Paradigm Shift— An Introduction To Fuzzy Logic

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FUZZY LOGIC SUGGESTS inaccuracyand imprecision. Webster’s dictionarydefines the word fuzzy as “not clear,distinct, or precise; blurred.” In a broadsense, fuzzy logic refers to fuzzy sets,which are sets with blurred boundaries,and, in a narrow sense, fuzzy logic is alogical system that aims to formalizeapproximate reasoning.Fuzzy logic is an approach to computer science that mimics the way a humanbrain thinks and solves problems. Theidea of fuzzy logic is to approximatehuman decision making using naturallanguage terms instead of quantitativeterms. It is formally defined asa form of knowledge representation suitable fornotions that cannot bedefined precisely, but whichdepend upon their contexts. Itenables computerized devicesto reason more like humans.Fuzzy-logic technology has createda paradigm shift evident through manyscientific and industrial applications.So, did it begin with fuzzy?Interestingly, fuzzy science started in the questioning minds ofphilosophers. Confused and inquisitive, from Buddha, to Aristotle, toPlato, these ancient philosopherswere constantly searching for a “ruleof law” beyond true or false.Observing that computer logicwas incapable of representing subjective ideas such as “very hot” or“very cold,” in 1965, Zadeh published his ideas of fuzzy set theorythat made it possible for computersto distinguish between differentshades of gray, similar to theprocess of human reasoning. Hedescribed fuzzy mathematics, devisingprecise rules for combining vagueexpressions such as “somewhat fast,”“very hot,” and “usually wrong,” whichare particularly useful for controllingrobots, machine tools, and variouselectronic systems.Prof. Terano was inspired byZadeh’s work and introduced fuzzylogic to the Japanese scientific community in 1972. As Bart Kosko, a Zadehprotégé and a professor of electricalengineering at the University ofSouthern California said: “Fuzzinessbegins where Western logic ends.”Japan embraced the technology andadapted it to physical control systems.In 1980, F.L. Smidth & Co. ofCopenhagen began marketing the first6commercial fuzzy expert system: a computer program that controlled the fuelintake rate and gas flow of a rotating kilnused to make cement. From Hitachi’ssubway system, to Nissan’s fuzzy autotransmission and antiskid braking systems, to Yamaichi Security’s fuzzy stockmarket investment program for signalingshifts in market sentiment, to Matsushita’sfuzzy automobile-traffic controller, Japanhas been taking the lead in fuzzy-logicWhy fuzzy logic?Fuzzy logic comes in when conventional logic fails. Fuzzy logic can dealwith virtually any proposition expressedin natural language. For example, theproposition, “It is very unlikely that theprice of gold will significantly increasein the near future,” which is beyond theclassical first-order predicate logic, isperfectly manageable by fuzzy logic.The meanings of propositions like thiscan be determined, forexample, by a methodknown as test-scoresemantics.An important concept in fuzzy logic liesin the concept of linguistic variables: variables whose values arewords or sentences innatural language. Ingeneral, any relationbetween two linguisticvariablescanbeexpressed in terms offuzzy if–then rules.Such rules, when properly elicited fromexperts, form theknowledge base offuzzy controllers orfuzzy expert systems.Once the meaningsof relevant propositionsare determined, fuzzylogic provides us withapproximate reasoningin linguistic terms thatare available in naturallanguage. The approxiJOSEPH BIHmate reasoning mayinvolve deductive infer DIGITALVISIONences as well as interpolative inferences, as shown in theresearch and development and transformfollowing example:ing the technology into industrial applicaOld coins are usually rare collectibles.tions. Some say that the Japanese culturalenvironment plays a significant role byRare collectibles are expensive.Old coins are usually expensive.embracing fuzzy logic. For these companies, fuzzy logic is a paradigm to introduce human subjectivity into objectiveFuzzy logic versusscience and a method to model and useneural networkshuman knowledge and senses as theyThe idea of fuzzy logic is to approxiare, without complicating abstraction.mate human decision-making using natSince NASA pioneered fuzzy-conural-language terms instead of quantitatroller experiments that could help astrotive terms. Fuzzy logic is similar to neurnauts pilot the space shuttle in earthal networks, and one can create behavorbit, there is growing interest at suchioral systems with both methodologies.aerospace firms as Rockwell and Boeing.A good example is the use of fuzzy logic“The only barrier remaining to wider usefor automatic control: a set of rules or aof fuzzy logic,” says Kosko, “is the philotable is constructed that specifies how ansophical resistance of the West.”effect is to be achieved, provided inputParadigm shift—an introductionto fuzzy logic0278-6648/06/ 20.00 2006 IEEEIEEE POTENTIALS

