Synthesis of fuzzy logic and Dempster–Shafer Theory for the simulation of the decision-making process in stock trading systems

Modern computerized stock trading systems (mechanical trading systems) are based on the simulation of the decision-making process and generate advice for traders to buy or sell stocks or other financial tools by taking into account the price history, technical analysis indicators, accepted rules of trading and so on. Two stock trading simulating systems based on trading rules defined using fuzzy logic are developed and compared. The first is based on the so-called “Logic-Motivated Fuzzy Logic Operators” (LMFL) approach and aims to avoid certain disadvantages of the classical Mamdani’s method, which has been developed for use in fuzzy logic controllers and not for solving the decision-making problems of stock trading. The LMFL   approach is based on the modified mathematical representation of t$t$-norm and Yager’s implication rule. The second trading system combines the tools of fuzzy logic and Dempster–Shafer Theory (DST  ) to represent the features of the decision-making process more transparently. The fuzzy representation of trading rules based on the theory of technical analysis is used in these expert systems. Since the theory of technical analysis is based on the indicators used by experts to predict stock price movements, the method maps these indicators into new inputs that can be used in a fuzzy logic system. The only required inputs to calculate these indicators are past sequences (history) of stock prices. The method relies on fuzzy logic to choose an appropriate decision when certain price movements or certain price formations occur. The optimization procedure based on historical (teaching) data is used as it significantly improves the performance of such expert systems. The efficiency of the developed expert systems is measured by comparing their outputs versus stock price movements. The results obtained using real NYSE$NYSE$ data allow us to say that the developed expert system based on the synthesis of fuzzy logic and DST provides better results and is more reliable. Moreover, such a conjunction of fuzzy logic, DST and technical analysis, makes it possible to make a profit even when trading against a dominating trend.     

A stock trading expert system based on the rule-base evidential reasoning using Level 2 Quotes

Generally, stock trading expert systems (STES) called also “mechanical trading systems” are based on the technical analysis, i.e., on methods for evaluating securities by analyzing statistics generated by the market activity, such as past prices and volumes (number of transactions during a unit of a timeframe). In other words, such STES are based on the Level 1 information. Nevertheless, currently the Level 2 information is available for the most of traders and can be successfully used to develop trading strategies especially for the day trading when a significant amount of transactions are made during one trading session. The Level 2 tools show in-depth information on a particular stock. Traders can see not only the “best” bid (buying) and ask (selling) orders, but the whole spectrum of buy and sell orders at different volumes and different prices. In this paper, we propose some new technical analysis indices bases on the Level 2 and Level 1 information which are used to develop a stock trading expert system. For this purpose we adapt a new method for the rule-base evidential reasoning which was presented and used in our recent paper for building the stock trading expert system based the Level 1 information. The advantages of the proposed approach are demonstrated using the developed expert system optimized and tested on the real data from the Warsaw Stock Exchange.     

Knowledge acquisition for fuzzy expert systems

Expert systems have been successfully applied to a wide variety of application domains. to achieve better performance, researchers have tried to employ fuzzy logic to the development of expert systems. However, as fuzzy rules and membership functions are difficult to define, most of the existing tools and environments for expert systems do not support fuzzy representation and reasoning. Thus, it is time-consuming to develop fuzzy expert systems. In this article we propose a new approach to elicit expertise and to generate knowledge bases for fuzzy expert systems. A knowledge acquisition system based upon the approach is also presented, which can help knowledge engineers to create, adjust, debug, and execute fuzzy expert systems. Some control techniques are employed in the knowledge acquisition system so that the concepts of fuzzy logic could be directly applied to conventional expert system shells; moreover, a graphic user interface is provided to facilitate the adjustment of membership functions and the display of outputs. the knowledge acquisition system has been integrated with a popular expert system shell, CLIPS, to offer a complete development environment for knowledge engineers. With the help of this environment, the development of fuzzy expert systems becomes much more convenient and efficient. © 1995 John Wiley & Sons, Inc.     

