Fuzzy Application Library/Technical Applications/Fuzzy in Appliances
Fuzzy Logic and NeuroFuzzy in Appliances
by Constantin von Altrock
Citation Reference: This paper was published at the Embedded Systems Conferences in 1994, 1995, and 1996 in Santa Clara.
Fuzzy Logic is an innovative technology that enables the implementation of 'intelligent' functions in embedded systems. One of its advantages is that even complicated functions and adaptive control loops can be implemented with the limited resources of low-cost 8 bit microcontrollers. Using three case studies in ABS, engine control, and automatic gearbox control, we will show how superior performance is achieved using fuzzy logic and neural-fuzzy design techniques. We will discuss development methodologies, tools used, and code speed/size requirements of three case studies.
The first case study shows how an existing product is enhanced with new, intelligent functions. In home air conditioners, the enhancement of the thermostat by fuzzy logic control techniques allows for a better adaptation to the requirements of the user. This results in a higher comfort level. Also, detection of low load situations yields energy savings.
The second case study covers the replacement of sensors with fuzzy logic state estimators. In the example of a central heating system control, a 35 outdoor temperature sensor and its installation were replaced. Comparisons show that the fuzzy logic solution better adapts to high and low heat demand periods, thus yielding higher comfort and energy savings at the same time. The presented system is now in production in Germany (350,000 units per year).
The third case study focuses on the automated generation of fuzzy logic systems or parts thereof. For laundry load detection in washing machines, neural-fuzzy technologies are employed that set up a fuzzy logic system using experimental data. The results of washing experiments, evaluated by experts, form this data base. The introduction of the resulting fuzzy logic laundry load detector saves an average of 20% on water and energy. The presented system is now in production in Germany (400,000 units per year).
The following discussion assumes the reader is familiar with basic fuzzy logic design principles. For a comprehensive hands-on course in practical fuzzy logic design, refer to [14].
1. Energy Saving AC Control
One of the major consumers of the total of all energy produced in the world is the heating and cooling of homes and office buildings. Hence, increasing efficiency of these systems has a great effect on energy savings. These savings can be realized either by constructional improvements, such as better insulation, more efficient heating/cooling systems or by using more intelligent control strategies for the operation of these devices. This case study focuses on the application of fuzzy logic control techniques for air conditioning systems.
Fuzzy logic allows for the formulation of a technical control strategy using elements of everyday language. In this application, fuzzy logic was used to design a control strategy that adapts to the individual user needs, thereby achieving both a higher comfort level and reduced energy consumption at the same time. Using a fuzzy logic software development system, the entire system, containing both conventional code for signal preprocessing and the fuzzy logic system, can be implemented on industry standard 8-bit microcontrollers. Using fuzzy logic on such a low-cost platform enables this solution to be implemented in most air conditioning systems.
Fuzzy Logic in AC Control
Quite a few air conditioning systems already use fuzzy logic control. In 1990, Mitsubishi introduced their first line of fuzzy logic controlled home air conditioners. Also, industrial air conditioning systems in Japan have been using fuzzy logic [7] since 1990. Four years later, most Korean, Taiwanese, and European AC controllers also use fuzzy logic as a standard control technique [6, 1, 15].There are different incentives to use fuzzy logic:
Air Condition Control Thermostats
The application discussed in this case study falls more into the second category. Each AC system has a thermostat that measures the room temperature and compares it with the set temperature that is set on a dial. Figure 1 shows the principle of such a thermostat.
Figure 1: A Conventional Thermostat Compares Room Temperature with the Set Temperature to Turn AC On and Off (large) |
The thermostat compares the set temperature that is selected on the dial by the user with the actual room temperature. To minimize the number of starts for the AC, a hysterisis is used. Both mechanical and electronic thermostats are used for this. Figure 1 shows the principle of an electronic analog AC controller.
Intelligent Fuzzy Logic Thermostat
This method works well to maintain a certain temperature level in a room. However, the actual room temperature does not always correspond to the subjective temperature feeling of the people in the room. A certain comfort level is reached with different room temperatures, depending on a number of conditions:
Empirical analysis on how people adjust the temperature dial on their ACs has shown even more factors:
The objective in this case study is to design an "intelligent" thermostat that "understands" both different environment conditions and the current needs of the user. For this, knowledge as contained in 1.-2. and A)-D) must be implemented in the thermostat. Since this kind of knowledge is hard to model mathematically, as well as hard to code in a conventional algorithm, fuzzy logic has been used for implementation.