Error-dot - (d(cmd-Temp)/dt)and know how to solve. Butand the current system state.computers would be so muchUsing fuzzy arithmetic, one usesConsequentBlockmore useful if they could doa model and makes a subset ofAntecedent Blockthings that we don’t exactlythe system components fuzzy so1. IF Cmd-Temp N AND d(Cmd-Temp)/dt N THEN Output Cknow how to do. This is wherethat fuzzy arithmetic must be2. IF Cmd-Temp Z AND d(Cmd-Temp)/dt N THEN Output Hneural networks come in. Neuralused when executing the model.3. IF Cmd-Temp P AND d(Cmd-Temp)/dt N THEN Output Hnetwork systems help when forIn a broad sense, fuzzy logic4. IF Cmd-Temp N AND d(Cmd-Temp)/dt Z THEN Output Cmulating an algorithmic solutionrefers to fuzzy sets, which are5. IF Cmd-Temp Z AND d(Cmd-Temp)/dt Z THEN Output NCis extremely difficult, lots ofsets with blurred boundaries,6. IF Cmd-Temp P AND d(Cmd-Temp)/dt Z THEN Output Hexamples of the behavior that areand, in a narrow sense, fuzzy7. IF Cmd-Temp N AND d(Cmd-Temp)/dt P THEN Output Crequired, or there is a need tologic is a logical system that8. IF Cmd-Temp Z AND d(Cmd-Temp)/dt P THEN Output C9. IF Cmd-Temp P AND d(Cmd-Temp)/dt P THEN Output Hpick out the structure from existaims to formalize approximateing data.reasoning.Error -(Cmd-Temp)For example, a temperaturecontrol system has three setFuzzy logic in controlNZPtings: cold, moderate, and hotsystems—case studies123(see Fig. 1). The first step is toNCHHdevelop a matrix. BecauseFuzzy logic in design456there are three conditions, themethodology and forZCNCHmatrix will be 3 3. There willnonlinear control systemsalso be quite a few variables.Fuzzy logic is a paradigm for789PCCHThese include N for negative, Pan alternative design methodolofor positive, and Z for that can be applied in develEach represents the possibleoping both linear and nonlinearinput error and its derivative, Fig. 1 Rule structure and rule matrixsystems for embedded control.the direction of temperatureUsing fuzzy logic, designers cancated or imprecise data, can be used tochange; in other words: it is hot, gettingrealize lower development costs, superiextract patterns and detect trends thathotter, or cold, getting older, or moderor features, and better end-product perare too complex to be noticed by eitherate. The variables inside the matrix repformance. Furthermore, products can behumans or other computer techniques.resent the responses to changing condibrought to market faster and more costNeural networks are a form of multitions. C represents a “cool” response,effectively.H represents a “heat” response, andprocessor computer system, withN C represents a “no change” response. simple processing elementsSimpler and faster design methodology a high degree of interconnectionTogether, these variables provide nineTo appreciate why a fuzzy-based simple scalar messagesrules to conditions and their responsesdesign methodology is very attractive in adaptive interaction betweendepending on varying situations. This isembedded control applications, let fuzzy logic “makes decisions.” Ifexamine a typical design flow. Figure 3A biological neuron may have asthe temperature is hot (N ) and gettingillustrates a sequence of design stepsmany as 10,000 different inputs, andhotter (N ), then the response should berequired to develop a controller using amay send its output (the presence orto turn the cooling feature on the temconventional and a fuzzy approach.absence of a short-duration spike) toperature control system (N ). This canUsing the conventional approach, themany other neurons. Neurons are wiredbe implemented very easily by computfirst step is to understand the physicalup in a three-dimensional (3-D) hardware, software, or a combinationsystem and its control requirements.Real brains, however, are orders ofof the two. While this is a very simpleBased on this understanding, the secondmagnitude more complex than any artiexample, more practical applicationsstep is to develop a model that includesficial neural network so far considered.would make up very large matrices andthe plant, sensors, and actuators. TheA simple, signle-unit adaptive neta more complex set of rules. It is key towork is shown in Fig. 2. The networknote, though, that conditional rules canhas two inputs and one output. All areeasily be stated linguistically and thatbinary. The output is 1 ifconditional statements can use theY I0 or I1W0 I0 W1 I1 Wb 0 , and 0 ifAND, OR, or NOT operators.W0 I0 W1 I1 Wb 0.Neural networks, however, are a difLinear Threshold Unitferent paradigm for computing. NeuralWe want it to learn simple OR: outnetworks process information in a simiput a 1 if either I0 or I1 is 1.lar way that the human brain does. TheConventional computers use an algoWbnetwork is composed of a large numberrithmic approach; i.e., the computer folWoW1of highly interconnected processing elelows a set of instructions in order toments (neurons) working in parallel tosolve a problem. Unless the specific steps( 1)solve a specific problem. Neural netthat the computer needs to follow areworks learn by example and cannot beknown, the computer cannot solve theBias UnitI0I1programmed to perform a specific task.problem. This restricts the problem-solvNeural networks, with their remarkableing capability of conventional computersFig. 2 A simple, single-unit adaptivenetworkability to derive meaning from complito problems that we already understandJANUARY/FEBRUARY 20067

