130: Rule-based Expert Systems. Ajith Abraham Oklahoma State University, Stillwater, OK, USA 1 PROBLEM SOLVING USING HEURISTICS

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1 : Rule-based Expert Systes Ajith Abraha Oklahoa State University, Stillwater, OK, USA Proble Solving Using Heuristics 99 What are Rule-based Systes? 9 Inference Engine in Rule-based Systes 9 Expert Syste Developent 9 5 Fuzzy Expert Systes 9 6 Modeling Fuzzy Expert Systes 9 7 Illustration of Fuzzy Expert Syste Design 9 8 Adaptation of Fuzzy Inference Systes 98 9 Suary 98 References 99 PROBLEM SOLVING USING HEURISTICS A general introduction to artificial intelligence ethods of easureent signal processing is given in Article 8, Nature and Scope of AI Techniques, Volue. Proble solving is the process of finding a solution when the path leading to that solution is uncertain. Even though we are failiar with several proble-solving techniques, in the real world, soeties any probles cannot be solved by a technique we are failiar with. Surprisingly, for soe coplicated probles, no straightforward solution technique is known at all. For these probles, heuristic solution techniques ay be the only alternative. A heuristic can be siplified as a strategy that is powerful and general, but not absolutely guaranteed to provide best solutions. Heuristic ethods are very proble specific. Previous experience and soe general rules often called rules of thub could help find good heuristics easier. Huans use heuristics a great deal in their proble solving. Of course, if the heuristic does fail, it is necessary for the proble solver to either pick another heuristic, or know that it is appropriate to give up. Choosing rando solutions, adopting greedy approaches, evolving the basic heuristics for finding better heuristics are just soe of the popular approaches used in heuristic proble solving (Michalewicz and Fogel, 999). Heuristic proble solving involves finding a set of rules, or a procedure, that finds satisfactory solutions to a specific proble. A good exaple is finding one s way through a aze. To ake the way toward the final goal, a stepby-step oveent is necessary. Very often false oves are ade but in ost cases we solve the proble without uch difficulty. For the aze proble, a siple heuristic rule could be choose the direction that sees to ake progress. Another good exaple is the job shop scheduling proble wherein the task is to schedule J n independent jobs, where n ={,,...N} on R heterogeneous resources and ={,,...,M}, with an objective of iniizing the copletion tie of all the jobs and utilizing all the resources effectively. Each job J n has processing requireent P j cycles and resource R has speed of S i cycles/unit tie. Any job J n has to be processed in resource R, until copletion. If C j is the copletion tie and the last job j finishes processing, then we define C ax = ax{c j,j =,...,N}, the akespan and C j, as the flow-tie. The task is to find an optial schedule that optiizes the flow-tie and ake-span. Soe siple heuristic rules to achieve this are by scheduling the Shortest Job on the Fastest Resource (SJFR), which would iniize C j or by Handbook of Measuring Syste Design, edited by Peter H. Sydenha and Richard Thorn. 5 John Wiley & Sons, Ltd. ISBN:

2 9 Eleents: B Signal Conditioning scheduling the Longest Job on the Fastest Resource (LJFR), which would iniize C ax. Miniizing C j asks that the average job finishes quickly, at the expense of the largest job taking a long tie, whereas iniizing C ax, asks that no job takes too long, at the expense of ost jobs taking a long tie. In suary, iniization of C ax will result in axiization of C j, which akes the proble ore interesting. By contrast, algoriths are straightforward procedures that are guaranteed to work every tie for they are fully deterinate and tie invariant. For exaple, certain daily routine tasks could be forulated in a strict algorith forat (exaple, starting up an autoobile). However, for a proble solver to be ore adaptive, novel eleents or new circustances ust be introduced. Many real-world probles cannot be reduced to algoriths, which leads us to the quest to find ore powerful techniques. WHAT ARE RULE-BASED SSTEMS? Conventional proble-solving coputer progras ake use of well-structured algoriths, data structures, and crisp reasoning strategies to find solutions. For the difficult probles with which expert systes are concerned, it ay be ore useful to eploy heuristics: strategies that often lead to the correct solution, but that also soeties fail. Conventional rule-based expert systes, use huan expert knowledge to solve real-world probles that norally would require huan intelligence. Expert knowledge is often represented in the for of rules or as data within the coputer. Depending upon the proble requireent, these rules and data can be recalled to solve probles. Rule-based expert systes have played an iportant role in odern intelligent systes and their applications in strategic goal setting, planning, design, scheduling, fault onitoring, diagnosis andsoon. With the technological advances ade in the last