Figure 2: Fuzzy Thermostat (large) |
Figure 2 shows the structure of the "intelligent" thermostat. To measure the brightness in the room, a LDR photo sensor is added. The fuzzy logic system corrects the signal before the threshold unit and sets its hysterisis. For that, the fuzzy logic system uses four input variables:
1. Difference between set and room temperature (Temp_Error)
When the difference between set temperature and room temperature is very large, the fuzzy logic system increases the signal so the desired temperature is reached faster (Rule 5 and 6). At the same time, the hysteresis is set to large, so minor disturbances do not cause unnecessary on/off switches.
2. Time differentiated set temperature (dTemp_by_dt)
The set temperature signal is differentiated with a time constant of 30 minutes. The fuzzy logic system uses this signal to understand when the user wants the AC to cool down a room quick (Rule 3). Also, the hysterisis is set large, so disturbances do not interrupt the cooling process. As this signal is a differentiated signal, it disappears if the user does not modify the dial.
3. Number of set temperature changes (Changes)
This input signal is used to identify a user who tries to set the room temperature very precisely (Rule 4). To satisfy such a user, the hysterisis is set to small. This variable counts each time the user moves the dial. Every 6 hours, this variable is counted down until 0 is reached.
4. Brightness in the room (Brightness)
If direct sunlight hits the room, the set temperature is automatically reduced (Rule 2). During the day or when lights are on in the room, the set temperature is slightly increased (Rule 1) and the hysterisis is set to small.
Figure 3: Structure of the Fuzzy Logic System in the Thermostat (large) |
Implementation of a Fuzzy Logic Control Strategy
Figure 3 shows the structure of the fuzzy logic system as designed with the fuzzyTECH development system [2]. All input variables have three (3) terms with standard membership functions. The output variable "Correction" has five (5) terms and uses Center-of-Maximum defuzzification. The output variable "Hysterisis" has three (3) terms and uses also Center-of-Maximum defuzzification.
Figure 4: The Fuzzy Logic Rules Represent the Knowledge That the Thermostat Uses to Correct the Set Temperature and the Hysterisis (large) |
Figure 4 shows part of the rule base that defines the strategy of the system. This spread sheet representation is appropriate for small rule bases. Each row represents a rule. The left part of the screen under the [IF] button shows all input variables of the rule block; the right part under the [THEN] button shows all output variables. The column [DoS] that is displayed for each output variable allows for the association of a weight to this conclusion. This enables fine tuning of the fuzzy logic system during optimization.
Simulation Results and Comparison
The fuzzy logic system has been tested using data that has been recorded in various rooms under various conditions. This test data has been preprocessed using the spreadsheet software MS-Excel™. To test the performance of the fuzzy logic solution, fuzzyTECH's Excel link has been used. It allows for MS-Excel cells be linked to fuzzy logic input and output variables. As this link is dynamic, the fuzzy logic system can be monitored and modified using the fuzzyTECH analyzers and editors while browsing through the data sets.
As a result, the room temperature as controlled by the fuzzy logic thermostat, results in an increased comfort level. In addition, the fuzzy logic thermostat detected situations where less cooling effort suffices. The simulation revealed that in an average residential house, the average energy consumption was reduced by 3.5%. At the same time, the comfort level was increased, since, depending on the situation, the fuzzy logic thermostat reduced the room temperature 5°F more than the conventional thermostat.
The fuzzy logic thermostat does not require any modification of the AC itself. Hence, by replacing existing temperature controllers, even old ACs can be upgraded. By also controlling the ventilation, an even more improved performance could be reached.
Picture of a Home Air Conditioner |
2. Adaptive Heating System Control
To maximize both the economics and comfort of a private home heating system, fuzzy-logic control has been used by a German company in a new generation of furnace controllers [13]. The fuzzy-logic controller ensures optimal adaptation to changing customer heating demands while using one sensor less than the former generation. Both the fuzzy-logic controller and the conventional control system were implemented on a standard 8-bit microcontroller. Design, optimization and implementation of the fuzzy controller were supported by the software development system fuzzyTECH.
European Heating Systems
Most European houses have a centralized heating system that uses a furnace for diesel-type fuel to heat the water supply (boiler). From the boiler, the hot water is distributed by a pipe system to individual radiators in the rooms of the house. To meet the different needs of customer heating habits, the temperature of the furnace-heated water must constantly be adjusted in relation to the outdoor temperature (heat characteristic). To measure the outdoor temperature, a sensor is installed on the outside of the house.
