Apparatus for controlling vehicle automatic transmission according to fuzzy set theory

An apparatus for controlling a vehicle automatic transmission having a plurality of operating positions, including a determining device for determining satisfaction degress of at least one basic fuzzy set theory rule corresponding to the respective operating positions of the transmission, based on a predetermined shift pattern, a first calculating device for calculating satisfaction degrees of fuzzy set control rules, corresponding to the respective operating positions of the transmission, depending upon a detected vehicle running condition, a second calculating device for calculating overall satisfaction degrees for selecting the respective operating positions, based on the calculated satisfaction degress of the basic fuzzy set theory rule or rules and the calculated satisfaction degrees of the fuzzy set control rules, and a selector for selecting one of the positions of the transmission, based on the calculated overall satisfaction degrees, so that the automatic transmission is shifted to the selected position.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to an apparatus for controlling an 
automatic transmission of a motor vehicle, and more particularly to 
improvements in such a control apparatus adapted to shift the transmission 
from one of operating positions to another according to a predetermined 
shift pattern. 
2. Discussion of the Related Art 
A power transmitting system of a motor vehicle generally includes an 
automatic transmission which has a fluid coupling device such as a torque 
converter which receives power from an engine of the vehicle, and an 
automatic speed changing device such as a planetary mechanism connected to 
the fluid coupling device. The automatic transmission is controlled by a 
suitable control apparatus, such that the transmission is shifted from one 
of a plurality of operating positions thereof to another, according to 
predetermined shift patterns. 
An example of a shift pattern for an automatic transmission having four 
forward drive positions is illustrated in FIG. 4. This shift pattern uses 
two control parameters, which consist of an accelerator position .theta.ac 
and a running speed V of the vehicle. Solid lines in FIG. 4 indicate 
boundaries for shift-up operations of the transmission which cause a 
decrease in the speed ratio of the transmission (input speed/output 
speed), while broken lines in the figure indicate boundaries for 
shift-down operations of the transmission which cause an increase in the 
speed ratio. Reference numerals and characters 1, 2, 3 and O/D denote the 
four operating positions of the transmission, i.e., first-speed position, 
second-speed position, third-speed position and overdrive position, 
respectively. The speed ratios of these first-speed, second-speed, 
third-speed and overdrive positions decrease in the order of description. 
Where the transmission is currently placed in the third-speed position 3 
with the accelerator position .theta.ac set at 40%, for example, three 
reference values V1, V2, V3 are determined by the shift pattern, so that 
the actually detected vehicle speed V is compared with these reference 
values V1 V2, V3, for selecting the position to which the transmission 
should be shifted up or down. Described more specifically, the first-speed 
position 1 is selected where V .ltoreq.V1, and the second-position 2 is 
selected where V1&lt;V.ltoreq.V2. The third-speed position 3 is selected 
where V2&lt;V.ltoreq.V3, and the overdrive position O/D is selected where 
V3&lt;V. The operating positions may be selected by comparing the detected 
accelerator position .theta.ac with reference values determined by the 
shift pattern for each vehicle speed V. 
For improving the adequacy of selection of the optimum operating position 
of the automatic transmission, it is considered to adjust or compensate 
the basic shift pattern according to compensating data maps, or use a 
large number of shift patterns, so that the selected position of the 
transmission best suits the specific vehicle running condition which is 
defined by two or more parameters such as: a rate of change in the 
accelerator position .theta.ac; a rate of change in the vehicle speed V; 
occurrence of repetition of frequent shift-up and shift-down actions of 
the transmission; a gradient of the road surface; a difference between the 
actual engine speed and the determined target or desired engine speed; and 
a steering angle of the vehicle. The compensation of the basic shift 
pattern or the use of many shift patterns permits optimum shifting 
operations of the transmission for enhanced driving comfort of the 
vehicle, depending upon the vehicle running condition. However, this 
arrangement which uses many control parameters requires a considerably 
increased amount of control program data (including data maps), and 
therefore requires a large-capacity memory for storing such data, 
resulting in an increase in the cost of the control apparatus. Namely, the 
required amount of control program data increases in proportion to the 
number of control parameters which is raised to n-th power. 
In view of the above drawback, the assignee of the present application 
developed a transmission control apparatus as disclosed in U.S. Pat. 
application, Ser. No. 352,498 filed May 16, 1989. This control apparatus 
does not use shift patterns or compensating data maps, but is adapted to 
control the transmission, according to calculated degrees of satisfaction 
of predetermined fuzzy set control rules associated with running 
parameters of the vehicle. Namely, the satisfaction degrees of the control 
rules are calculated for each of the operating positions of the 
transmission, and the operating position having the highest satisfaction 
degree is selected as the position which best suits the current running 
condition of the vehicle. In this arrangement, the required amount of 
control program data is proportional to the number of the control 
parameters (vehicle running parameters), and is therefore comparatively 
small, whereby the control apparatus may be simplified and available at a 
relatively reduced cost. 
In the above arrangement, however, the required amount of control program 
data is larger than that in the arrangement using only the shift patterns, 
in the case where the number of control parameters for selecting the 
operating positions of the transmission is relatively small, for example, 
where only the accelerator position and the vehicle speed are used as the 
control parameters. Thus, the conventional and recently proposed 
arrangements are not completely satisfactory in terms of the control 
reliability and simplicity. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide an apparatus 
for controlling an automatic transmission of a motor vehicle, with a 
relatively reduced amount of control program data. 
The above object may be achieved according to the principle of the present 
invention, which is adapted to select one of operating positions of the 
transmission, by utilizing both a shift pattern and determination 
according to the fuzzy set theory. 
More particularly, the present invention provides an apparatus for 
controlling an automatic transmission for a motor vehicle having a 
plurality of operating positions such that the operating positions are 
selected according to a predetermined shift pattern, comprising: (a) 
determining means for determining satisfaction degrees of at least one 
basic fuzzy set theory rule corresponding to the plurality of operating 
positions of the transmission, respectively, based on the predetermined 
shift pattern; (b) detecting means for detecting a running condition of 
the vehicle; (c) first calculating means for calculating satisfaction 
degrees of fuzzy set control rules, corresponding to the plurality of 
operating positions, respectively, depending upon the running condition of 
the vehicle detected by the detecting means; (d) second calculating means 
for calculating overall satisfaction degrees for selecting the plurality 
of operating positions, respectively, based on the satisfaction degrees of 
the at least one basic fuzzy set theory rule determined by the determining 
means and the satisfaction degrees of the fuzzy set control rules 
calculated by the first calculating means; and (e) selecting means for 
selecting one of the plurality of operating positions of the transmission, 
based on the overall satisfaction degrees calculated by the second 
calculating means, so that the automatic transmission is shifted to the 
selected operating position. 