Focusing and polarization in linear,intuitionistic, and classical logics

A focused proof system provides a normal form to cut-free proofs in which the application of invertible and non-invertible inference rules is structured. Within linear logic, the focused proof system of Andreoli provides an elegant and comprehensive normal form for cut-free proofs. Within intuitionistic and classical logics, there are various different proof systems in the literature that exhibit focusing behavior. These focused proof systems have been applied to both the proof search and the proof normalization approaches to computation. We present a new, focused proof system for intuitionistic logic, called LJF, and show how other intuitionistic proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing. We also use LJF to design a focused proof system LKF for classical logic. Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard’s LC and LU proof systems.     

Profitability Edge by Dynamic Back Testing Optimal Period Selection for Technical Parameters Optimization,in Trading Systems with Forecasting

Back testing process is widely used today in forecasting experiments tests. This method is to calculate the profitability of a trading system, applied to specific past period. The data which are used, correspond to that specific past period and are called “historical data” or “training data”. There is a plethora of trading systems, which include technical indicators, trend following indicators, oscillators, control indicators of price level, etc. It is common nowadays for calculations of technical indicator values to be used along with the prices of securities or shares, as training data in fuzzy, hybrid and support vector machine/regression (SVM/SVR) systems. Whether the data are used in fuzzy systems, or for SVM and SVR systems training, the historical data period selection on most occasions is devoid of validation (In this research we designate historical data as training data). We substantiate that such an expert trading system, has a profitability edge—with regard to future transactions—over currently applied trading strategies that merely implement parameters’ optimization. Thus not profitable trading systems can be turned into profitable. To that end, first and foremost, an optimal historical data period must be determined, secondarily a parameters optimization computation must be completed and finally the right conditions of parameters must be applied for optimal parameters’ selection. In this new approach, we develop an integrated dynamic computation algorithm, called the “d-BackTest PS Method”, for selection of optimal historical data period, periodically. In addition, we test conditions of parameters and values via back-testing, using multi agent technology, integrated in an automated trading expert system based on Moving Average Convergence Divergence (MACD) technical indicator. This dynamic computation algorithm can be used in Technical indicators, Fuzzy, SVR and SVM and hybrid forecasting systems. The outcome crystalizes in an autonomous intelligent trading system.     

Systemic approach to fuzzy logic formalization for approximate reasoning

L.A. Zadeh, E.H. Mamdani, M. Mizumoto, et al., R.A. Aliev and A. Tserkovny have proposed methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form “If x is A then y is B”, with A and B being fuzzy concepts (fuzzy sets). A formulation of fuzzy antecedent/consequent chains is one of the most important topics within a wide spectrum of problems in fuzzy sets in general and approximate reasoning, in particular. From the analysis of relevant research it becomes clear that for this purpose, a so-called fuzzy conditional inference rules comes as a viable alternative. In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. For this reason, we put together some comparative analysis of fuzzy reasoning methods in which antecedents contain a conditional proposition with fuzzy concepts and which are based on implication operators present in various types of fuzzy logic. We also show a process of a formation of the fuzzy logic regarded as an algebraic system closed under all its operations. We examine statistical characteristics of the proposed fuzzy logic. As the matter of practical interest, we construct a set of fuzzy conditional inference rules on the basis of the proposed fuzzy logic. Continuity and stability features of the formalized rules are investigated.     

Fuzzy logic system based prediction effort: A case study on the effects of tire parameters on contact area and contact pressure

Various methodologies of artificial intelligence have been recently used for estimating performance parameters of soil working machines and off-road vehicles. Due to nonlinear and stochastic features of soil–wheel interactions, application of knowledge-based Mamdani max–min fuzzy expert system for estimation of contact area and contact pressure is described in this paper. Fuzzy logic model was constructed by use of the experience of contact area and contact pressure utilizing data obtained from series of experimentations in soil bin facility and a single-wheel tester. Two paramount tire parameters: wheel load and tire inflation pressure are the input variables for our model, each has five membership functions. As a fundamental aspect of the fuzzy logic based prediction systems, a set of fuzzy if-then rules were used in accordance with fuzzy logic principles. 25 linguistic if-then rules were included to develop a complicated highly intelligent predicting model based on Centroid method at defuzzification stage. The model performance was assessed on the basis of several statistical quality criteria. Mean relative error lower than 10%, satisfactory scattering around unity-slope line (T), and high coefficient of determination, R², were obtained by the fuzzy logic model proposed in this study.     