Viessmann Home Heating System (large). |
The basic structure of a controller for this system is shown in Figure 6. The controller itself realizes an on-off characteristic. If the water temperature in the furnace drops to 2 Kelvin below the set temperature, the fuel valve opens and the ignition system starts the burning process. When the water temperature in the boiler itself rises to 2 Kelvin above the set temperature, the fuel valve closes. This on-off control strategy involving hysterisis minimizes the number of starts while assuring that the boiler temperature remains within the desired tolerance.
Figure 5: Schematic of a Centralized Heating System (large) |
Although the structure of this control loop is quite simple, the task of determining the appropriate set boiler temperature is not. The maximum heat dissipation of the room radiators depends on the temperature of the incoming water (approximately the boiler temperature). For that, the set point for the water temperature in the boiler must never be set so low that it cannot warm the house when necessary. On the other hand, an excessively high setting of the boiler temperature would result in energy loss in both the furnace and the piping system. Thus the set boiler temperature needs to be carefully set to ensure both user comfort and energy efficiency.
Figure 6: Block Schematic of the Conventional Furnace Controller (large) |
In the 1950´s, the German Electrical Engineering Society (VDE) defined a procedure for this. The assumption is that the maximum amount of heat required by the house depends on the outdoor temperature (T_{outdoor}). A parametric function T^{set}_{boiler}=f(T_{outdoor}) adjusts the set boiler temperature in relation to the outside temperature. This function is also called the "heat characteristic". Parameters are the insulation coefficient of the house and a so-called "comfort parameter". The physical model of this is one in which the maximum amount of available heat equals the amount of heat disposed by the house plus some excess energy to compensate occasional door and window opening.
The assumption that the amount of energy a heating system has to deliver is largely outdoor-temperature dependent, was true back in those days when most houses only had poor thermal insulation. Today, this is obsolete. Due to rising energy costs and environmental concerns, modern houses are built with improved insulation. Therefore, to achieve high efficiency, the outdoor temperature is not the only parameter which reflects the required energy amount. Other factors, such as ventilation, door/window openings and personal lifestyle, have to be considered as well.
The Fuzzy Controller
Two approaches for determining the appropriate set boiler temperature for a well-insulated house exist:
Since the use of extensive sensors is expensive and the construction of a comprising mathematical model is of overwhelming complexity, the second approach has been chosen for realizing the new generation of heating system controllers.
Figure 7: Actual Energy Consumption of the House (draft) (large) |
The most important criterion about individual customer heat demand patterns comes from the actual energy consumption curve of the house, which is measured by the on/off-ratio of the burner. An example of such a curve is given in Figure 7. From this curve, four descriptive parameters are derived:
Figure 8: Average Outside Temperatures in Munich (large) |
These parameters were used to heuristically form rules for the determination of the appropriate set boiler temperature. To allow for the formulation of plausibility rules (such as "temperatures below thirty degrees Fahrenheit are rare in August") the appropriate average outdoor temperature for that season is also a system input parameter. These curves are plotted in Figure 8. Since the average temperature curves are given, no outdoor temperature needs to be measured. Hence, the outdoor temperature sensor can be eliminated.
The structure of the new furnace controller is shown in Figure 9. The fuzzy controller uses a total of five inputs: four of which are derived from the energy consumption curve using conventional digital filtering techniques; the fifth is the average outdoor temperature. This input comes from a look-up table within the system clock. The output of the fuzzy system represents the estimated heat requirement of the house and corresponds to the T_{outdoor} value in the conventional controller (Figure 6).
Figure 9: Schematic of the New Furnace Controller (large) |
Development of the System
The objective of the fuzzy controller is to estimate the actual heat requirement of the house. For this, if-then rules were defined to express the engineering heuristics of this parameter estimation:
IF current_energy_consumption IS low
AND medium_term_tendency IS increasing
AND short_term_tendency IS decreasing
AND yesterday_average IS medium
AND average_outside_temperature IS very_low
THEN estimated_heat_requirement IS medium_high
In total, 405 rules were defined for the parameter estimation. To develop and optimize such a large system efficiently, fuzzyTECH's matrix representation was used [9]. This technique enables rule bases to be viewed and defined graphically rather than in text form. Figure 10 shows a screen shot of such a rule matrix. In this representation, all linguistic labels of two selected linguistic variables (established heating requirement and yesterday's average energy consumption) are displayed. All other variables (medium term tendency) are kept at a selected label. The matrix may be browsed to show the entire rule base by selecting other terms for these variables.