In the control apparatus of the present invention constructed as described 
above, the satisfaction degrees of the basic fuzzy set theory rule or 
rules are determined by the determining means, for the individual 
operating positions of the transmission, based on the predetermined shift 
pattern. In the meantime, the satisfaction degrees of the fuzzy set 
control rules associated with the running parameters of the vehicle which 
collectively determine the vehicle running condition are calculated by the 
first calculating means, for the respective operating positions of the 
transmission. Based on the determined satisfaction degrees of the fuzzy 
set theory rule or rules and the calculated satisfaction degrees of the 
fuzzy set control rules, the overall satisfaction degrees for selecting 
the individual operating positions of the transmission are determined by 
the second calculating means, so that the selecting means selects one of 
the operating positions of the transmission, based on the calculated 
overall satisfaction degrees. For example, one of the operation positions 
which has the highest overall satisfaction degree is selected as the 
optimum position to which the transmission is shifted or in which the 
transmission is maintained. The present arrangement permits the 
transmission to be shifted up and down, so as to meet a wide variety of 
running parameters of the vehicle, which cannot be dealt with by the known 
arrangement wherein the shift pattern is determined by the accelerator 
position and the vehicle speed, for example. 
The present control apparatus which utilizes both the shift pattern and the 
fuzzy set theory requires a reduced amount of control program data, as 
compared with ar arrangement which uses many shift patterns or pattern 
compensating maps, to control the transmission depending upon the running 
parameters of the vehicle, even where the number of the parameters is 
relatively large. 
Further, since the basic shift pattern is used (since the satisfaction 
degrees of the basic fuzzy set theory rule or rules are determined 
according to the basic shift pattern), the required overall amount of 
control program data is smaller in the present arrangement, than in the 
arrangement which uses only the fuzzy set theory to select the optimum 
position of the transmission. 
In the present control apparatus, the overall satisfaction degree for 
selecting each of the operating positions of the transmission is 
calculated based on the basic shift pattern (satisfaction degree of the 
basic fuzzy set theory rule or rules) and the satisfaction degree of the 
appropriate fuzzy set control rule associated with the running condition 
of the vehicle. This arrangement does not require a procedure otherwise 
required for improving the control accuracy, as practiced in the 
arrangement wherein the shift pattern is compensated by obtaining the 
center of distribution of the calculated satisfaction degrees of the fuzzy 
set control rules. In this respect, too, the present control apparatus 
reduces the required amount of the control program data. 
In one form of the present invention, the determining means provisionally 
selects one of the operating positions of the transmission as a 
provisional position N* according to the predetermined shift pattern, and 
the at least one basic fuzzy set theory rule consists of a basic fuzzy set 
theory rule whose satisfaction degree decreases with a difference in the 
number of positions between the selected provisional position N* and each 
of the operating positions. For example, the value of the satisfaction 
degree of the basic fuzzy set theory rule of the selected provisional 
position N* is set to "1", and those of the operating positions adjacent 
to the provisional position N* are set to "0.5", while the values of the 
positions next adjacent to the positions whose value is "0.5" are set to 
"0.25". Namely, the basic fuzzy set theory rule determines a degree in 
which each of the operating positions of the transmission is close to the 
determined provisional position. 
In another form of the invention, the determining means determines 
satisfaction degrees of two or more basic fuzzy set theory rules, for 
example, a first basic fuzzy set theory rule Q1 for determining a degree 
in which each of the operating positions is close to the provisional 
position N*, a second basic fuzzy set theory rule Q2 for determining a 
degree in which each operating position is more or less close to the 
provisional position N*, and a third basic fuzzy set theory rule Q3 for 
determining a degree in which each operating position is very close to the 
provisional position N*. 
In a further form of the invention, the fuzzy set control rules whose 
satisfaction degrees are calculated by the first calculating means are 
formulated so as to control the transmission, depending upon various 
running parameters of the vehicle, such as: a rate of change in the 
accelerator pedal position (a rate of change in the throttle valve 
opening); a rate of change in the vehicle speed; occurrence of frequently 
repeated alternate shift-up and shift-down actions of the transmission; a 
gradient of the road surface; a difference between the actual engine speed 
and the determined target or desired engine speed; and a steering angle of 
the vehicle. The fuzzy set control rules for determining the adequacy of 
selecting the individual operating positions are selected depending upon 
the number of positions between each operating position and the currently 
established position. 
For instance, the fuzzy set control rules may consist of a first control 
rule R1 for checking the running condition to determine whether the 
transmission should be maintained in a currently established position, a 
second control rule R2 for checking the running condition to determine 
whether the transmission should be shifted up one position from the 
currently established position, a third control rule R3 for checking the 
running condition to determine whether the transmission should be shifted 
up by two or three positions from the currently established position, and 
a fourth control rule R4 for checking the running condition to determine 
whether the transmission is shifted down by one position or two or three 
positions from the currently established position. These first, second, 
third and fourth control rules R1, R2, R3 and R4 may be formulated as 
follows: R1=A and B and C; R2=A and B' and C and {(D and E) or (F and G)}; 
R3=A and B' and C and F and G; and R4=A and B' and C and (D or H), where 
"A" represents a sub-rule A for determining a degree in which the 
transmission is capable of providing a determined desired vehicle drive 
torque T.sub.D *, "B" represents a sub-rule B for determining a degree in 
which a presumed speed Ne' of an engine output shaft of the vehicle is 
close to a determined desired value Ne*, "B'" represents a sub-rule B' for 
determining a degree in which the presumed speed Ne' is very close to the 
desired value Ne*, "C" represents a sub-rule C for determining a degree in 
which the presumed speed Ne' falls within a permissible range, "D" 
represents a sub-rule D for determining a degree in which an accelerator 
pedal is kept at a constant position, "E" represents a sub-rule E for 
determining a degree in which a time T after a last shifting action of the 
transmission is long, "F" represents a sub-rule F for determining a degree 
in which the accelerator pedal is rapidly released, "G" represents a 
sub-rule G for determining a degree in which a steering angle of the 
vehicle is small, and "H" represents a sub-rule H for determining a degree 
in which the accelerator pedal is rapidly depressed. 
Alternatively, the fuzzy set control rules may be incorporated in 
respective complex control rules which include at least one basic fuzzy 
set theory rule. For example, the complex control rules consist of a first 
complex control rule R1 for checking the running condition to determine 
whether the transmission should be maintained in a currently established 
position, a second complex control rule RII for checking the running 
condition to determine whether the transmission should be shifted up one 
position from the currently established position, a third complex control 
rule RIII for checking the running condition to determine whether the 
transmission should be shifted up by two or three positions from the 
currently established position, a fourth complex control rule RIV for 
checking the running condition to determine whether the transmission is 
shifted down by one position from the currently established position, and 
a fifth complex control rule RV for checking the running condition to 
determine whether the transmission is shifted down by two or three 
positions from the currently established position. 
