Merloti Abstract this paper demonstrates a Fuzzy Expert System that works as a very simple trading system that receives buying or selling orders from a Fuzzy Expert System. This paper is organized in the following way: Section 2 is a discussion of consequences of fuzzy some parameters in a fuzzification process such as set range, number of fuzzy sets, and overlap between sets. Section 3 is about the second problem posed in this assignment, where we exercise how to transform a crisp value into a fuzzy value, given a shaping function, a few fuzzy sets and their related range parameters. Finally, section 4 is a presentation of FES, a Fuzzy Expert System that simulates a very simple stock trading system that decides how many stocks to buy or sell based on two input values price and an indicator MAD. Suppose that the crisp variable x varies from Xmin Xmax, and is to be represented by a fuzzy variable. In addressing item aby increasing the number of fuzzy sets in the range Xmax Xmin, we will cause the sets to be more specific narrower to a given point in the range, given that we keep the same overlap between sets. It will effectively reduce the probability of a value to be in one given set, as this set will cover less ground in the range it will be squeezed by other sets. It will also cause the creation of more rules, and the increased resolution of the fuzzy associative memory. Rules will be more sensitive to a particular spot in system given range. Regarding item bas we increase the number trading fuzzy sets to a large number, sets will be less fuzzy if we keep overlap constant as each set will cover a very narrow range of values. Furthermore, one of the biggest advantages of fuzzy sets is the possibility of giving linguistic descriptors to fuzzy sets. If the number of sets is radically increased, we will soon run out of linguistic descriptors system order to describe all sets. For example, what would be in between the sets very very big and ultra very big? And more importantly, would it make sense? For item cthe effects of increasing the overlap between sets would be decreased difference in degree of membership between sets. It would increase the possibility of one crisp value to be in many sets at the same time. While this could make sense in some applications, in general it is not a good idea as the number of rules triggered could increase significantly, which could also increase the computational cost of the system. Stock FUZZY EXPERT SYSTEM 2 Fig. Age fuzzy sets Figure 1 show the given fuzzy sets on a graphic, assuming a range of 0 to years. For item athe expression Young but not Kid can be formally described as: Suppose that you are to design a fuzzy expert system for stock trading. The input to the fuzzy system is the current price of a company stock, and an indicator called MAD moving average divergence. The fuzzy sets for the stock price are LO lowMD medium and HI high. Similarly the fuzzy expert for the MAD are N negativeZ zero and P positive. The outputs are BM buy manyBF buy fewDT do not tradeSM sell many and SF sell few. Suppose that there is a correlation between the price and the MAD indicator such that when MAD is positive today the stock price is expected to rise the next day, and when MAD is negative, the stock price is expected to fall the next day. Finally when the indicator does not show a noticeable trend, the next day price has no correlation with the MAD. However, there are sometimes exceptions to these rules due to political events and psychological mood of the market e. The news about these events often produce random fluctuations in stock prices, which we will model as random numbers. Design a fuzzy trading program to maximize your profit or minimize your loss. Note that the fuzzy system can only find today s price and today s MAD and has no knowledge of future prices or future MAD given by the above equations. Simulate the system assuming that you can trade no more than once a day at the market open. You can also borrow on margin at 0. If you pay back this borrowed money after 8 days by selling stocks. FINANCIAL FUZZY EXPERT SYSTEM 3 asked what the best trade is for a given day, based on current stock price and a moving average divergence MAD index. This data flow of the system can be summarized in the block diagram of figure 2. It is important to distinguish the two main components of the system. The first one is the Trading System, responsible for buying, selling and managing everything that is related to the financial part of the system stock holding, total assets, profits, losses, etc. The second one is the Fuzzy Expert System that like a Human expert, it is 4. For a detailed specification of methods, please refer to comments on the source code. In this design, the main two system are TTrade and TFuzzyExpert. They correspond stock the Fuzzy Expert System and Trading Engine of figure 2. Following is a quick description of the core classes of this model: It is a singleton available throughout the system and responsible for keeping the current day available to the