decade, today s users can choose fro dozens of coercial software packages having friendly graphic user interfaces (Ignizio, 99). Conventional coputer progras perfor tasks using a decision-aking logic containing very little knowledge other than the basic algorith for solving that specific proble. The basic knowledge is often ebedded as part of the prograing code, so that as the knowledge changes, the progra has to be rebuilt. Knowledge-based expert systes collect the sall fragents of huan knowhow into a knowledge base, which is used to reason through a proble, using the knowledge that is appropriate. An iportant advantage here is that within the doain of the knowledge base, a different proble can be solved using the sae progra without reprograing efforts. Moreover, expert systes could explain the reasoning process and handle levels of confidence and uncertainty, which conventional algoriths do not handle (Giarratano and Riley, 989). Soe of the iportant advantages of expert systes are as follows: ability to capture and preserve irreplaceable huan experience; ability to develop a syste ore consistent than huan experts; iniize huan expertise needed at a nuber of locations at the sae tie (especially in a hostile environent that is dangerous to huan health); solutions can be developed faster than huan experts. The basic coponents of an expert syste are illustrated in Figure. The knowledge base stores all relevant inforation, data, rules, cases, and relationships used by the expert syste. A knowledge base can cobine the knowledge of ultiple huan experts. A rule is a conditional stateent that links given conditions to actions or outcoes. A frae is another approach used to capture and store knowledge in a knowledge base. It relates an object or ite to various facts or values. A frae-based representation is ideally suited for object-oriented prograing techniques. Expert systes aking use of fraes to store knowledge are also called frae-based expert systes. The purpose of the inference engine is to seek inforation and relationships fro the knowledge base and to provide answers, predictions, and suggestions in the way a huan expert would. The inference engine ust find the right facts, interpretations, and rules and asseble the correctly. Two types of inference ethods are coonly used Backward chaining is the process of starting with conclusions and working backward to the supporting facts. Forward chaining starts with the facts and works forward to the conclusions. Knowledge base Expert knowledge Knowledge base acquisition facility Inference engine Figure. Architecture of a siple expert syste. Users User interface Explanation facility

3 Rule-based Expert Systes 9 The explanation facility allows a user to understand how the expert syste arrived at certain results. The overall purpose of the knowledge acquisition facility is to provide a convenient and efficient eans for capturing and storing all coponents of the knowledge base. Very often specialized user interface software is used for designing, updating, and using expert systes. The purpose of the user interface is to ease use of the expert syste for developers, users, and adinistrators. INFERENCE ENGINE IN RULE-BASED SSTEMS A rule-based syste consists of if-then rules, a bunch of facts, and an interpreter controlling the application of the rules, given the facts. These if-then rule stateents are used to forulate the conditional stateents that coprise the coplete knowledge base. A single if-then rule assues the for if x is A then y is B and the if-part of the rule x is A is called the antecedent or preise, while the then-part of the rule y is B is called the consequent or conclusion. There are two broad kinds of inference engines used in rule-based systes: forward chaining and backward chaining systes. In a forward chaining syste, the initial facts are processed first, and keep using the rules to draw new conclusions given those facts. In a backward chaining syste, the hypothesis (or solution/goal) we are trying to reach is processed first, and keep looking for rules that would allow to conclude that hypothesis. As the processing progresses, new subgoals are also set for validation. Forward chaining systes are priarily data-driven, while backward chaining systes are goal-driven. Consider an exaple with the following set of if-then rules Rule : If A and C then Rule : If A and then Z Rule : If B then Rule : If Z then D IfthetaskistoprovethatD is true, given A and B are true. According to forward chaining, start with Rule and go on downward till a rule that fires is found. Rule is the only one that fires in the first iteration. After the first iteration, it can be concluded that A, B, and are true. The second iteration uses this valuable inforation. After the second iteration, Rule fires adding Z is true, which in turn helps Rule to fire, proving that D is true. Forward chaining strategy is especially appropriate in situations where data are expensive to collect, but few in quantity. However, special care is to be taken when these rules are constructed, with the preconditions specifying as precisely