third step is to use linear-control theoryin order to determine a simplified version of the controller, such as the parameters of a proportional-integral-derivative (PID) controller. The fourth step isto develop an algorithm for the simplified controller. The last step is to simulate the design including the effects ofnonlinearity, noise, and parameter variations. If the performance is not satisfactory, we need to modify our systemmodeling, re-design the controller,rewrite the algorithm, and retry.Fuzzy-logic approach reduces thedesign process to three steps, startingwith understanding and characterizingthe system behavior through knowledge and experience. The second stepis to directly design the control algorithm using fuzzy rules that describe theprinciples of the controller’s regulationin terms of the relationship between itsinputs and outputs. The last step is tosimulate and debug the design. The factthat one only needs to modify somefuzzy rules and retry the process satisfies the performance requirements.Though the two design methodologies are similar, fuzzy-based methodology substantially simplifies the designloop, resulting in significantly reduceddevelopment time, simpler design, andfaster time to market.Fuzzy-logic design methodologysimplifies the steps, especially duringthe debugging and tuning cycle, inwhich the system can be changed bysimply modifying rules rather thanredesigning the controller. The fuzzyrule-based feature focuses more on theapplication instead of programming,therefore substantially reducing theoverall development cycle.Commercial applications in embedded control require a significant development effort, a majority of which isspent on the software portion of theproject. Due to its simplicity, thedescription of a fuzzy controller is notonly is transportable across designteams, but also provides a superiormedium to preserve, maintain, andupgrade intellectual property.A better alternative solutionto nonlinear controlUnderstand Physical Systemand Control RequirementsUnderstand Physical Systemand Control RequirementsDevelop a Linear Model ofPlant Sensors and ActuatorsDetermine a SimplifiedController from Control TheoryDesign the Control forUsing Fuzzy RulesDevelop an Algorithmfor the ControllerSimulate, Debug, andImplement DesignSimulate, Debug, andImplement DesignFig. 3 Conventional and fuzzy designFan SpeedHighMedLowTemperatureZeroHotWarmCool ColdFig. 4 Rules and membership function approximating a nonlinear function8Most real-life physical systems are actually nonlinear systems. Conventionaldesign approaches use different approximation methods to handle nonlinearity:linear, piecewise linear, and lookup tableapproximations to trade off factors of complexity, cost, and system performance.Fuzzy logic rules and membershipfunctions approximate any continuousfunction to a degree of precision used asin Fig. 4, which shows an approximatedesired control curve for temperaturecontroller using four rules (or points).More rules can be added to increase theaccuracy of the approximation, whichyields improved control performance.Rules are much simpler to implementand much easier to debug and tune thanpiecewise linear or lookup table techniques. The desired control curve for thetemperature controller can be approximated using four points (or four rules)as in the following.IF temperature IS cold THEN forceIS high.IF temperature IS cool THEN forceIS medium.IF temperature IS warm THEN forceIS low.IF temperature IS hot THEN forceIS zeroThe fuzzy arithmetic interpolates theshape of the nonlinear function. Thecombined memory required for thelabels and fuzzy inference is substantiallyless than a lookup table, especially formultiple input systems. As a result, processing speed can be improved as well.Most control applications have multiple inputs and require modeling andtuning of a large number of parameters which makes implementation timeconsuming. Fuzzy rules can helpIEEE POTENTIALS

simplify implementation by combiningmultiple inputs into single if-thenstatements while still handling nonlinearity as the following shows:IF temperature IS cold AND humidityIS high THEN fan spd IS high.IF temperature IS cool AND humidityIS high THEN fan spd IS medium.IF temperature IS warm AND humidityIS high THEN fan spd IS low.IF temperature IS hot AND humidityIS high THEN fan spd IS zero.IF temperature IS cold AND humidityIS med THEN fan spd IS medium.IF temperature IS cool AND humidityIS med THEN fan spd IS low.IF temperature IS warm AND humidity IS med THEN fan spd IS zero.IF temperature IS hot AND humidityIS med THEN fan spd IS zero.IF temperature IS cold AND humidityIS low THEN fan spd IS medium.IF temperature IS cool AND humidityIS low THEN fan spd IS low.IF temperature IS warm ANDhumidity IS low THEN fan spd IS zero.IF temperature IS hot AND