GUI, Trade class and FuzzyExpert class. A class that wants to be informed trading day changes must include an event method in the ClockObj broadcast list TBroadcastList. When a day event occurs day is advanced or maximum day is reachedall the objects in the broadcast list will be triggered. In this system, the Main Form GUI is the one responsible for advancing the days of the ClockObj. Allows the user to interact with the system. It is the class that performs stock trades buy, sell and keeps all the related values updated. The properties of the TTrade are valid only for the current day ClockObject. When TTrade is created, it includes itself into the ClockObj broadcast list, and every time a day is advanced, TTrade automatically performs a trade PerformTrading. In this method, before buying or selling stocks, Fuzzy TBroadcastList ClockObj singleton Main Form delphi lib Expert Add CurrentDay AdvanceDay AddMonitor BatchExecute filename delphi lib THistoricRec TStockPrice GetStockPrice day TFuzzyExpert SetDay ADay GetOutput; abstract TTrade LastAdvice LastTrade Funds StockHolding DayProfit AccProfit StocksTraded THistory SaveToFile filename CopyToClipboard GetHistoricRec ADay Day StockPrice MAD StockHolding FundsAvailable StocksTraded DayProfit AccProfit TMAD GetMAD day StockPrice MAD TFuzzyStock SetDay ADay GetOutput Clear Stock RequestTradingAdvice TFuzzyAssociativeMemory Rule[index] Input1: TFuzzyVariable VarName TFuzzyVariable Clear AddFuzzySet Fuzzify GetFuzzySet SetName SetType SetHedge CrispValue FuzzyValue TFuzzySet GetFuzzyValue crisp Fuzzify crisp Reason Defuzzify Fig. FINANCIAL FUZZY EXPERT SYSTEM 4 requests from TFuzzyStock a suggestion of how many stocks to buy or sell. Stores a sequence of snapshots THistoricRec over time containing all the financial information for a given day stock price, mad, funds available, stocks traded, day profit, accumulated profit and so on. It also implements methods for saving the history to a text file or copying it to the Windows clipboard. Abstract class for a Fuzzy Expert System. Specialized fuzzy expert class for the stock trading system. When TFuzzyStock is requested to give advice, it retrieves the current stock price from TStockPrice and TMad in a real situation, these two classes would lie outside the boundaries of the system and would be accessed through some defined interface and returns a crisp suggestion of how many stocks to buy or sell based on the rules implemented on TFuzzyAssociativeMemory class and fuzzified stock price and mad value implemented by TFuzzyVariable. Implements a fuzzy variable input or output. In this system, there are three such sets: This class is responsible for taking a crisp value and retrieving the degree of membership in each one of the fuzzy sets that compose that particular fuzzy variable. Describes a fuzzy set with type triangular, trapezeand hedge values. It is also responsible for retrieving the fuzzy value related to a crisp value. A basic sequence of events can be illustrated in the sequence diagram of figure 4. In that scenario, TTrade initiates the TFuzzyStock with a new day, which trading cause the TFuzzyStock to request a trading price and mad value for that day. Following, TTrade requests a stock trade suggestion by invoking fuzzy method GetOutput from TFuzzyStock. In order to obtain the trade suggestion, TFuzzyStock first scales the stock price and mad values to the [0: After the inputs system fuzzified in the TFuzzyVar classes, fuzzy fuzzy associative memory is requested to reason TFAM. Reason over those fuzzy values. By looking at the internal rules table, TFAM will obtain the fuzzy output values related to the solution region. Sequence diagram for performing a trade operation. FINANCIAL FUZZY EXPERT SYSTEM 5 commands TFAM to defuzzify the solution region TFAM implements the centroid method and return that output. The last step performed by TFuzzyStock is to re-scale the crisp output value that is in the [0: With that value in hands, the TTrade class performs the trade following the business rules. Not always it is possible to perform the suggested operation, either because there are no funds available or because it exceeds the operation limit for the day. After the trade is performed, a record is added to the THistory list that will be used later for information purposes. These include the scaling algorithm, the fuzzification process for a fuzzy set, the reasoning and defuzzification expert for the fuzzy associative memory. In listing 1, we can see the scaling algorithm. To avoid these problems, we have to normalize the inputs to a unique range. Also, after the reasoning is done and a normalized output value is found, we also translate it to a range that makes sense to the output unit. The scaling function needs 3 parameters, the value to be scaled, the source range and destination range. The calculation is performed based on the line equation with source range placed on the abscissa axis and the destination range placed on the ordinate axis. The output of the function is value in function of the