Within the matrix, a white square indicates rule plausibility whereas a black square indicates rule implausibility (not existent in the rule base). For instance, the highlighted rule in Figure 10 is valid. Its textual representation (in the lower part of the window) can be read as:
IF medium_term_tendency IS stable
AND yesterday_avg IS medium
THEN est._heat_req. IS medium.
For the formulation of these IF-THEN rules, an initial systems prototype was built. During system optimization, however, it became apparent that some rules were more important than others and that mere rule addition/deletion was too inexact of a system-tuning method. Thus the inference strategy had to be extended to allow rules to be associated with a "degree of support". Such a degree of support is a number between 0 and 1 that expresses the individual importance of each rule with respect to all other rules. The degree of support for each rule is indicated in the matrix by a gray-shaded square. This allows for the expression of rules like:
IF medium_term_tendency IS stable
AND yesterday_avg IS very_high
THEN est_heat_req IS between high and very_high, rather more high.
Figure 10: Screen Shot of Rule Base as Matrix Representation (large) |
The inference method used to represent individual degrees of support is based on approximate reasoning and Fuzzy Associative Map (FAM) techniques. After fuzzification, all rule premises are calculated using the minimum operator for the representation of the linguistic AND and the maximum operator for the representation of the linguistic OR. Next, the premise's degree of validity is weighted with the individual degree of support of the rule, resulting in the degree of truth for the conclusion. In the third step, all conclusions are combined using the maximum operator. The result of this is a fuzzy set. The Center-of-Maximum defuzzification method is used to arrive at a real value from a fuzzy output.
The entire structure of the fuzzy controller is shown in Figure 11. In this screen shot, the large block in the middle represents the previously described rule base while the small blocks represent input and output interfaces. The icons show the fuzzification/defuzzification methods used in the respective interfaces.
Figure 11: Structure of the Fuzzy Logic Controller (large) |
Implementation and Optimization
After completion of the design of the fuzzy controller and the definition of linguistic variables, membership functions and rules, the system was compiled to the assembly language of the target microcontroller. With this technology, the fuzzy controller only uses 2 KB ROM on a standard 8-bit microcontroller. Once the fuzzy controller had been linked to the entire furnace controller code, the system was optimized.
Figure 12: Optimization Using the "Online" Technique Allows for Cross-Debugging and "on-the-fly" Modifications (large) |
To achieve the most efficient system optimization, fuzzyTECH's online module was used and the target hardware using an 8-bit microcontroller was connected to the developer's workstation (Windows-PC). The online technique allows for the graphical visualization of the information flow while the system is running. All fuzzification, defuzzification and rule inference steps can be graphically cross-debugged in real-time. In addition, the fuzzy controller can be modified and optimized "on-the-fly" during run-time using the graphical editors [8, 9].
During optimization, the fuzzy logic controller was connected to a real heating system. This enabled the optimization of the system robustness against process disturbances such as:
Performance
To evaluate system performance, both the conventional controller and the fuzzy controller were connected to a test house. One such example is shown in Figure 13. Over a period of 48 hours, three graphs were plotted:
The result of the comparative performance tests showed that the fuzzy controller was highly responsive to the actual heat requirement of the house. It was very reactive to sudden heat demand changes like the return of house inhabitants from vacation. Besides this, the elimination of the outdoor temperature sensor saved about $30 in production costs and even more in installation costs that average about $120. By setting the set boiler temperature beneath the level typically used by a conventional controller in low load periods, the fuzzy controller saves energy. Long-term studies collecting statistical data for quantifying exactly how much energy per house could be saved annually are currently being investigated. In addition to this, the two knobs parameterizing the heat characteristic for the individual house (confer Figure 6) used by conventional heating systems, are no longer necessary with the fuzzy logic controller. This eases the use of the heating system, since setting the parameters of the heating curves requires an expertise most home owners do not have.
Figure 13: Comparative Performance Test (Schematic) (large) |
With this new generation of fuzzy logic heating controller, we achieved:
Taking into account the benefits of introducing engineering heuristics, formulated using fuzzy logic technologies, the price was rather low. In the product, the fuzzy logic controller only requires 2 KB of ROM. Using matrix rule representation and online development technology, the optimization of a complex fuzzy logic system containing 405 rules was done efficiently. Click here to view the Fuzzy Logic Viessmann Heating System Controller.