as possible when different rules should fire. In the backward chaining ethod, processing starts with the desired goal, and then attepts to find evidence for proving the goal. Returning to the sae exaple, the task to prove that D is true would be initiated by first finding a rule that proves D. Rule does so, which also provides a subgoal to prove that Z is true. Now Rule coes into play, and as it is already known that A is true, the new subgoal is to show that is true. Rule provides the next subgoal of proving that B is true. But that B is true is one of the given assertions. Therefore, it could be concluded that is true, which iplies that Z is true, which in turn also iplies that D is true. Backward chaining is useful in situations where the quantity of data is potentially very large and where soe specific characteristic of the syste under consideration is of interest. If there is not uch knowledge what the conclusion ight be, or there is soe specific hypothesis to test, forward chaining systes ay be inefficient. In principle, we can use the sae set of rules for both forward and backward chaining. In the case of backward chaining, since the ain concern is with atching the conclusion of a rule against soe goal that is to be proved, the then (consequent) part of the rule is usually not expressed as an action to take but erely as a state, which will be true if the antecedent part(s) are true (Donald, 986). EPERT SSTEM DEVELOPMENT Steps in the expert systes developent process include deterining the actual requireents, knowledge acquisition, constructing expert syste coponents, ipleenting results, and forulating a procedure for aintenance and review. Knowledge acquisition is the ost iportant eleent in the developent of expert syste (Niwa, Sasaki and Ihara, 988). Knowledge could be obtained by interviewing doain experts and/or learning by experience. Very often people express knowledge as natural language (spoken language), or using letters or sybolic ters. There exist several ethods to extract huan knowledge. Cognitive Work Analysis (CWA) and the Cognitive Task Analysis (CTA) provide fraeworks to extract knowledge. The CWA is a technique to analyze, design, and evaluate the huan coputer interactive systes (Vicente, 999). The CTA is a ethod to identify cognitive skill, ental deands, and needs to perfor task proficiency (Militallo and Hutton, 998). This focuses on describing the representation of the cognitive eleents that defines goal generation and decision-aking. It is a reliable ethod for extracting

4 9 Eleents: B Signal Conditioning huan knowledge because it is based on the observations or an interview. Most expert systes are developed using specialized software tools called shells. These shells coe equipped with an inference echanis (backward chaining, forward chaining, or both), and require knowledge to be entered according to a specified forat. One of the ost popular shells widely used throughout the governent, industry, and acadeia is the CLIPS (CLIPS, ). CLIPS is an expert syste tool that provides a coplete environent for the construction of rule- and/or object-based expert systes. CLIPS provides a cohesive tool for handling a wide variety of knowledge with support for three different prograing paradigs: rule-based, object-oriented, and procedural. CLIPS is written in C for portability and speed and has been installed on any different operating systes without code changes. 5 FUZZ EPERT SSTEMS The world of inforation is surrounded by uncertainty and iprecision. The huan reasoning process can handle inexact, uncertain, and vague concepts in an appropriate anner. Usually, the huan thinking, reasoning, and perception process cannot be expressed precisely. These types of experiences can rarely be expressed or easured using statistical or probability theory. Fuzzy logic provides a fraework to odel uncertainty, the huan way of thinking, reasoning, and the perception process. Fuzzy systes were first introduced by Zadeh (965). A fuzzy expert syste is siply an expert syste that uses a collection of fuzzy ebership functions and rules, instead of Boolean logic, to reason about data (Schneider et al., 996). The rules in a fuzzy expert syste are usually of a for siilar to the following: If A is low and B is high then = ediu where A and B are input variables, is an output variable. Here low, high, and ediu are fuzzy sets defined on A, B, and respectively. The antecedent (the rule s preise) describes to what degree the rule applies, while the rule s consequent assigns a ebership function to each of one or ore output variables. Let be a space of objects and x be a generic eleent of. A classical set A, A, is defined as a collection of eleents or objects x, such that x can either belong or not belong to the set A. A fuzzy set A in is defined as a set of ordered pairs A ={(x, µ A (x)) x } () where µ A (x) is called the ebership function (MF) for the fuzzy set A. The MF aps each eleent of to a ebership grade (or ebership value) between zero and one. Obviously () is a siple extension of the definition of a classical set in which the characteristic