The complex control rules RI-RV may include one of the basic fuzzy set 
theory rules such as the rules Q1, Q2 and Q3 as described above, and one 
of the sub-rules D-H described above with respect to the fuzzy set control 
rules R1-R4, and a sub-rule I for determining a degree in which the 
accelerator pedal is placed at the non-operated position (corresponding to 
the fully closed position of the throttle valve). 
The fuzzy set control rules may include suitable sub-rules for adjusting or 
modifying the shift pattern, depending upon the type of the vehicle, load 
acting on the vehicle, specifications of the engine, and driver's desire 
or taste concerning the drivability of the vehicle. Further, some of the 
running parameters of the vehicle except for those (e.g., accelerator 
pedal position and vehicle speed) used for the shift pattern need not be 
covered by the fuzzy set control rules but may be dealt with by modifying 
the shift pattern or using two or more different shift patterns. 
The values of the satisfaction degrees of the basic fuzzy set theory 
rule(s) and fuzzy set control rules (and their sub-rules) are "1" when the 
rules are completely satisfied, and are "0" when the rules are not 
satisfied at all. Usually, the values between "1" and "0" indicate the 
degree in which the rules are satisfied. However, the satisfaction degrees 
may take only two values, i.e., either "1" or "0" . 
The second calculating means may be adapted to calculate the overall 
satisfaction degrees by obtaining an algebraic product of the satisfaction 
degrees of the at least one basic fuzzy set theory rule determined by the 
determining means and the satisfaction degrees of the fuzzy set control 
rules calculated by the first calculating means. The selecting means is 
usually adapted to select one of the operating positions of the 
transmission, whose overall satisfaction degree is the highest of all the 
overall satisfaction degrees calculated by the second calculating means. 
In the case where the fuzzy set theory rule or rules is/are included in the 
complex control rules, the satisfaction degrees of the complex control 
rules represent the overall satisfaction degrees for selecting the 
respective operating positions of the transmission. In this case, it may 
be considered that single calculating means serves as the first and second 
calculating means.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring first to FIG. 1, there is shown a part of a power transmitting 
system of a motor vehicle, which includes an automatic transmission to 
which the present invention is applicable. The automatic transmission 
includes a torque converter 10 and a planetary gear mechanism 12. The 
automatic transmission 10, 12 is controlled by a control apparatus 14 
constructed according to the present invention. 
The torque converter 10 has a pump impeller connected to an output shaft 16 
of an engine of the vehicle, and a turbine impeller connected to an input 
shaft 18 of the planetary gear mechanism 12. A lock-up clutch CL is 
provided for selectively coupling the output shaft 16 and the input shaft 
18. 
The planetary gear mechanism 12 includes a first, a second and a third 
single-pinion type planetary gear unit 20, 22, 24. The first gear unit 20 
is connected to the input shaft 18, while the second and third gear units 
22, 24 are connected to an output shaft 26 of the gear mechanism 12. The 
output shaft 26 is linked with drive wheels of the vehicle via a 
differential gear device. The first, second and third planetary gear units 
20, 22, 24 have the following component members: members which are 
integrally fixed to each other; members which are selectively connected to 
each other by means of three clutches C1, C2 and C3; members which are 
selectively fixed to a housing 28 of the transmission by means of four 
brakes B1, B2, B3 and B4; and members which are selectively connected to 
each other or fixed to the housing 28, by means of three one-way clutches 
F1, F2, F3, depending upon the direction of rotation of the driving 
members. 
The clutches C1, C2, C3 may be a multiple-disk clutch, and the brakes B1, 
B2, B3, B4 may be a band brake having a single band, or two bands whose 
winding directions are opposite to each other. These clutches and brakes 
are operated, i.e., engaged and disengaged, by suitable hydraulic 
actuators which are controlled by the control apparatus 14, so that the 
automatic transmission (planetary gear mechanism 12) is shifted from one 
operating position to another so as to change the speed ratio, i.e., speed 
of the input shaft 18/speed of the output shaft 26. As indicated in FIG. 
2, the planetary gear transmission 12 has four forward drive positions 1ST 
(first-speed position), 2ND (second-speed position), 3RD (third-speed 
position) and O/D (overdrive position), and one reverse drive position 
(Rev). The speed ratio of the transmission 10, 12 (planetary gear 
mechanism 12) decreases in steps as the transmission is shifted up in the 
direction from the first-speed position 1ST toward the overdrive position 
O/D. 
In FIG. 1, only a half of the transmission 10, 12 on one side of the axis 
of rotation is shown, because the two halves are completely symmetric with 
each other, with respect to the rotation axis. 
The control apparatus generally indicated at 14 in FIG. 1 includes a 
hydraulic control device 30 having control valves, and a microcomputer 32 
for controlling the operation of the hydraulic control device 30. The 
hydraulic control device 30 are equipped with three solenoid coils No. 1, 
No. 2 and No. 3. The coils Nos. 1 and 2 are selectively energized or 
deenergized to operate the clutches C1-C3 and brakes B1-B4, so as to 
selectively establish the operating positions of the transmission. On the 
other hand, the coil No. 3 is used to operate the lock-up clutch CL for 
directly connecting the input shaft 18 of the planetary gear mechanism 12 
to the output shaft 16 of the engine, when needed. 
To the microcomputer 32, there are connected a vehicle speed sensor 34, an 
accelerator sensor 36, a shift lever sensor 38, an engine speed sensor 40 
and a steering angle sensor 42. The vehicle speed sensor 34 generates a 
VEHICLE SPEED signal SV indicative of a running speed V (km/h) of the 
vehicle. The accelerator sensor 36 generates an ACCELERATOR POSITION 
signal S.theta.ac indicative of a currently established operating position 
.theta.ac of an accelerator pedal (corresponding to an angle of opening of 
a throttle valve of the engine). The shift lever sensor 38 generates a 
SHIFT LEVER POSITION signal SS indicative of a currently selected 
operating position of a shift lever. The engine speed sensor 40 generates 
an ENGINE SPEED signal SNe indicative of a speed Ne of the engine output 
shaft 16. The steering angle sensor 42 generates a STEERING ANGLE signal 
S.theta.s indicative of a currently established steering angle .theta.s of 
the steering wheel. The sensors 34, 36, 38, 40, 42 are provided by 
commonly used detecting means such as angular velocity detectors. 
The shift lever of the vehicle has a total of six operating positions D 
(drive), 2 (second), L (low), R (reverse), P (parking) and N (neutral). In 
the drive position D, the transmission 10, 12 is selectively placed in one 
of the four positions b 1ST, 2ND, 3RD and O/D. In the second position 2, 
the transmission is selectively placed in one of the three positions 1ST, 
2ND and 3RD. 