Developing a rule change trading system for the futures market using rough set analysis

Many technical indicators have been selected as input variables in order to develop an automated trading system that determines buying and selling trading decision using optimal trading rules within the futures market. However, optimal technical trading rules alone may not be sufficient for real-world application given the endlessly changing futures market. In this study, a rule change trading system (RCTS) that consists of numerous trading rules generated using rough set analysis is developed in order to cover diverse market conditions. To change the trading rules, a rule change mechanism based on previous trading results is proposed. Simultaneously, a genetic algorithm is employed with the objective function of maximizing the payoff ratio to determine the thresholds of market timing for both buying and selling in the futures market. An empirical study of the proposed system was conducted in the Korea Composite Stock Price Index 200 (KOSPI 200) futures market. The proposed trading system yields profitable results as compared to both the buy-and-hold strategy, and a system not utilizing a genetic algorithm for maximizing the payoff ratio.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference

Information systems, which contain only crisp data, precise and unique attribute values for all objects, have been widely investigated. Due to the fact that in realworld applications imprecise data are abundant, uncertainty is inherent in real information systems. In this paper, information systems are called fuzzy information systems, and formalized by (objects; attributes; f), in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values. To interpret and extract fuzzy decision rules from fuzzy information systems, the meta-theory based on modal logic proposed by Resconi et al. is modified. The modified meta-theory not only expresses uncertainty between objects and their attributes, but also uncertainty in the process of recognizing fuzzy information systems. In addition, according to perception computing (proposed by Zadeh), granules of fuzzy information systems can be represented by fuzzy decision rules, so that, fuzzy inference methods can be used to obtain the decision attribute of a new object. Finally, a novel way of combining evidences based on the modified meta-theory is introduced, which extends the concept of combining evidences based on Dempster-Shafer theory.     

Combining technical trading rules using particle swarm optimization

Technical trading rules have been utilized in the stock market to make profit for more than a century. However, only using a single trading rule may not be sufficient to predict the stock price trend accurately. Although some complex trading strategies combining various classes of trading rules have been proposed in the literature, they often pick only one rule for each class, which may lose valuable information from other rules in the same class. In this paper, a complex stock trading strategy, namely performance-based reward strategy (PRS), is proposed. PRS combines the two most popular classes of technical trading rules – moving average (MA) and trading range break-out (TRB). For both MA and TRB, PRS includes various combinations of the rule parameters to produce a universe of 140 component trading rules in all. Each component rule is assigned a starting weight, and a reward/penalty mechanism based on rules’ recent profit is proposed to update their weights over time. To determine the best parameter values of PRS, we employ an improved time variant particle swarm optimization (TVPSO) algorithm with the objective of maximizing the annual net profit generated by PRS. The experiments show that PRS outperforms all of the component rules in the testing period. To assess the significance of our trading results, we apply bootstrapping methodology to test three popular null models of stock return: the random walk, the AR(1) and the GARCH(1, 1). The results show that PRS is not consistent with these null models and has good predictive ability.     

Implementation of a microcontroller-based simplified FITA-FIS model

The paper describes basic approach to building a general purpose MISO-FITA (multiple inputs single output rule based system) fuzzy logic inference system. It is also discussed classic and simplified models of the inference systems and some optimization methods of its architecture. The fuzzy engine of the proposed system is based on simplified Mamdani’s fuzzy inference model. It has been implemented on the sample platform based on ARMv7 Cortex-M4 microcontroller. The performance of the fuzzy inference system, defined as a time to obtain an output crisp inference result, is higher or comparable to another software and hardware solutions. For proposed system it even takes 10 μs.     