function is peritted to have any values between zero and one. The intersection of two fuzzy sets A and B is specified in general by a function T : [,] [,] [,], which aggregates two ebership grades as follows: µ A B (x) = T(µ A (x), µ B (x)) = µ A (x) µ B (x) () where is a binary operator for the function T.Thisclass of fuzzy intersection operators are usually referred to as T-nor operators (Jang, Sun and Mizutani, 997). Four of the ost frequently used T-nor operators are Miniu: T in (a, b) = in(a, b) = a b () Algebraic product: T ap (a, b) = ab () Bounded product: T bp (a, b) = (a + b ) (5) a, if b = Drastic product: T dp (a, b) = b, if a = (6), if a,b < Like intersection, the fuzzy union operator is specified in general by a function S: [,] [,] [,], which aggregates two ebership grades as follows: µ A B (x) = S(µ A (x), µ B (x)) = µ A (x) µ B (x) (7) where is the binary operator for the function S. Thisclass of fuzzy union operators are often referred to as T-conor (or S-nor) operators (Jang, Sun and Mizutani, 997). Four of the ost frequently used T-conor operators are Maxiu: S ax (a, b) = ax(a, b) = a b (8) Algebraic su: S as (a, b) = a + b ab (9) Bounded su: S bs (a, b) = (a + b) () a, if b = Drastic su: S ds (a, b) = b, if a = (), ifa,b > Both the intersection and union operators retain soe properties of the classical set operation. In particular, they are associative and coutative. Figure illustrates the basic architecture of a fuzzy expert syste. The ain coponents are a fuzzification interface, a fuzzy rule base (knowledge base), an inference engine (decision-aking logic), and a defuzzification interface. The input variables are fuzzified whereby the ebership functions defined on the input variables are applied to their actual values, to deterine the degree of truth for each rule antecedent. Fuzzy if-then rules and fuzzy reasoning are the backbone of fuzzy expert systes, which are the ost

5 Rule-based Expert Systes 9 Crisp input Fuzzification interface Fuzzy input Inference engine Fuzzy output Defuzzification interface Crisp output Rules Fuzzy rule base Figure. Basic architecture of a fuzzy expert syste. Input MF in Output MF ax A B C c C A B C c Z Z (COA) Z Output Z Input (x,y) Figure. Madani fuzzy inference syste using in and ax for T-nor and T-conor operators. iportant odeling tools based on fuzzy set theory. The fuzzy rule base is characterized in the for of if-then rules in which the antecedents and consequents involve linguistic variables. The collection of these fuzzy rules fors the rule base for the fuzzy logic syste. Using suitable inference procedure, the truth value for the antecedent of each rule is coputed, and applied to the consequent part of each rule. This results in one fuzzy subset to be assigned to each output variable for each rule. Again, by using suitable coposition procedure, all the fuzzy subsets assigned to each output variable are cobined together to for a single fuzzy subset for each output variable. Finally, defuzzification is applied to convert the fuzzy output set to a crisp output. The basic fuzzy inference syste can take either fuzzy inputs or crisp inputs, but the outputs it produces are always fuzzy sets. The defuzzification task extracts the crisp output that best represents the fuzzy set. With crisp inputs and outputs, a fuzzy inference syste ipleents a nonlinear apping fro its input space to output space through a nuber of fuzzy if-then rules. In what follows, the two ost popular fuzzy inference systes are introduced that have been widely deployed in various applications. The differences between these two fuzzy inference systes lie in the consequents of their fuzzy rules, and thus their aggregation and defuzzification procedures differ accordingly. According to Madani, fuzzy inference syste (Madani and Assilian, 975) see Figure the rule antecedents and consequents are defined by fuzzy sets and has the following structure: if x is A and y is B then z = C () There are several defuzzification techniques. The ost widely used defuzzification technique uses the centroid of area ethod as follows Z Centroid of area Z COA = µ A (z) z dz Z µ A (z) dz () where µ A (z) is the aggregated output MF. Takagi and Sugeno (985) proposed an inference schee in which the conclusion of a fuzzy rule is constituted by a weighted linear cobination of the crisp inputs rather than a fuzzy set. A basic Takagi Sugeno fuzzy inference syste is illustrated in Figure and the rule has the following structure if x is A and y is B, then z = p x + q y + r () where p,q, and r are linear paraeters. TSK Takagi Sugeno Kang fuzzy controller usually needs a saller