The microcomputer 32 incorporates a read-only memory which stores various 
control data and control programs, a random-access memory for temporarily 
storing data, and a central processing unit for controlling the solenoid 
coils Nos. 1, 2 and 3 for operating the clutches C1-C3 and brakes B1-B4 
and the lock-up clutch CL, according to the control programs stored in the 
read-only memory, and based on the control data stored in the read-only 
memory, depending upon the running condition of the vehicle, while 
utilizing the temporary data storage function of the random-access memory. 
The control data stored in the read-only memory include: shift pattern 
data for shifting the planetary gear mechanism 12; fuzzy set theory rules 
whose degrees of satisfaction are determined for the respective operating 
positions of the transmission, based on the shift pattern data; control 
rules for determining the next selected operating position of the 
transmission, according to the determined satisfaction degrees of the 
fuzzy set theory rules, depending upon the running condition of the 
vehicle; and shift pattern data for operating the lock-up clutch CL. 
The table in FIG. 2 indicates the operating states of the solenoid coils 
Nos. 1, 2 and 3, clutches C1-C3, brakes B1-B4 and one-way clutches F1-F3, 
in relation to the operating positions of the shift lever and the 
operating positions of the transmission 10, 12 (planetary gear mechanism 
12). Marks "o" and "x" associated with the solenoid coils indicate the 
energized and deenergized states of the coils, respectively. Mark "*" 
indicates the energization of the coils only when the lock-up clutch CL is 
engaged. Marks "o" associated with the clutches C1-C3 indicate the engaged 
state of the clutches, while the absence of the mark "o" indicates the 
disengaged or released state of the clutches. Marks ".DELTA." associated 
with the one-way clutches F1-F3 indicate the engagement of the one-way 
clutches when power is transmitted in the direction from the engine toward 
the vehicle drive wheels. The absence of the marks .-+..DELTA." indicates 
the released state of the one-way clutches. 
Referring next to the flow chart of FIG. 3, there will be described an 
operation of the control apparatus 14 for shifting the transmission 10, 12 
with the shift lever placed in the drive position D, for illustrative 
purpose only. 
Initially, the control flow executes step S1 to determine a provisional 
position N* to which the transmission is shifted from the currently 
established position N. This determination is effected according to the 
stored shift pattern, and based on the detected accelerator pedal position 
.theta.ac and the detected vehicle speed V. The shift pattern for the 
drive position D of the shift lever is different from that for the second 
position 2. The shift patterns are determined, with the vehicle speed V 
and accelerator pedal position .theta.ac used as parameters representative 
of the vehicle running condition. An example of the shift pattern for the 
drive position D is illustrated in a rectangular coordinate system of FIG. 
4, wherein the vehicle speed V and accelerator pedal position .theta.ac 
are taken along one and the other of the mutually perpendicular two axes. 
Stepped solid lines superposed on the coordinate system indicate shift-up 
boundaries across which the transmission is shifted up, while stepped 
broken lines indicate shift-down boundaries across which the transmission 
is shifted down. 
According to the shift pattern, three reference vehicle speeds V1, V2 and 
V3 are determined based on the currently established position N of the 
transmission and the current accelerator pedal position .theta.ac. The 
provisional position N* of the transmission which is provisionally 
selected as the position to be selected next is determined by comparing 
the currently detected vehicle speed V with those reference speeds V1, V2 
and V3. In FIG. 4, the three reference speeds V1, V2 and V3 are those 
where the transmission 10, 12 is currently placed in the third-speed 
position 3RD while the accelerator pedal position .theta.ac is 40%. If the 
currently detected vehicle speed V is equal to or lower than the first 
reference speed V1, the first-speed position 1ST is selected as the 
provisional position N*. If the current vehicle speed V is higher than the 
first reference speed V1 and is equal to or lower than the second 
reference speed V2, the second-speed position 2ND is selected as the 
provisional position N*. If the current vehicle speed V is higher than the 
second reference speed V2 and is equal to or lower than the third 
reference speed V3, the third-speed position 3RD is selected as the 
provisional position N*. The overdrive position O/D is selected as the 
provisional position N* if the current vehicle speed V is higher than the 
third reference value V3. 
The currently established position N of the transmission 10, 12 (planetary 
gear mechanism 12) is detected based on the output signals applied to the 
solenoid coils Nos. 1 and 2. The accelerator pedal position .theta.ac and 
the vehicle speed V are detected based on the ACCELERATOR POSITION signal 
S.theta.ac and VEHICLE SPEED signal SV. In the following description, it 
is assumed that the currently established position N and the determined 
provisional position N* are both the third-speed position 3RD. 
Step S1 is followed by step S2 in which degrees of satisfaction 
.gamma.Q1(j) of a basic fuzzy set theory rule Q1 are determined for the 
four operating positions 1ST, 2ND, 3RD and O/D of the transmission, where 
j=1, 2, 3, 4 corresponding to the four operating positions. The fuzzy set 
theory rule Q1 is determined depending upon whether each of the selectable 
operating position of the transmission is close to the determined 
provisional position N*, that is, depending upon the number of positions 
between the provisional position N* and each selectable position. For 
example, the satisfaction degree .gamma.Q1(j) for the provisional position 
N* is equal to 1, and the satisfaction degrees .gamma.Q1(j) for the 
positions N*.+-.1 adjacent to the provisional position N* are equal to 
0.5. Similarly, the satisfaction degrees .gamma.Q1(j) for the positions 
N*.+-.2 are equal to 0.25, and the satisfaction degrees .gamma.Q1(j) for 
the positions N*.+-.3 are equal to 0.15. FIG. 5 indicates the satisfaction 
degrees .gamma.Q1(j) of the basic fuzzy set theory rule Q1 for the four 
operating positions (1ST, 2ND, 3RD and O/D) where the provisional position 
N* is the third-speed position 3RD. In FIG. 5, numerals 1, 2, 3 and 4 
indicate the first-speed, second-speed, third-speed and overdrive 
positions 1ST, 2ND, 3RD and O/D which are selectively established while 
the shift lever is placed in the drive position D. In the present 
embodiment, the portions of the microcomputer 32 assigned to execute steps 
S1 and S2 constitute means for determining the satisfaction degrees 
.gamma.Q1(j) of the fuzzy set theory rule for the operating positions of 
the transmission, based on the predetermined shift pattern. 