3. NeuroFuzzy Signal Analysis in Washing Machines
In some applications, the knowledge about the system solution is contained in sample data. In these cases, NeuroFuzzy is the method of choice. The following case study is a good example to show the potential of NeuroFuzzy technologies. The German home appliance manufacturer AEG used the fuzzyTECH NeuroFuzzy Module to design an environment-friendly washing machine. The NeuroFuzzy system analyzes the signal of an existing sensor to estimate the laundry volume and type. This information is used to optimize the washing program. In an average home, this technology saves about 20% on water and energy [12]. Click here for a picture of the AEG NeuroFuzzy washing machine or its presentation at the INFORM Fuzzy Logic User's Conference.
Figure 14: Outside View of the Washing Machine | |
Cut View of the Washing Machine |
European Washing Machines
Washing machines in Europe are different from those used in the U.S. and in Japan. The washing process is much more complicated and takes about 2 hours. On the other hand, water consumption is much lower. A typical water consumption ranges from 50 to 60 liters (13 - 18 gallons). White laundry, such as underwear, tableware, and bed sheets, is washed at temperatures up to 95°C (203°F). Hence, washing machines do not use the hot water from the house but rather heat up the water electrically.
The complex washing process consists of multiple wash, process, bleach, rinse and spin steps. To control this, today's washing machines use microcontroller hardware and multiple sensors:
To determine the optimal washing program, actual laundry load (type and volume) of the washing machine must be known. Sensors that could measure these parameters directly are expensive and unreliable. Hence, the objective for AEG was to design a system that estimates the actual laundry load only from the existing sensors.
Water Absorption Curves
Figure 15 plots the pressure sensor curve over time. The plot starts when the water intake valve first opens.
Figure 15: Water Level in the Drum of the Washing Machine During Initial Water Intake. By Interpreting the Curves, an Estimation of Laundry Type and Volume Is Possible. (large) |
As there is no mathematical model on the relation of the water absorption curves to the laundry load, AEG decided to use fuzzy logic to design a solution based on the knowledge of their washing experts. Figure 16 shows the structure of the fuzzy logic system that estimates the water requirement in washing and rinse steps. The input variables of the fuzzy logic system stem from the water absorption curve.
Figure 16: The Multi Level Fuzzy Logic System interprets the water intake function and determines the amount of water to be used in the subsequent washing steps. Also, the further washing program is optimized according to the load (large) |
The upper fuzzy logic rule block estimates the water requirement during washing (WaterLev1) from absorption speed (AbsorbSp) and absorption volume (AbsorbVol). Both these input variables are calculated from T1 - T0 and T2 - T1. The two lower fuzzy logic rule blocks estimate the water requirement during rinse (WaterLev2). Inputs to the intermediate rule block are water requirement during washing, as determined by the upper rule block, and total absorption volume. These are combined to describe the total absorption characteristic (AbsorbChar). This variable is not an output of the fuzzy logic system, but only used as one input for the lower fuzzy logic rule block.
The lower rule block estimates the water requirement during the rinse step (WaterLev2). Other inputs are the ration of the bounded soap, the number of rinse steps given by the selected washing program, and the selected intensity of the spin step. All membership functions are of Standard type (Z, Lambda, S) and the defuzzification employs Center-of-Maximum (CoM) method.
Fuzzy Logic vs. NeuroFuzzy
The approach of interpreting the water absorption curve to estimate the laundry load is innovative, and hence, not much engineering "know-how" on the interpretation of the curves exists. As engineering "know-how" on the application is essential to building a solution with fuzzy logic, the first try of AEG to find a satisfying set of fuzzy logic rules failed.
On the other hand, AEG already recorded water absorption curves for various known laundry loads. The optimal water requirement for these laundry loads can easily be determined by the washing experts. Using these experimental results as training examples, AEG's next try was to use NeuroFuzzy techniques [4]. Figure 17 shows some of these training examples. The left column (Laundry load) lists the materials used for this washing experiment, the next two columns (Water absorption speed and volume) give parameters from the water absorption curve. AEG showed the washing experts the first columns with the actual known load and asked them to recommend the optimum water requirement for this load.
The NeuroFuzzy training used the right column as the desired output and the middle two columns as the respective inputs. The training cannot use the left column as the actual load is not known to the washing machine during operation. The aim of this training is that after training, the fuzzy logic system, which the NeuroFuzzy Module trains, responds with the appropriate water level recommendation determined of the actual values of the input variables [4].