6 9 Eleents: B Signal Conditioning A B w z = p *x + q *y + r A B w z = p *x + q *y + r w Z = *z + w *z w + w Input (x,y) Output Z Figure. Takagi Sugeno fuzzy inference syste using a in or product as T-nor operator. nuber of rules, because their output is already a linear function of the inputs rather than a constant fuzzy set. 6 MODELING FUZZ EPERT SSTEMS Large R 7 R 8 R 9 Fuzzy expert syste odeling can be pursued using the following steps. Select relevant input and output variables. Deterine the nuber of linguistic ters associated with each input/output variable. Also, choose the appropriate faily of ebership functions, fuzzy operators, reasoning echanis, and so on. Choose a specific type of fuzzy inference syste (for exaple, Madani, Takagi Sugeno etc.). In ost cases, the inference of the fuzzy rules is carried out using the in and ax operators for fuzzy intersection and union. Design a collection of fuzzy if-then rules (knowledge base). To forulate the initial rule base, the input space is divided into ultidiensional partitions and then actions are assigned to each of the partitions. In ost applications, the partitioning is achieved using onediensional ebership functions using fuzzy if-then rules as illustrated in Figure 5. The consequent parts of the rule represent the actions associated with each partition. It is evident that the MFs and the nuber of rules are tightly related to the partitioning. 7 ILLUSTRATION OF FUZZ EPERT SSTEM DESIGN This section illustrates the developent of a reactive power prediction odel using Madani and Takagi Sugeno fuzzy inference expert systes. The MatLab fuzzy logic toolbox was used to siulate the various experients (Fuzzy Logic Tool Box, ). Input- Mediu Sall R 6 R Sall R 5 R Mediu Input- R R Large Figure 5. Exaple showing how the two-diensional spaces are partitioned using three trapezoidal ebership functions per input diension. A siple if-then rule will appear as If input- is ediu and input is large, then rule R 8 is fired. The task is to develop a fuzzy expert syste to forecast the reactive power (P) at tie t + by knowing the load current (I) and voltage (V ) at tie t. The experient syste consists of two stages: developing the fuzzy expert syste, and perforance evaluation using the test data. The odel has two in out variables (V and I) and one output variable (P ). Training and testing data sets were extracted randoly fro the aster dataset. Sixty percent of data was used for training and the reaining % for testing (Abraha and Khan, ). 7. Design and experients: fuzzy expert systes First, the effects of (a) shape and quantity of ebership functions (b) T-nor and T-conor operators (c) defuzzification ethods and (d) inference ethod for

7 Rule-based Expert Systes 95 designing the fuzzy expert syste is analyzed. Experients were carried out using four different settings using the sae rule base. Experient (To evaluate the effect on the nuber of ebership functions) The following settings were used for designing the expert syste. Two triangular ebership functions (MFs) for each input variable and four triangular MFs for the output variable (power). Using the grid partitioning ethod (Figure 5), four if-then rules were developed.. Three triangular MFs for each input variable and nine triangular MFs for the output variable (power). The rule base consisted of nine if-then rules. in and ax were used as T-nor and T-conor operators and the centroid ethod of defuzzification for Madani inference ethod and weighted average defuzzification ethod for Takagi Sugeno Fuzzy Inference Syste (FIS). The developed fuzzy inference systes using Madani and Takagi Sugeno odels are depicted in Figures 6 to 9. Table suarizes the training and testing Root Mean Squared Error (RMSE) values. Experient (To evaluate the effect of shape of ebership functions) For the Madani FIS, three Gaussian MFs for Table. Epirical coparison of fuzzy inference systes and quantity of Mebership Functions (MFs). No. of Madani FIS Takagi Sugeno FIS MFs Root ean squared error Training Test Training Test each input variable and nine Gaussian MFs for the output variable were used. The rule base consisted of nine ifthen rules. in and ax as T-nor and T-conor operators, and the centroid ethod of defuzzification for Madani FIS and the weighted average defuzzification ethod for Takagi Sugeno FIS were also used. The developed fuzzy inference systes using Madani and Takagi Sugeno odels are depicted in Figures and. Table suarizes the training and testing RMSE values. Experient (To evaluate the effect of fuzzy operators) For Madani FIS, three Gaussian MFs for each input variable and nine Gaussian MFs for the output variable were used. The rule base consisted of nine if-then rules. T-nor and T- conor operators were product and su and the centroid ethod of defuzzification for Madani FIS, and weighted average defuzzification ethod for Takagi Sugeno FIS were used. Table suarizes the training and testing RMSE values. Experient (To evaluate the effect of defuzzification operators) For the Madani FIS, three Gaussian MFs for each input variable and nine Gaussian MFs for the output variable were used. The rule base consisted of nine ifthen rules. T-nor and T-conor operators were product and su and the following defuzzification operators were tested for Madani FIS. Table. Epirical coparison of fuzzy inference systes using Gaussian MFs. Madani FIS Root ean squared error Takagi Sugeno FIS Training Test Training Test....9 Voltage =.5 Current =.5 Power =.5 Figure 6. Madani fuzzy inference syste using two triangular MFs for input variables.