Then, the control flow goes to step S3 in which the variable "j" is set to 
"1". Step S3 is followed by step S4 in which a difference .DELTA.N between 
"j" and N (currently selected position) is calculated. Step S5 is then 
executed to calculate satisfaction degree .gamma.R(j) of fuzzy set control 
rules for the four operating positions of the transmission, depending upon 
the currently detected running condition of the vehicle. More 
specifically, different fuzzy set control rules R1, R2, R3 and R4 are used 
depending upon the value of the calculated difference .DELTA.N. The 
control rules R1-R4 use sub-rules A, B, B', C, D, E, F, G and H, as 
indicated below: 
______________________________________ 
R1 = A and B and C 
R2 = A and B' and C and {(D and E) or (F and G)} 
R3 = A and B' and C and F and G 
R4 = A and B' and C and (D or H) 
______________________________________ 
The control rule R1 is used where .DELTA.N =0, to check the vehicle running 
condition in which the currently established position N should be 
maintained or not. The control rule R2 is used where .DELTA.N =+1, to 
check the vehicle running condition in which the transmission should be 
shifted up by one position from the current position N. The control rule 
R3 is used where .DELTA.N =+2 or +3, to check the vehicle running 
condition in which the transmission should be shifted up by two or three 
positions from the current position N. The control rule R4 is used where 
.DELTA.N=-1, -2 or -3, to check the vehicle running condition in which the 
transmission should be shifted down by one, two or three positions from 
the current position N. 
The sub-rules A, B, B', C, D, E, F, G and H will be described. 
SUB-RULE A 
Possible to provide desired vehicle drive torque T.sub.D * 
The vehicle drive torque that is produced in each operating position of the 
transmission is determined by the characteristics of the engine. The 
sub-rule A is used to determine whether the determined desired or target 
vehicle drive torque T.sub.D * is equal to or smaller than the maximum 
torque that can be produced in the relevant selected position of the 
transmission. An example of a membership function f.sub.A (T.sub.D *) 
which indicates the degree of satisfaction of the sub-rule A is 
illustrated in FIG. 6. Threshold values C1 and C2 are predetermined by 
calculation or based on experimental data and stored in the microcomputer 
32, for each of the operating positions of the transmission which are 
represented by the variable "j". The logical value of the membership 
function f.sub.A (T.sub.D *) is between "0" and "1" (inclusive). The 
sub-rule A is completely satisfied when the value of the membership 
function is "1". This applies to other membership functions which will be 
described. It is noted that the desired vehicle drive torque T.sub.D * is 
determined by a predetermined relationship between the value T.sub.D * and 
the vehicle speed V and accelerator pedal position .theta.ac, as indicated 
in FIG. 12 by way of example. This relationship is represented by data map 
stored in the read-only memory of the microcomputer 32. 
SUB-RULE B 
Presumed engine output speed Ne' close to desired speed Ne* 
This sub-rule B is provided to select the optimum operating position of the 
transmission, based on the determined desired speed Ne*, in the case where 
the desired vehicle drive torque T.sub.D * is relatively small and can be 
produced in every one of the operating positions of the transmission. To 
this end, a presumed speed Ne' of the engine output shaft 16 (i.e., engine 
speed) is determined for each of the operating positions (represented by 
the variable "j"), as a function of the vehicle speed V or speed ratio of 
the operating positions. To select the optimum operating position, a 
determination is made for each operating position, as to whether the 
determined desired speed Ne* falls within a predetermined range whose 
center is the presumed speed Ne'. An example of a membership function 
f.sub.B (Ne*) indicative of the degree of satisfaction of this sub-rule B 
is indicated in solid lines in FIG. 7. The desired speed Ne* is determined 
by a predetermined relationship between the value Ne* and a desired 
horsepower PS (proportional to desired drive torque T.sub.D * x vehicle 
speed V), as indicated in FIG. 13 by way of example. This relationship is 
predetermined for an optimum compromise between the fuel economy and 
operating stability (freedom from knocking) of the engine, and is 
represented by data map stored in the microcomputer 32. 
SUB-RULE B' 
Presumed engine output speed Ne' very close to desired speed Ne* 
This sub-rule B' is substantially the same as the above sub-rule B, but 
uses a membership function f.sub.B '(Ne*) different from that of the 
sub-rule B, so as to determine whether the desired speed Ne* falls within 
a predetermined range narrower than that of the sub-rule B. This sub-rule 
B' is used to determine whether the transmission should be shifted from 
the current position to another. An example of the membership function 
f.sub.B '(Ne*) which represents the satisfaction degree of this sub-rule 
B' is indicated in one-dot chain lines in FIG. 7. 
SUB-RULE C 
Presumed speed Ne' falling within a permissible range 
This sub-rule C is provided to protect the engine against abnormal or 
undesired operating conditions. More specifically, the engine may stall if 
the engine speed Ne is too low, and may be overrun if the engine speed is 
too high. To avoid this abnormal conditions or maintain the engine speed 
Ne within a permissible or safe-running range, the sub-rule C is used to 
determine whether the presumed output shaft speed Ne' falls within the 
permissible range. An example of a membership function f.sub.C (Ne') 
representing the satisfaction degree of this sub-rule C is illustrated in 
FIG. 8. Threshold values C3 and C4 indicated in FIG. 8 are predetermined 
depending upon the specific operating characteristics of the engine. 
SUB-RULE D 
Accelerator position kept constant 
The accelerator position .theta.ac corresponding to the angle of opening of 
the engine throttle valve represents the engine output required by the 
vehicle driver, namely, the driver's intention to shift the transmission. 
A change of the accelerator position can be detected based on a rate 
.theta.ac (d.theta.ac/dt) of change of the accelerator position .theta.ac. 
This sub-rule D is used to determine whether the accelerator pedal 
position is kept constant, that is, whether the vehicle driver wishes to 
maintain the currently established operating position of the transmission, 
or not. An example of a membership function f.sub.D (.theta.ac) which 
represents the satisfaction degree of the sub-rule D is illustrated in 
solid line in FIG. 9. 
SUB-RULE E 
Time T after the last shifting action exceeding a predetermined threshold 
This sub-rule E is provided to avoid frequent shifting actions of the 
transmission at excessively short time intervals. An example of a 
membership function f.sub.E (T) representing the satisfaction degree of 
this sub-rule E is illustrated in FIG. 10. 
SUB-RULE F 
Rapid accelerator pedal release 
This sub-rule F is provided to determine whether the accelerator pedal is 
rapidly released, or not, namely, whether the rate .theta.ac of change of 
the accelerator position .theta.ac in the negative position (toward the 
non-operated position) exceeds a predetermined threshold, or not. An 
example of a membership function f.sub.F (.theta.ac) representing the 
satisfaction degree of this sub-rule F is illustrated in one-dot chain 
line in FIG. 9. 
SUB-RULE G 
Vehicle not running on a curved road 
This sub-rule is provided to avoid a shift-up operation of the transmission 
upon releasing of the accelerator pedal when the vehicle curves. If the 
steering angle .theta.s is smaller than a predetermined threshold, this 
means that the vehicle is not running along a curve. An example of a 
membership function f.sub.G (.theta.s) representing the satisfaction 
degree of this sub-rule G is illustrated in FIG. 11. 
SUB-RULE H 
Rapid accelerator pedal depression 
This sub-rule H is provided to determine whether the accelerator pedal is 
rapidly depressed or not, namely, whether the rate .theta.ac of change in 
the accelerator position .theta.ac in the positive direction (toward the 
fully operated position) is larger than a predetermined threshold. An 
example of a membership function f.sub.H (.theta.ac) representing the 
satisfaction degree of this sub-rule H is illustrated in two-dot chain 
lines in FIG. 9. 