FuzzyShell: a large-scale expert system shell using fuzzy logic foruncertainty reasoning

There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. However, unfortunately, much of what has been proposed can only be applied to small-scale expert systems; that is, when the number of rules is in the dozens as opposed to in the hundreds. The more traditional (nonfuzzy) expert systems are able to cope with large numbers of rules by using Rete networks for maintaining matches of all the rules and all the facts. (A Rete network obviates the need to match the rules with the facts on every cycle of the inference engine.) In this paper, we present a more general Rete network that is particularly suitable for reasoning with fuzzy logic. The generalized Rete network consists of a cascade of three networks: the pattern network, the join network, and the evidence aggregation network. The first two layers are modified versions of similar layers for the traditional Rete networks and the last, the aggregation layer, is a new concept that allows fuzzy evidence to be aggregated when fuzzy inferences are made about the same fuzzy variable by different rules     

Application of fuzzy expert systems in assessing operational risk of software

Risk is the potential for realization of undesirable consequences of an event. Operational risk of software is the likelihood of untoward events occurring during operations due to software failures. NASA IV&V Facility is an independent institution which conducts Independent Assessments for various NASA projects. Its responsibilities, among others, include the assessments of operational risks of software. In this study, we investigate Independent Assessments that are conducted very early in the software development life cycle.Existing risk assessment methods are largely based on checklists and analysis of a risk matrix, in which risk factors are scored according to their influence on the potential operational risk. These scores are then arithmetically aggregated into an overall risk score. However, only incomplete project information is available during the very early phases of the software life cycle, and thus, a quantitative method, such as a risk matrix, must make arbitrary assumptions to assess operational risk.We have developed a fuzzy expert system, called the Research Prototype Early Assessment System, to support Independent Assessments of projects during the very early phases of the software life cycle. Fuzzy logic provides a convenient way to represent linguistic variables, subjective probability, and ordinal categories. To represent risk, subjective probability is a better way than quantitative objective probability of failure. Furthermore, fuzzy severity categories are more credible than numeric scores. We illustrated how fuzzy expert systems can infer useful results by using the limited facts about a current project, and rules about software development. This approach can be extended to add planned IV&V level, history of past NASA projects, and rules from NASA experts.     

Contour diagram fuzzy model for maximum surface ozone prediction

A contour diagram approach is presented for the identification of surface ozone concentration feature based on a set of rules by considering the meteorological variables such as the solar radiation, wind speed, temperature, humidity and rainfall. A fuzzy rule system approach is used because of the imprecise, insufficient, ambiguous and uncertain data available. The contour diagrams help to identify qualitative ozone concentration variability rules which are more general than conventional statistical or time series analysis. In the methodology, ozone concentration contours are based on a fixed variable as ozone precursor, namely, NO_x and as the third variable one of the meteorological factors. Such contour diagrams for ozone concentration variation are prepared for six months. It is possible to identify the maximum ozone concentration episodes from these diagrams and then to set up the valid rules in the form of IF-THEN logical statements. These rules are obtained from available daily ozone, NO_x and meteorological data as a first approximate reasoning step. In this manner, without mathematical formulations, expert maximum ozone concentration systems are identified. The application of the contour diagram approach is performed for daily ozone concentration measurements on European side of Istanbul city. It is concluded that through approximate reasoning with fuzzy rules, the maximum ozone concentration episodes can be identified and predicted without any mathematical expression.     

Fuzzy concepts in an object oriented expert system shell

Fuzzy logic is one of the methods to model the vagueness and imprecision of human knowledge. Some rule-based expert system shells have been successfully developed and have demonstrated the power of fuzzy logic in dealing with inexact reasoning and rule inferences. However, using rules for knowledge representation is not structured enough. In addition, knowledge cannot be easily represented in an abstracted (hierarchical) from. In this article the introduction of fuzzy concepts into object oriented knowledge representation (OOKR), which is a structured knowledge representation scheme, is presented. A framework for handling all the possible fuzzy concepts in OOKR at both the dynamic and static levels is proposed. In order to handle the inheritance mechanism and to model the relations among classes, instances, and attributes, some new fuzzy concepts and operations are introduced. These concepts and operations are developed from the semantic meaning rather than by an ad hoc approach. A prototype of the expert system shell. System FX-I, has been successfully developed based on the above framework, showing the feasibility of handling inexact knowledge in a structural way.     