humidityIS low THEN fan spd IS zero.Fuzzy logic is used to describe theoutput as a function of two or moreinputs linked with operators such asAND. It requires significantly lessentries than a lookup table dependingupon the number of labels for eachinput variable. Rules are much easier todevelop and simpler to debug and tunethan a lookup table, as in Fig. 5.The lookup table for the two-inputtemperature controller requires 64 Kb ofmemory, while the fuzzy approach isaccomplished with less than 0.5 Kb ofmemory for labels and the object codecombined. This difference in memorysavings implies a cheaper hardwareimplementation. Conventional techniquesin most real life applications wouldrequire complex mathematical analysisand modeling, floating point algorithms,and complex branching. This typicallyyields a substantial size of object code,which requires a high end DSP chip torun. The fuzzy-logic approach uses asimple, rule-based approach that offerssignificant cost savings, both in memoryand processor class.of fuzzy-logic-based control rather thantraditional control algorithms.ABS is implemented in automobilesto ensure optimal vehicle control andminimal stopping distances during hardor emergency braking. The number ofcars equipped with ABS is on the rise.ABS is now accepted as an essentialcontribution to vehicle safety. Themethods of control utilized by ABS areresponsible for system performance.Fuzzy ABSABS systems were introduced to thecommercial vehicle market in the early1970s to improve vehicle braking irrespective of road and weather conditions. Electronic control units (ECUs),wheel speed sensors, and brake modulators are major components of an ABSmodule. Wheel-speed sensors transmitpulses to the ECU with a frequencyproportional to wheel speed. The ECUthen processes this information and regulates the brake accordingly. The ECUand control algorithm are at least partially responsible for how well the ABSsystem performs.Since ABS systems are nonlinear anddynamic in nature, they are prime candidates for fuzzy-logic control. For mostdriving surfaces, as vehicle braking forceis applied to the wheel system, the longitudinal relationship of friction betweenvehicle and driving surface rapidlyincreases. Increasing brake force in adecreasing frictional environment oftenresults in full wheel lockup. It has beenboth mathematically and empiricallyproven a sliding wheel produces lessfriction a moving wheel. Inputs to theIntel Fuzzy ABS are derived from wheelspeed. Acceleration and slip for eachwheel may be calculated by combiningthe signals from each wheel. These signals are then processed in the IntelMany electronic control systems inthe automotive industry, such as automatic transmissions, engine control, andantilock brake systems (ABS) realizesuperior characteristics through the useJANUARY/FEBRUARY 2006modelBUILDERUnlike a conventional ABS system,performance of the Intel Fuzzy ABSSystem can be optimized with lessdetailed knowledge of the internal systemdynamics. This is achieved by the processused to refine the rule base and in theinitial development of the system usingInform Software Corporation fuzzyTECH(R)3.0 MCU-96 software tuned for the IntelArchitecture with optimized code outputand the associated Real Time CrossDebugger. Rapid development is attainedby the software tool set combined with alinguistic approach to control implemented in the Intel Fuzzy ABS solution. A cornerstone of this rapid development is theIntel fuzzy logic modeling software kitcalled fuzzyBUILDER.fuzzyTECH MCU-96 contains a fullygraphical computer-aided software engineering (CASE) tool to support all designsteps for fuzzy system engineering and asimulation and optimization tool forfuzzy systems. It is specifically optimizedfor the MCS 96 architecture. This tooldisplays system performance and can beinterfaced to conventional simulators toobtain performance data; a code generator which generates complete C-code forthe fuzzy system. The C-code calls optimized assembly routines on the targetcontroller for fast performance.Conventional ABS control algorithms, however, must account for nonlinearity in brake torque because of thetemperature variation and dynamics ofaaTemperatureTemperatureCold Cool Warm HotaHumidityFuzzy antilockbrake system solutionFuzzy ABS system to achieve thedesired control. Unlike earlier 8-bmicrocontroller architectures with limitedmath capability, Intel Fuzzy ABS example utilizes a high performance, lowcost, 16-b 8XC196Kx architecture totake advantage of improved math execution timing.255 Rows 255 Cols64 KbaLow Med Low Zero ZeroMed Med Low Zero ZeroHumidityHigh High Med Low ZeroaFan SpeedaFan SpeedFig. 5 Lookup table versus rules and membership

Fuzzy logic versus neural networks The idea of fuzzy logic is to approxi-mate human decision-making using nat-ural-language terms instead of quantita-tive terms. Fuzzy logic is similar to neur-al networks, and one can create behav-ioral systems with both methodologies. A good example is the use of fuzzy logic for automatic control: a set of .

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