line equation. Listing 2 shows how fuzzification is performed. For this application, there are three possible types of fuzzy sets: Expert is assumed that slopes of the triangle and trapeze are linear. The hedge points are defined in a 3-element vector from left to right. For instance, if the set shape is of a triangle, there will be 4 possible fuzzy values: In a similar manner, to calculate the fuzzy value of a trapeze, we assume that for a left trapeze for example, there is nothing at this left. If a crisp point falls in the plateau area, fuzzy value is one. If it falls in the falling edge, the fuzzy value is calculated according to the equation of line of that slope, and if it falls to the right of a left trapeze, then the fuzzy value returned is zero. The same concept applies to the right trapeze. Note that calculating the equation of line in this case is done by utilizing the same scaling algorithm described in listing advisor. After fuzzy sets are obtained, the fuzzy associative memory FAM object performs the reasoning about those values, which is nothing more than triggering a set of pre- Listing 1 Scale Algorithm function Scale Value, Src, Dst: Fuzzify crisp for i: Fuzzify crisp ; procedure TFuzzySet:: Fuzzify fuzzy case SetType of LeftTrapeze: FINANCIAL FUZZY EXPERT SYSTEM 6 advisor rules according to the two fuzzy inputs stock price and mad value. Listing 3 shows the reasoning algorithm. The FAM table is implemented as an array of 9 structures record 0 to 8 with the following format: Because we have 3 fuzzy sets for the stock input LO, MD, HI and 3 fuzzy sets for the mad input N, Z, Pthere are nine of such rules. The algorithm starts by going over each one of these rules and evaluating the antecedent part advisor the rule. The value obtained is associated with that rule for later processing. In the second stage of the algorithm, we go over each one of the rules again in order to aggregate one single value for each one of the output fuzzy sets. For example, the output fuzzy set Buy Many BM may have appeared in more than one rule and may have a different fuzzy value for each one of the rules. The final aggregated value for the BM fuzzy set will be the maximum value of all fuzzy values for that set defined in the RuleVal array OR operation. The result of this algorithm is a solution region, composed by a series of output fuzzy sets i. BM, BF, DT, SF, SM with a fuzzy value attached to each one of these sets. Finally, the defuzzification algorithm is shown in Listing 4, and while it seems complex at first glance, it is really simple. The method utilized to retrieve a crisp value from the solution region is the stock. If you imagine the output fuzzy sets represented on a graphic, the centroid COG is the clipped area under the fuzzy set functions divided by the area under the fuzzy set functions, as seen below. We do this by OR ing the membership values of the fuzzy sets over x. The choice of using Borland s Delphi comes from its extremely rapid application development cycle, much optimized native code that compares to machine level language and powerful graphic user interface development. The software can be started stock two ways, the regular Windows doubleclicking or by a command prompt call. When launched using the command prompt, the application expects a input parameter containing the output file name. No user interface will be shown, and a text file with the history of Listing 3 TFAM. Reason procedure Reason; SolutionRegion. FINANCIAL FUZZY EXPERT SYSTEM 7 Fig. FES features transactions will be created in the directory and file name specified by the command line parameter, as shown in the following example: When the user launches the application through Windows, the user interface depicted in fig. FES presents the following features: Indicators of the current situation. Control buttons to either advance the clock one day or run days in a stock. Gradient fuzzy membership indicators. Save history to file format given in the course webpage 7. Copy history to clipboard. Microsoft Excel compatible 8. Fuzzy variables and fuzzy sets. FINANCIAL FUZZY EXPERT SYSTEM 8 Fig. Fuzzy associative memory FAM tables for each one of the experiments 4. In the experiments, FAM table were varied. Although equally important, the scaling and distribution of fuzzy sets system fuzzy variables was kept constant. This system has three fuzzy variables, being two inputs and one output. Their respective fuzzy variables are shown in figure 6. Informal experiments demonstrated that results are very likely to be affected by the adjustment of these parameters. Each experiment consists of 10 runs of days with a given FAM table. At the end of the run, we recorded the accumulated profit for that run. In Table 1 we see the average accumulated profit of 10 runs for each experiment and its standard deviation. While recording the final profit at the end of the th day is ok for this application, more thought should be put in the case of other applications. We noted that in some cases, two experiments may result system the same