8 96 Eleents: B Signal Conditioning Voltage =.5 Current =.5 Power =. Figure 7. Takagi Sugeno fuzzy inference syste using two triangular MFs for input variables..6.8 Voltage =.5 Current =.5 Power = Figure 8. Madani fuzzy inference syste using three triangular MFs for input variables. Voltage =.5 Current =.57 Power = Figure 9. Takagi Sugeno fuzzy inference syste using three triangular MFs for input variables..9.58

9 Rule-based Expert Systes Voltage =.5 Current =.5 Power =.58 Figure. Madani fuzzy inference syste using three Gaussian MFs for input variables. Voltage =.5 Current =.5 Power = Figure. Takagi Sugeno fuzzy inference syste using three Gaussian MFs for input variables. Table. Epirical coparison of fuzzy inference systes for different fuzzy operators. Madani FIS Root ean squared error Takagi Sugeno FIS Training Test Training Test Centroid Bisector of Area (BOA) Mean of Maxiu (MOM) Sallest of Maxiu (SOM). For the Takagi Sugeno FIS, the weighted su and weighted average defuzzification ethods were used. Table suarizes the training and testing of RMSE values. Discussions of Results and Proble Solution As depicted in Table, when the nuber of input MFs were increased fro two to three, the RMSE values reduced regardless of the inference syste used. However, when the shape of the MF was changed to Gaussian, RMSE values for Madani FIS decreased but the RMSE values for Takagi Sugeno FIS increased (Table ). Using Gaussian MFs, when the T-nor and T-conor operators were changed to product and su (instead of in and ax ) both the inference ethods perfored better (Table ). Finally, the selection of an ideal defuzzification operator also has a direct influence in the perforance of FIS as shown in Table.

10 98 Eleents: B Signal Conditioning Table. Epirical coparison of fuzzy inference systes for different defuzzification operators. Madani FIS Takagi Sugeno FIS Defuzzification RMSE Defuzzification RMSE Training Test Training Test Centroid..9 Weighted su.9.8 MOM.. Weighted average.85.8 BOA.8.6 SOM.9. The design of the rule base (nuber of rules and how the inputs and outputs are related) is also very iportant for the good perforance of FIS. The role of weighting factors ephasizing the iportance of certain rules also bears a proinent role for the overall perforance. When the input/output diensions becoe larger, anual design becoes tedious and soeties could even lead to poor design and ipleentation. 8 ADAPTATION OF FUZZ INFERENCE SSTEMS Expert knowledge is often the ain source to design the fuzzy expert systes. Figure illustrates the various paraeters and coponents that need to be adapted for controlling a process. According to the perforance easure of the proble environent, the ebership functions, rule bases, and the inference echanis are to be adapted (Abraha, ). Neural network learning, self-organizing aps and clustering ethods could be used to generate rules. Gradient descent and its variants could be applied to finetune the paraeters of paraeterized input/output ebership functions and fuzzy operators (Abraha, ). Adaptation of fuzzy inference systes using evolutionary Adaptation of fuzzy inference syste Perforance easure coputation techniques has been widely explored. Evolutionary Coputation (EC) is a population based adaptive ethod, which ay be used to solve optiization probles, based on the genetic processes of biological organiss (Michalewicz and Fogel, 999). Over any generations, natural populations evolve according to the principles of natural selection and survival of the fittest, first clearly stated by Charles Darwin in On the Origin of Species. By iicking this process, EC could evolve solutions to real-world probles, if they have been suitably encoded (proble representation is called chroosoe). Autoatic adaptation of ebership functions is popularly known as self tuning and the chroosoe encodes paraeters of trapezoidal, triangle, logistic, hyperbolic-tangent, Gaussian ebership functions, and so on. Evolutionary search of fuzzy rules can be carried out using three approaches. In the first ethod (Michigan