According to the fuzzy set theory, "and" represents an algebraic 
multiplication (ordinary multiplication), or a minimum operation, and "or" 
represents a logical sum or a maximum operation. Where the "and" and "or" 
represent the algebraic multiplication and the maximum operation, 
respectively, satisfaction degrees .gamma.R(j) of the fuzzy set control 
rules R1, R2 R3 and R4 are obtained from the following equations (1), (2), 
(3) and (4), respectively: 
##EQU1## 
In the case where j=1, and N (currently established position) =3, the 
difference .DELTA.N between j and N is equal to "-2", whereby the 
satisfaction degree .gamma.R(1) of the fourth control rule R4 is 
calculated in step S5 of the flow chart of FIG. 3, according to the 
corresponding equation (4). 
Then, the control flow goes to step S6 to calculate the overall 
satisfaction degree .gamma.(1), according to the following equation (5), 
by algebraic multiplication of the satisfaction degree .gamma.R(1) 
obtained in step S5 and the satisfaction degree .gamma.Q1(1) obtained in 
step S2. The calculated overall satisfaction degree .gamma.(1) means the 
degree of adequacy in which the transmission should be shifted from the 
current position N to the first-speed position 1ST. 
EQU .gamma.(j)=.gamma.R(j).times..gamma.Q1(j) (5) 
Step S6 is followed by step S7 to determine whether the variable "j" is 
smaller than "4" or not. If the variable "j" is smaller than "4", the 
control flow goes to step S8 to increment the variable "j", and returns to 
step S4. Steps S4 through S8 are repeatedly executed until the variable 
"j" becomes equal to "4". In this manner, the overall satisfaction degrees 
.gamma.(1), .gamma.(2), .gamma.(3) and .gamma.(4) for selecting the 
positions 1ST, 2ND, 3RD and O/D of the transmission are calculated one 
after another. 
More specifically, where j=2, the difference .DELTA.N is equal to "-1". 
Consequently, the satisfaction degree .gamma.R(2) of the control rule R4 
for selecting the second-speed position 2ND is calculated in step S5 
according to the equation (4), and the overall satisfaction degree 
.gamma.(2) for selecting the second-speed position 2ND is calculated in 
step S6 according to the above equation (5). Where j=3, the difference 
.DELTA.N is equal to "0" , and the satisfaction degree .gamma.R(3) of the 
control rule R1 for selecting the third-speed position 3RD is calculated 
in step S5 according to the equation (1). The overall satisfaction degree 
.gamma.(3) for the third-speed position 3RD is calculated in step S6 
according to the above equation (5). Where j=4, the difference .DELTA.N is 
equal to "+1", and the satisfaction degree .gamma.R(4) of the control rule 
R2 for selecting the overdrive position O/D is calculated in step S5 
according to the equation (2). The overall satisfaction degree .gamma.(4) 
for the overdrive position O/D is calculated in step S6 according to the 
above equation (5). 
An example of the satisfaction degrees .gamma.R(j) calculated in step S5 is 
indicated in FIG. 14, and an example of the overall satisfaction degrees 
.gamma.(j) calculated in step S6 is indicated in FIG. 15. In the present 
embodiment, the portions of the microcomputer 32 assigned to execute step 
S5 constitute first calculating means for calculating the satisfaction 
degrees .gamma.R(j) of fuzzy set control rules for the different operating 
positions of the transmission, depending upon the running condition of the 
vehicle. Further, the portions of the microcomputer 32 assigned to execute 
step S6 constitute second calculating means for calculating overall 
satisfaction degrees .gamma.(j) for selecting the operating positions, 
based on the satisfaction degrees .gamma.Q1(j) determined in step S2, and 
the satisfaction degrees .gamma.R(j) calculated in step S5. 
In the present example wherein the currently established position N of the 
transmission is the third-speed position 3RD, the control rule R3 for the 
difference .DELTA.N=2 or 3 is not used. However, this control rule R3 is 
used for calculating the satisfaction degree for selecting the third-speed 
or overdrive position 3RD or O/D, where the transmission is currently 
placed in the first-speed or second-speed position 1ST or 2ND. 
When the variable "j" becomes equal to "4" as a result of repetition of 
steps S4 through S8, a negative decision (NO) is obtained in step S7, and 
the control flow goes to step S9 in which the highest or maximum overall 
satisfaction degree .gamma.(k) is selected from the four values .gamma.(j) 
calculated in step S6. In the example of FIG. 15, the overall satisfaction 
degree .gamma.(2) is selected as the highest satisfaction degree 
.gamma.(k). Namely, "k" is determined as "2". In the next step S10, the 
second-speed position 2ND represented by k=2 is determined as the position 
to which the transmission is shifted from the current position N 
(third-speed position 3RD). According to this determination, the solenoid 
coils Nos. 1 and 2 are both energized to shift down the planetary gear 
mechanism 12 from the third-speed position 3RD to the second-speed 
position 2ND. Portions of the microcomputer 32 assigned to execute steps 
S9 and S10 constitute means for determining, based on the determined 
highest overall satisfaction degree .gamma.(k), the position to which the 
transmission (10, 12) is shifted. 
In the control apparatus 14 including the microcomputer 32 and the 
hydraulic control device 30, satisfaction degrees .gamma.Q1(j) of the 
basic fuzzy set theory rule Q1 are determined in steps S1 and S2, for each 
of the operating positions of the transmission, based on the predetermined 
shift pattern. Further, the satisfaction degrees .gamma.R(j) of the 
control rules R1-R4 are determined in step S5, for the individual 
operating positions, depending upon the running condition of the vehicle 
(represented by the satisfaction degrees of the sub-rules). Based on the 
obtained satisfaction degrees .gamma.Q1(j) and .gamma.R(j), the overall 
satisfaction degrees .gamma.(j) for selecting the individual positions of 
the transmission are calculated in step S6. Based on the highest value 
.gamma.(k) of the calculated overall satisfaction degrees .gamma.(j) is 
determined in step S9, and one of the positions of the transmission is 
determined in step S10 as the position to be established next, i.e., as 
the position to which the transmission is shifted from the current 
position. Therefore, the present control apparatus 14 permits the 
transmission to be shifted to the most optimum position, depending upon 
the various running parameters of the vehicle (which collectively define 
the running condition), which cannot be dealt with by the arrangement 
adapted to control the transmission based on only predetermined shift 
patterns which use the accelerator position .theta.ac and vehicle running 
speed V as the control parameters. 
Further, the present control apparatus 14 which relies on both the shift 
patterns and the fuzzy set control rules as explained above requires a 
reduced amount of control program data, as compared with an arrangement 
which uses many shift patterns and pattern compensating maps to control 
the transmission depending upon many running parameters of the vehicle. 