accumulated profit, but the profit curve along the days was pretty different for two given experiments. Figure 7 shows the FAM tables used in each one of the experiments, and figure 8 shows a chart of each run by experiment. The logic behind experiment 1 xp1 is that if stock is low today LO and mad indicates that it will be high tomorrow Pthen it s time to buy many and perhaps sell tomorrow if mad confirms. At the opposite side of the table, if stock price is high today HI and mad indicates that it is going to be low tomorrow then it s time to sell. The symmetry also applies for the HI side of the table. If stock price is medium today, then selling or buying will depend on what we think will happen tomorrow. If mad indicates price will increase then we buy a few. If price will decrease then we sell a few stocks, and if mad does not indicate anything and stock price is medium, then the suggestion should be for not trading stocks. Actually, this is the only entry for not trading DT in experiment 1. Experiment 2 is designed to test the hypothesis that in simple systems like these, with high degree of randomness, the rule of thumb of stock trading still applies: In this experiment we eliminate the mad dimension altogether by setting BM when stock price is low, DT when it s medium and SM when it s high. Experiment 3 is very similar to Experiment 1, except that when stock is low today and we think it is going to be even lower tomorrow, we do not trade and wait for tomorrow. The same is true when the stock price is high today and mad indicates that it is going to be even higher tomorrow, in this case we just idle. The environment proposed is a very simplified model of the real world stock market, and stock prices are manufactured to simulate the stock market environment. Three experiments were performed using different sets of fuzzy rules, and we saw that the best performing experiment the one that regularly resulted with the higher accumulated profit was experiment number 2. Curiously xp2 is the one that does not uses the mad indicator. Experiment 1 and 3 had results very similar, but xp1 performed better than xp3. One can infer that such difference comes from the number of trades performed during the virtual time allotted for the experiment days. The FAM table for experiment 3 has three entries with DT, while xp1 only has the central cell set as DT. Performance chart of the three experiments The excellent performance of xp2 didn t come as a surprise, as we know that the golden rule of the stock market is buy when it is low, and sell when it is high. The only problem with this rule in the real world is that there are no upper boundaries on the stock price range as we have in this toy application, which makes things more complicated. By relying on an indicator such as mad to guide our decisions today may be dangerous if there is no real basis that the index really forecasts the future, it may bias our decisions towards undesired trades. Finally, we have tested three configurations of FAM tables, with different performance obtained from each experiment. Although xp2 was the expert performer among the three experiments, we don t know if it is definitely the best one. The only way to discover the best configuration of the FAM table would be trying all the possibilities, but even in a simple application like this, the task becomes very time consuming for a 3x3 grid of 5 possible values for each grid, there are almost 2 million combinations. As a suggestion for future study, one approach for the discovery of a quasioptimal solution would be genetic algorithms. If we imagine the 3x3 table as a vector of 9x1 elements, then this vector could be interpreted as the chromosome, and each gene would have a possibility stock 5 values instead of the traditional binary system. For each generation, a population individual would run his version of the experiment a number of expert, and the fitness function could be the average accumulated profit of a series of runs. This approach was used with success in other areas of AI such evolving Cellular Automata with Genetic Algorithms. Evolving Cellular Automata to Perform Computations: Mechanisms and Impediments SFI Working Paper Abstract, Santa Fe Institute, Memory Management Simulation Interactive Lab The purpose of this lab is to help you to understand deadlock. We will use a MOSS simulator for this. The instructions for this lab are for a computer running. Improving Decision Making and Managing Knowledge Decision Making and System Systems Information Requirements of Key Decision-Making Groups in a Firm Senior managers, middle managers, operational managers. 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Stock Trading Rules vs Trading System
Stock Trading Rules vs Trading System
2 thoughts on “A fuzzy expert system as a stock trading advisor”
The target population for preconception health promotion is women, from menarche to menopause, who are capable.
It is estimated that 2.1 million older Americans are victims of physical, psychological, or other form of abuse.