, d)               |
 263  | \ref A_MF_TRI     | a_mf_tri(x, a, b, c)                   |
 264  | \ref A_MF_LINS    | a_mf_lins(x, a, b)                     |
 265  | \ref A_MF_LINZ    | a_mf_linz(x, a, b)                     |
 266  | \ref A_MF_S       | a_mf_s(x, a, b)                        |
 267  | \ref A_MF_Z       | a_mf_z(x, a, b)                        |
 268  | \ref A_MF_PI      | a_mf_pi(x, a, b, c, d)                 |
 269  @param[in] x input value for which to compute membership value.
 270  @param[in] a is an array that stores parameters.
 271   @arg \b a[2] \ref a_mf_gauss \ref a_mf_sig \ref a_mf_lins \ref a_mf_linz \ref a_mf_s \ref a_mf_z
 272   @arg \b a[3] \ref a_mf_gbell \ref a_mf_tri
 273   @arg \b a[4] \ref a_mf_gauss2 \ref a_mf_dsig \ref a_mf_psig \ref a_mf_trap \ref a_mf_pi
 274  @return membership value.
 275 */
 276 A_EXTERN a_float a_mf(unsigned int e, a_float x, a_float const *a);
 277
 278 #if defined(__cplusplus)
 279 } /* extern "C" */
 280 #endif /* __cplusplus */
 281
 282 /*! @} A_MF */
 283
 284 #endif /* a/mf.h */