approach), the fuzzy knowledge base is adapted as a result of antagonistic roles of copetition and cooperation of fuzzy rules. The second ethod (Pittsburgh approach), evolves a population of knowledge bases rather than individual fuzzy rules. Reproduction operators serve to provide a new cobination of rules and new rules. The third ethod (iterative rule learning approach), is very uch siilar to the first ethod with each chroosoe representing a single rule, but contrary to the Michigan approach, only the best individual is considered to for part of the solution, discarding the reaining chroosoes of the population. The evolutionary learning process builds up the coplete rule base through an iterative learning process (Cordón et al., ). + Mebership functions if-then rules Process Fuzzy operators Knowledge base Fuzzy inference syste Figure. Adaptation of fuzzy inference systes. 9 SUMMAR Rule-based expert systes have been applied in a vast nuber of application areas. An iportant advantage of the fuzzy expert syste is that the knowledge is expressed as easy-to-understand linguistic rules. If we have data, the fuzzy expert syste can be taught using neural network

11 Rule-based Expert Systes 99 learning, EC, or other adaptation techniques. It is to be expected that the nuber of applications will grow considerably in the future now that success is clearly proven for these ethods. REFERENCES Abraha, A. () Neuro-Fuzzy Systes: State-of-the-Art Modeling Techniques, Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence, in Lecture Notes in Coputer Science, Vol. 8, (eds. Mira., Jose and Prieto., Alberto) Springer Verlag, Gerany (pp ). Abraha, A. () Intelligent Systes: Architectures and Perspectives, Recent Advances in Intelligent Paradigs and Applications, in Studies in Fuzziness and Soft Coputing, Chapter, (eds A., Abraha, L., Jain and J., Kacprzyk), Springer Verlag, Gerany (pp. 5). Abraha, A. and Khan, M.R. () Neuro-Fuzzy Paradigs for Intelligent Energy Manageent, Innovations in Intelligent Systes: Design, Manageent and Applications, in Studies in Fuzziness and Soft Coputing, Chapter, (eds A., Abraha, L., Jain and B., Jan van der Zwaag), Springer Verlag, Gerany (pp. 85 ). CLIPS () Expert Syste Shell < CLIPS.htl>. Cordón, O., Herrera, F., Hoffann, F. and Magdalena, L. () Genetic Fuzzy Systes: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases, World Scientific Publishing Copany, Singapore. Donald, W.A. (986) A Guide to Expert Systes, Addison- Wesley, Boston, MA. Fuzzy Logic Toolbox, The MathWorks () athworks.co/products/fuzzylogic/. Giarratano, J. and Riley, G. (989) Expert Systes: Principles and Prograing, PWS-Kent Publishing Co, Boston, MA. Ignizio, J.P. (99) Introduction to Expert Systes: The Developent and Ipleentation of Rule-Based Expert Systes, McGraw-Hill, Inc, USA. Jang, J.S.R., Sun, C.T. and Mizutani, E. (997) Neuro-Fuzzy and Soft Coputing: A Coputational Approach to Learning and Machine Intelligence, Prentice Hall Inc, USA. Madani, E.H. and Assilian, S. (975) An Experient in Linguistic Synthesis with a Fuzzy Logic Controller. International Journal of Man-Machine Studies, 7(),. Michalewicz, Z. and Fogel, D.B. (999) How to Solve It: Modern Heuristics, Springer Verlag, Gerany. Militallo, L.G., Hutton, R.J.B. (998) Applied Cognitive Task Analysis (ACTA): A Practitioner s Toolkit for Understanding Cognitive. Ergonoics, (), Niwa, K., Sasaki, K. and Ihara, H. (988) An Experiental Coparison of Knowledge Representation Schees, in Principles of Expert Systes, (Eds A., Gupta and E.B., Prasad), IEEE Press, New ork (pp. ). Schneider, M., Langholz, G., Kandel, A. and Chew, G. (996) Fuzzy Expert Syste Tools, John Wiley & Sons, USA. Takagi, T. and Sugeno, M. (985) Fuzzy identification of systes and its applications of odeling and control, IEEE Transactions of Systes. Man and Cybernetics, USA (pp. 6 ). Vicente, K.J. (999) Cognitive Work Analysis: Towards Safe, Productive, and Healthy Coputer-Based Work, Lawrence Erlbau Associates, Inc. Press, USA. Zadeh, L.A. (965) Fuzzy Sets. Inforation and Control, 8, 8 5.