Where the control rules are used to monitor the vehicle running parameters 
for determining the position of the transmission to be established next, 
the required amount of control data is proportional to the number of the 
parameters. Where the shift patterns or compensating maps are provided 
corresponding to many different running conditions (combinations of 
running parameters) of the vehicle, the number of the required patterns or 
compensating maps is proportional to the number of the running parameters 
raised to n-th power. Accordingly, the required amount of control program 
data exponentially increases as the number of the parameters increases for 
improving the shift control accuracy of the transmission. 
It is also noted that the present control apparatus 14 uses the two shift 
patterns, one for the drive position D of the shift lever, and the other 
for the second position 2. Each shift pattern is formulated with the 
vehicle speed V and accelerator position .theta.ac used as the two basic 
parameters. This arrangement reduces the required overall amount of 
control program data, as compared with the arrangement which uses only the 
fuzzy set control rules. The graph in FIG. 16 shows the required amounts 
of control program data, in relation to the number of the running 
parameters of the vehicle used for controlling the transmission. Solid 
line indicates the amount required by the control apparatus 14 of the 
present invention, while one-dot chain line indicates the amount required 
by the arrangement which uses only the fuzzy set control rules. Two-dot 
chain line indicates the amount required by the arrangement which uses 
only the shift patterns and pattern compensating data maps. 
In the present control apparatus 14, the overall satisfaction degrees 
.gamma.(j) for all the selectable operating positions of the transmission 
are calculated, and the position to be established next is selected based 
on the highest satisfaction degree .gamma.(j). This arrangement does not 
require a procedure otherwise required for improving the control accuracy, 
as practiced in the arrangement wherein the shift patterns are compensated 
or modified by obtaining the center of distribution of the calculated 
satisfaction degrees of the fuzzy set control rules. In this respect, too, 
the present control apparatus 14 reduces the required amount of the 
control program data. However, the present control apparatus may be 
modified to determine the optimum shift position of the transmission, in 
consideration of the center of the one-dimensional or two-dimensional 
distribution of the calculated satisfaction degrees .gamma.(j). 
In the present control apparatus 14, the membership functions representing 
the satisfaction degrees of the sub-rules A, B, B' and C-H include a 
gradient or gradients as indicated in FIGS. 6-11, so that the manner of 
controlling the transmission may be adjusted so as to meet the driver's 
desire or intention, by suitably determining the gradient or gradients. In 
addition, the operation of the present control apparatus 14 adapted to 
control the transmission according to the fuzzy set theory is less likely 
to be significantly influenced by malfunction or trouble of any sensors 
34, 36, 38, 40, 42 used to detect the running parameters (running 
condition) of the vehicle. Generally, it is difficult to accurately detect 
the rate .theta.ac of change of the accelerator position .theta.ac. 
However, the determination of the next selected shift position k according 
to the fuzzy set theory is not considerably affected by an error in the 
measurement of the rate. 
Referring next to FIG. 17, another embodiment of the present invention will 
be described. The control program used in this embodiment is different 
from that in the preceding embodiment, only in terms of steps SS2 and SS5. 
Step SS2 is substituted for step S2, while step SS5 is substituted for 
steps S5 and S6. In the interest of brevity and simplification, only these 
steps SS2 and SS5 will be described. 
In step SS2' satisfaction degrees .gamma.Q1(j), .gamma.Q2(j and 
.gamma.Q3(j) of respective three basic fuzzy set theory rules Q1, Q2 and 
Q3 are determined for each of the selectable operating positions of the 
transmission. The basic fuzzy set theory rule Q1 is the same as described 
above with respect to the preceding embodiment. Namely, the satisfaction 
degrees .gamma.Q1(j) of the rule Q1 are determined as indicated in FIG. 5, 
depending upon whether each of the selectable positions of the 
transmission is close to the determined provisional position N*. The 
satisfaction degrees .gamma.Q2(j) of the basic fuzzy set theory rule Q2 
are determined depending upon whether each selectable position of the 
transmission is more or less close to the provisional position N*. The 
satisfaction degrees .gamma.Q3(j) of the basic fuzzy set theory rule Q3 
are determined depending upon whether each selectable position is very 
close to the provisional position N*. Examples of the satisfaction degrees 
.gamma.Q2(j) and .gamma.Q3(j) of the rules Q2 and Q3 where the third-speed 
position 3RD is the provisional position N* are illustrated in FIGS. 18 
and 19, respectively. Namely, the values of the satisfaction degrees 
.gamma.Q2(1), .gamma.Q2(2) and .gamma.Q2(4) for the first-speed, 
second-speed and overdrive positions 1ST, 2ND and O/D are comparatively 
larger than the corresponding satisfaction degrees .gamma.QI(1), 
.gamma.Q1(2) and .gamma.Q1(4), and the values of the satisfaction degrees 
.gamma.Q3(1), .gamma.Q3(2) and .gamma.Q3(4) for the first-speed, 
second-speed and overdrive positions 1ST, 2ND and O/D are comparatively 
smaller than the corresponding satisfaction degrees .gamma.Q1(1), 
.gamma.Q1(2) and .gamma.QI(4). 
In step SS5, overall satisfaction degrees .gamma.(j) of five complex 
control rules RI, RII, RIII, RIV and RV are determined for each selectable 
operating position of the transmission, depending upon the detected 
running condition (running parameters) of the vehicle. As indicated below, 
the complex control rules RI, RII, RIII, RIV and RV use the basic fuzzy 
set theory rules Q1, Q2 and Q3, as well as the fuzzy set control rules 
consisting of the sub-rules D, E, F, G and H (explained above) and an 
additional sub-rule I. Although the rule RI uses only the basic fuzzy set 
theory rule Q2, the rule RI is referred to as "complex control rule" for 
distinction from the fuzzy set control rules R1-R4 used in the first 
embodiment. The sub-rule I is used to determine whether the accelerator 
pedal is positioned at the non-operated position (corresponding to the 
fully closed position of the throttle valve). An example of a membership 
function f.sub.I (.theta.ac) representing the satisfaction degree of the 
sub-rule I is illustrated in FIG. 20. The complex control rule RI is used 
where .DELTA.N=0, to check the vehicle running condition in which the 
currently established position N should be maintained or not. The complex 
control rule RII is used where .DELTA.N=+1, to check the vehicle running 
condition in which the transmission should be shifted up by one position 
from the current position N. The complex control rule RIII is used where 
.DELTA.N=+2 or +3, to check the vehicle running condition in which the 
transmission should be shifted up by two or three positions from the 
current position N. The complex control rule RIV is used where 
.DELTA.N=-1, to check the vehicle running condition in which the 
transmission should be shifted down by one position from the current 
position N. The complex control rule RV is used where .DELTA.N=-2 or -3, 
to check the vehicle running condition in which the transmission should be 
shifted down by two or three positions from the current position N. 