Laundry load | Water absorption speed | Water absorption volume | Water requirement in subsequent washing steps (from expert) |
4 kg Wool / 1 kg Cotton | 0.67 | 2.44 | 3.5 |
3 kg Wool / 1 kg Cotton | 0.61 | 2.10 | 3.1 |
2 kg Wool / 2kg Cotton | 0.62 | 1.99 | 2.8 |
... | ... | ... | ... |
Figure 17: The Sample Data for the NeuroFuzzy Training Has Been Gained Through Extensive Washing Experiments. In Each Experiment, Different Laundry Types and Volumes Were Used. For Each Experiment, the Washing Expert Gave His Recommendation for the Amount of Water to Be Used in Subsequent Washing Steps.
The NeuroFuzzy learning process created 159 rules in the fuzzy logic system shown in Figure 16. The solution was able to estimate the water requirement with a maximum difference from the optimum value of 0.35 liters (0.09 gallons). In an average home, this saves about 20% of the water consumption. As most of the electricity consumed by the washing machine is used to heat up water, 20% of energy is saved too. The fuzzy logic system that the NeuroFuzzy learning process generated, was implemented on a standard 8 bit microcontroller.
4. Literature
[1] | Katayama, R., "Neuro, Fuzzy and Chaos Technology and its Application to (Sanyo) Consumer Electronics", Japanese-European Symposium on Fuzzy Systems (1992). |
[2] | N.N., "fuzzyTECH 4.2 MCU Edition Manual", INFORM GmbH Aachen / Inform Software Corp., Chicago (1996). |
[3] | N.N., "Fuzzy Logic Benchmarks for Standard MCUs", http://www.fuzzytech.com/e_ftedbe.htm (1998). |
[4] | N.N., "fuzzyTECH 4.2 NeuroFuzzy Module Manual", INFORM GmbH Aachen / Inform Software Corp., Chicago (1996). |
[5] | N.N., "fuzzyTECH 4.2 DataAnalyzer Module Manual", INFORM GmbH Aachen / Inform Software Corp., Chicago (1996). |
[6] | Terai, H. et. al., "Application of fuzzy logic technology to home appliances", IFES'91 - Fuzzy Engineering toward Human Friendly Systems, p.1118-1119. |
[7] | Tobi, T. and Hanafusa, T., "A practical application of fuzzy control for an air-conditioning system", International Journal of Approximate Reasoning 5 (1991), p. 331 - 348. |
[8] | von Altrock, C., Krause, B. and Zimmermann, H.-J. "Advanced fuzzy logic control of a model car in extreme situations", Fuzzy Sets and Systems, Vol 48, Nr 1 (1992), p. 41 - 52. |
[9] | von Altrock, C. and Krause, B., "On-Line-Development Tools for Fuzzy Knowledge-Base Systems of Higher Order", 2nd Int'l Conference on Fuzzy Logic and Neural Networks Proceedings, IIZUKA, Japan (1992), ISBN 4-938717-01-8. |
[10] | von Altrock, C., Krause, B. and Zimmermann, H.-J., "Advanced Fuzzy Logic Control Technologies in Automotive Applications", IEEE Conference on Fuzzy Systems (1992), ISBN 0-7803-0237-0, p. 831-842. |
[11] | von Altrock, C., Franke, S., and Froese, Th., "Optimization of a Water-Treatment System with Fuzzy Logic Control", Computer Design Fuzzy Logic '94 Conference in San Diego (1994). |
[12] | von Altrock, C., "Fuzzy Logic Technologies in Automotive Engineering", Computer Design Fuzzy Logic '94 Conference in San Diego (1994). |
[13] | von Altrock, C., Arend, H.-O., Krause, B., Steffens, C., and Behrens-Rommler, E., "Customer-Adaptive Fuzzy Control of Home Heating System", IEEE Conference on Fuzzy Systems in Orlando (1994). |
[14] | von Altrock, "Fuzzy Logic and NeuroFuzzy Applications Explained", ISBN 0-1336-8465-2, Prentice Hall 1995. |
[15] | Wakami, N. "Engineering Application of Fuzzy Systems - Fuzzy Control and Neural Networks: Applications for (Matsushita) Home Appliances", Japanese-European Symposium on Fuzzy Systems in Berlin (1992). |