A type-2 fuzzy rule-based expert system model for stock price analysis

In this paper, a type-2 fuzzy rule based expert system is developed for stock price analysis. Interval type-2 fuzzy logic system permits us to model rule uncertainties and every membership value of an element is interval itself. The proposed type-2 fuzzy model applies the technical and fundamental indexes as the input variables. This model is tested on stock price prediction of an automotive manufactory in Asia. Through the intensive experimental tests, the model has successfully forecasted the price variation for stocks from different sectors. The results are very encouraging and can be implemented in a real-time trading system for stock price prediction during the trading period.     

Multi-objective optimal reactive power dispatch considering voltage stability in power systems using HFMOEA

This paper proposes a new hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) based approach for solving complex multi-objective, mixed integer nonlinear problems such as optimal reactive power dispatch considering voltage stability (ORPD-VS). In HFMOEA based optimization approach, the two parameters like crossover probability (P_C) and mutation probability (P_M) are varied dynamically through the output of a fuzzy logic controller. The fuzzy logic controller is designed on the basis of expert knowledge to enhance the overall stochastic search capability for generating better pareto-optimal solution. Two detailed case studies are presented: Firstly, the performance of HFMOEA is tested on five benchmark test problems such as ZDT1, ZDT2, ZDT3, ZDT4 and ZDT6 as suggested by Zitzler, Deb and Thiele; Secondly, HFMOEA is applied to multi-objective ORPD-VS problem. In both the case studies, the optimization results obtained from HFMOEA are analysed and compared with the same obtained from two versions of elitist non-dominated sorting genetic algorithms such as NSGA-II and MNSGA-II in terms of various performance metrics. The simulation results are promising and confirm the ability of HFMOEA for generating better pareto-optimal fronts with superior convergence and diversity.     

MGP-INTACTSKY: Multitree Genetic Programming-based learning of INTerpretable and ACcurate TSK sYstems for dynamic portfolio trading

In this paper, a Multitree Genetic Programming-based method is developed to learn an INTerpretable and ACcurate Takagi-Sugeno-Kang (TSK) fuzzy rule based sYstem (MGP-INTACTSKY) for dynamic portfolio trading. The MGP-INTACTSKY utilizes a TSK model with a new structure to develop a more interpretable and accurate system for dynamic portfolio trading. In the new structure of TSK, disjunctive normal form rules with variable structured consequent parts are developed in which the absence of some input variables is allowed. Input variables are the most influential technical indices which are selected by stepwise regression analysis. The technical indices are computed using wavelet transformed stock price series to eliminate the noise. The proposed system directly induces the preferred portfolio weights from the stock's technical indices through time. Here, genetic programming with the multitree structure is applied to learn the TSK fuzzy rule bases with the Pittsburgh approach. With this approach, the correlation of different stocks is properly considered during the evolutionary process. To evaluate the performance of the MGP-INTACTSKY for portfolio trading, the proposed model is implemented on the Tehran Stock Exchange as an emerging market as well as Toronto and Frankfurt Stock Exchanges as two mature markets. The experimental results show that the proposed model outperforms other methods such as the momentum strategy, the multitree genetic programming-based crisp system, the genetic algorithm-based first order TSK system, the buy and hold approach and the market's main index in terms of accuracy and interpretability.     

Computer networks design using hybrid fuzzy expert systems

 Designing and configuring large computer networks to support a variety of applications and computational environments is difficult, as it not only requires highly specialized technical skills and knowledge, but also a deep understanding of a dynamic commercial market. Hybrid fuzzy expert systems integrate fuzzy expert systems and neural networks methods replacing classical hard decision methods and providing better performance than traditional techniques. In this paper, we present an integrated fuzzy expert system, machine learning, and neural networks approach to large structured computer networks design and evaluation. After presenting an overview of the system and the major research choices, we describe in detail the system's modules and present examples of its potential use.