______________________________________ 
RI = Q2 
RII = Q1 and {(D and E) or F} 
RIII = Q3 and F 
RIV = Q1 and (H or I) 
RV = Q3 and G and H 
______________________________________ 
Where "and" and "or" represent the algebraic multiplication and maximum 
operation, respectively, the satisfaction degrees .gamma.(j) of the 
complex control rules RI-RV are obtained from the following equations (6), 
(7), (8), (9) and (10), respectively: 
##EQU2## 
In the case where N (currently established position) =3, and j=1, the 
difference .DELTA.N between j and N is equal to "-2", whereby the 
satisfaction degree .gamma.(1) of the complex control rule RV is 
calculated according to the corresponding equation (10). Where j=2, the 
difference .DELTA.N is equal to "-1". Consequently, the satisfaction 
degree .gamma.(2) of the complex control rule RIV for selecting the 
second-speed position 2ND is calculated according to the equation (9). 
Where j=3, the difference .DELTA.N is equal to "0" , and the satisfaction 
degree .gamma.(3) of the complex control rule RI for selecting the 
third-speed position 3RD is calculated according to the equation (6). 
Where j=4, the difference .DELTA.N is equal to "+1", and the satisfaction 
degree .gamma.(4) of the control rule RII for selecting the overdrive 
position O/D is calculated according to the equation (7). 
After the satisfaction degrees .gamma.(1), .gamma.(2), .gamma.(3) and 
.gamma.(4) have been calculated in step SS5 and a negative decision (NO) 
is obtained in step S7, the control flow goes to step S9 in which the 
highest value .gamma.(k) is selected from the calculated four satisfaction 
degrees in step S9, and then goes to step S10 for determining the position 
k as the position to which the transmission is shifted. It will be 
understood, however, that where the provisional position N* determined 
based on the appropriate shift pattern is the currently established 
position N, the satisfaction degree .gamma.(j) of the complex control rule 
RI is "1", that is, the complex control rule RI is completely satisfied, 
whereby the currently established position N is maintained, irrespective 
of the detected running condition of the vehicle (represented by the 
sub-rules). 
The present embodiment of FIG. 17 provides the same advantages as the 
preceding embodiment of FIG. 3. In addition, the use of the three basic 
fuzzy set theory rules Q1, Q2 and Q3 to obtain the satisfaction degrees 
.gamma.Q1(j), .gamma.Q2(j) and .gamma.Q3(j) permits the transmission to be 
controlled in a manner that more suitably meets the driver's desire or 
taste. Further, the overall satisfaction degrees .gamma.(j) of the complex 
control rules RI, RII, RIII, RIV and RV which include one of the three 
fuzzy set theory rules Q1, Q2, Q3 are calculated in one step in step SS5. 
Accordingly, the required amount of control program data is further 
reduced. 
In the present modified embodiment, the portions of the microcomputer 32 
assigned to execute steps S1 and SS2 constitute means for determining the 
satisfaction degrees .gamma.QI(j), .gamma.Q2(j) and .gamma.Q3(j), based on 
the predetermined shift pattern. Further, the portions of the 
microcomputer 32 assigned to execute step SS5 serve as first calculating 
means for calculating the satisfaction degrees of the sub-rules D through 
I, depending upon the running condition of the vehicle. The portions of 
the microcomputer 32 assigned to execute step SS5 also serve as second 
calculating means for calculating the overall satisfaction degrees 
.gamma.(j), by multiplying the satisfaction degrees calculated by the 
first calculating means, by the satisfaction degrees .gamma.Q1(j), 
.gamma.Q2(j) and .gamma.Q3(j) determined in step SS2 by the determining 
means. Thus, it will be understood that the sub-rules D through I of the 
complex control rules RI-RV correspond to the fuzzy set control rules 
R1-R4 of the preceding embodiment. 
While the present invention has been described in its presently preferred 
embodiments, it is to be understood that the invention is not limited to 
the details of the illustrated embodiment, and may be otherwise embodied. 
While the preceding embodiment uses the three basic fuzzy set theory rules 
Q1, Q2 and Q3 as illustrated in FIGS. 5, 18 and 19, it is possible to use 
other basic fuzzy set theory rules such as Q4 and Q5 as illustrated in 
FIGS. 21 and 22, respectively. The basic fuzzy set theory rule Q4 is 
formulated so as to give a larger weight to a high-gear position 
(overdrive position O/D) of the transmission which has a lower speed ratio 
than the determined provisional position N* (third-speed position 3RD, in 
the illustrated embodiment). On the other hand, the rule Q5 is formulated 
so as to give larger weights to low-gear positions of the transmission 
which have higher speed ratios than the provisional position N*. 
In the illustrated embodiments, the logical values of the satisfaction 
degrees of the basic fuzzy set theory rules Q1, Q2, Q3 (Q4, Q5) are set to 
"1" for the provisional position N*, while those for the other positions 
are smaller than "1". The logical values of the satisfaction degrees of 
these rules may be set otherwise for improved accuracy, for example, 
according to arithmetic equations based on the actually detected vehicle 
running speed V and the reference values V1, V2, V3 used for the shift 
pattern. 
In the illustrated embodiments, the shift pattern used for the shift lever 
position D is defined by 90.degree.-stepped shift-up and shift-down 
boundaries represented in a rectangular coordinate system wherein the 
accelerator position .theta.ac and the vehicle speed V are taken along the 
mutually perpendicular axes, as indicated in FIG. 4. However, the shift 
pattern boundaries may be defined by straight, curved or other lines. 
Further, the shift pattern may use parameters other than the accelerator 
position .theta.ac and the vehicle speed V. The shift pattern may be 
modified or compensated according to a suitable data map, so as to meet 
the specific characteristics of the vehicle engine or the driver's taste, 
so that the provisional position N* is determined according to the 
compensated shift pattern. 
Although the "and" and "or" used in the furry set control rules R1-R4 and 
complex control rules RI-RV represent the algebraic multiplication and the 
maximum operation, respectively, the "and" and "or" may be defined to 
represent other operations. Further, the fuzzy set control rules or 
complex control rules may use operators other than "and" and "or". 
While the automatic transmission 10, 12 controlled by the control apparatus 
14 of the illustrated embodiments has four forward drive positions and one 
rear drive position and is provided with the lock-up clutch C.sub.L, the 
control apparatus according to the present invention may apply to other 
types of automatic transmission, whose planetary gear mechanism (12) is 
constructed otherwise to provide desired drive positions. The automatic 
transmission to which the present invention is applicable may be 
constructed without a lock-up clutch. 
It will be understood that the invention may be embodied with various other 
changes, modifications and improvements, which may occur to those skilled 
in the art, without departing from the spirit and scope of the invention 
defined in the following claims.