Fuzzy System Theory Research Articles

Fuzzy-Based Techniques in Human-Like Processing of Social Network Data

Social networks have gained a lot attention. They are perceived as a vast source of information about their users. Variety of different methods and techniques has been proposed to analyze these networks in order to extract valuable information about the users – things they do and like/dislike. A lot of effort is put into improvement of analytical methods in order to grasp a more accurate and detailed image of users. Such information would have an impact on many aspects of everyday life of people – from politics, via professional life, to shopping and entertainment.The theory of fuzzy sets and systems, introduced in 1965, has the ability to handle imprecise and ambiguous information, and to cope with linguistic terms. The theory has evolved into such areas like possibility theory and computing with words. It is very suitable for processing data in a human-like way, and providing the results in a human-oriented manner.The paper presents a short survey of works that use fuzzy-based technologies for analysis of social networks. We pose an idea that fuzzy-based techniques allow for introduction of humancentric and human-like data analysis processes. We include here detailed descriptions of a few target areas of social network analysis that could benefit from applications of fuzzy sets and systems methods.

Soil compaction optimization with soft constrain

The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In soil mechanics relationship between the causes and effects can be observed with laboratory tests but is difficult to develop analytical functions or numerical relations between input and output. In geotechnical optimization the most usual constraints represent state variables of structural response for each loading case. The aim of this paper is to define the soft constrain with adaptive network-based fuzzy inference system (ANFIS) in the soil mechanics. The developed soft constrain is than applied in non-linear programming (NLP) to obtain optimal solution. In the case of soil compaction the performance of the proposed optimization algorithm is evaluated. The main aim of soil compaction is to define optimal water content at which soil can be compacted to a densest state that improve their mechanical and physical properties.

An FDES-Based Shared Control Method for Asynchronous Brain-Actuated Robot.

The asynchronous brain-computer interface (BCI) offers more natural human-machine interaction. However, it is still considered insufficient to control rapid and complex sequences of movements for a robot without any advanced control method. This paper proposes a new shared controller based on the supervisory theory of fuzzy discrete event system (FDES) for brain-actuated robot control. The developed supervisory theory allows the more reliable control mode to play a dominant role in the robot control which is beneficial to reduce misoperation and improve the robustness of the system. The experimental procedures consist of real-time direct manual control and BCI control tests from ten volunteers. Both tests have shown that the proposed method significantly improves the performance and robustness of the robotic control. In an online BCI experiment, eight of the participants successfully controlled the robot to circumnavigate obstacles and reached the target with a three mental states asynchronous BCI while the other two participants failed in all the BCI control sessions. Furthermore, the FDES-based shared control method also helps to reduce the workload. It can be stated that the asynchronous BCI, in combination with FDES-based shared controller, is feasible for the real-time and robust control of robotics.

A Fuzzy Trustworthiness System with Probability Presentation Based on Center-of-gravity Method

Fuzzy methods are widely used in the study of trustworthiness. Based on this fact, the paper researches the fuzzy trustworthiness system and probability presentation theory based on bounded product implication and Larsen square implication. Firstly, we convert a group of single-input and single-output data into fuzzy inference rules and generate fuzzy relation by selecting the appropriate fuzzy implication operator, then calculate joint probability density function of two-dimensional random variables by using of this fuzzy relation. Two specific probability density functions can be obtained by selecting the fuzzy implication as bounded product implication or Larsen square implication. Secondly, we study the marginal distribution and numerical characteristics of these two kinds probability distributions and point out that two of these probability distributions have the same mathematical expectation and nearly the same variance and covariance. Finally, we study of the center-of-gravity fuzzy trustworthiness system based on these two probability distributions. We gave the sufficient conditions of universal approximations for those fuzzy trustworthiness systems.

Dynamical Models of Stock Prices Based on Technical Trading Rules Part I: The Models

In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of this paper, we will show the details of how to transform the technical trading heuristics into nonlinear dynamic equations. First, we define fuzzy sets to represent the fuzzy terms in the technical trading rules; second, we translate each technical trading heuristic into a group of fuzzy IF-THEN rules; third, we combine the fuzzy IF-THEN rules in a group into a fuzzy system; and finally, the linear combination of these fuzzy systems is used as the excess demand function in the price dynamic equation. We transform a wide variety of technical trading rules into fuzzy systems, including moving average rules, support and resistance rules, trend line rules, big buyer, big seller and manipulator rules, band and stop rules, and volume and relative strength rules. Simulation results show that the price dynamics driven by these technical trading rules are complex and chaotic, and some common phenomena in real stock prices such as jumps, trending and self-fulfilling appear naturally.

Enhancing Fingrams to deal with precise fuzzy systems

Interpretability is a highly valued capability of fuzzy systems that turns essential when dealing with human interaction. Precise fuzzy modeling prioritizes performance at the cost of harming interpretability. Fuzzy Inference-grams (Fingrams) permit the graphical representation of fuzzy systems facilitating their comprehension, analysis and interpretation at inference level. We enhance Fingrams to better represent and analyze precise fuzzy systems. A specific metric and new representations handle the particularities of such systems. A new visual artifact allows to discover the set of data instances not covered by a given fuzzy system. A novel visual representation allows to study in detail the elements that are involved in the inference of a single data instance. The potentials of the enhanced methodology are sketched by taking the Fuzzy Unordered Rule Induction Algorithm (FURIA) as an illustrative example of precise fuzzy system. For instance, a highly valuable representation is obtained for the stretching mechanism of FURIA, thus facilitating its comprehensibility.

Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

The supervisory control theory of fuzzy discrete event systems (FDESs) for fuzzy language equivalence has been developed. However, in a way, language equivalence has limited expressiveness. So if the given specification can not be expressed by language equivalence, then the control for language equivalence does not work. In this paper, we further establish the supervisory control theory of FDESs for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence. First, we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs. Then we present a method for deciding whether there is a fuzzy simulation or not. In addition, we also show several basic properties of fuzzy simulation relations. Afterwards, we put forward the notion of fuzzy simulation-based controllability, and particularly show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of FDESs. Moreover, we study the "range" control problem of FDESs. Some examples are given to illustrate the main results obtained.

Theory of Generalized Fuzzy Discrete-Event Systems

There exist a large number of systems whose state variables are continuous signals, and transit based on event-driven mechanisms. To model the transitions of these state variables, the theory of extended fuzzy discrete-event systems (EFDESs) was developed by extending the fuzzy discrete-event system (FDES) theory. However, the EFDES theory remains limited in modeling these event-driven systems. A primary reason for this is that the EFDES theory allows every event to be characterized by one variable only, and thus every event can be modeled by a fuzzy set (FS) only. Although the EFDES theory provides the steps for computing the next states of the state variables, how to compute their next states remains unknown when any event is modeled by multiple FSs. To overcome this limitation, this paper will present the theory of generalized fuzzy discrete-event systems (GFDESs) by generalizing the EFDES theory. In the proposed GFDES theory, events are characterized by their multiple attributes which may determine the transitions of the state variables, and are modeled by representing each of their attributes using one FS. To establish the GFDES theory, models for GFDESs will be presented by extending the concepts of EFDESs. To make this theory complete, the procedures for computing the next states of the state variables will also be provided. In addition, numerical examples will be presented to further illustrate the proposed GFDES theory.

Intelligent modelling of continuous stirred tank reactor process

In this paper, we discuss the theory and design of the probabilistic fuzzy inference system, one that model and minimise the effects of rule uncertainties, i.e., existing randomness in many real world systems. This approach ascends from the combination of the concepts of degree of truth and probability of truth in a unique framework. This combination is carried out both in fuzzy sets and fuzzy rules, which leads to probabilistic fuzzy sets and probabilistic fuzzy rules. Using these probabilistic elements, an innovative probabilistic fuzzy logic system is obtained as a fuzzy probabilistic model of a complex non-deterministic system. We designed probabilistic fuzzy inference system for modelling the CSTR process, which shows dynamic nonlinearity and demonstrated its upgraded performance over the conventional fuzzy inference system.

Postmodern Fuzzy System Theory: A Deconstruction Approach Based on Kabbalah

Modern general system theory proposed a holistic integrative approach based on input-state-output dynamics as opposed to the traditional reductionist detail based approach. Information complexity and uncertainty required a fuzzy system theory, based on fuzzy sets and fuzzy logic. While successful in dealing with analysis, synthesis and control of technical engineering systems, general system theory and fuzzy system theory could not fully deal with humanistic and human-like intelligent systems which combine technical engineering components with human or human-like components characterized by their cognitive, emotional/motivational and behavioral/action levels of operation. Such humanistic systems are essential in artificial intelligence, cognitive and behavioral science applications, organization management and social systems, man-machine systems or human factor systems, behavioral knowledge based economics and finance applications. We are introducing here a “postmodern fuzzy system theory” for controlled state dynamics and output fuzzy systems and fuzzy rule based systems using our earlier postmodern fuzzy set theory and a Kabbalah possible worlds model of modal logic and semantics type. In order to create a postmodern fuzzy system theory, we “deconstruct” a fuzzy system in order to incorporate in it the cognitive, emotional and behavioral actions and expressions levels characteristic for humanistic systems. Kabbalah offers a structural, fractal and hierarchic model for integrating cognition, emotions and behavior. We obtain a canonic deconstruction for a fuzzy system into its cognitive, emotional and behavioral fuzzy subsystems.

Exploiting expert systems in cardiology: a comparative study.

An improved Adaptive Neuro-Fuzzy Inference System (ANFIS) in the field of critical cardiovascular diseases is presented. The system stems from an earlier application based only on a Sugeno-type Fuzzy Expert System (FES) with the addition of an Artificial Neural Network (ANN) computational structure. Thus, inherent characteristics of ANNs, along with the human-like knowledge representation of fuzzy systems are integrated. The ANFIS has been utilized into building five different sub-systems, distinctly covering Coronary Disease, Hypertension, Atrial Fibrillation, Heart Failure, and Diabetes, hence aiding doctors of medicine (MDs), guide trainees, and encourage medical experts in their diagnoses centering a wide range of Cardiology. The Fuzzy Rules have been trimmed down and the ANNs have been optimized in order to focus into each particular disease and produce results ready-to-be applied to real-world patients.

Theory of fuzzy non homogeneous Markov systems with fuzzy states

In this paper the theory of fuzzy logic and fuzzy reasoning is combined with the theory of Markov systems and the concept of a fuzzy non homogeneous Markov system with fuzzy states is introduced for the first time. This is an effort to deal with the uncertainty introduced in the estimation of the transition probabilities, especially when social mobility is being measured, and the fact of fuzzy states, in the sense that the categories cannot be precisely measured and are therefore fuzzy. A full description of the methodology is outlined and the basic parameters of the system are provided. Moreover, the expected population structure of the system is estimated in a closed analytic form and the asymptotic behaviour, variability of the state sizes of the system and the rate of convergence of the relative population structure are given. The proposed methodology is illustrated through an example of measuring intergenerational educational mobility.

Speculative Dynamical Systems: How Technical Trading Rules Determine Price Dynamics

In this paper, we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound.In Part I of this paper, we will show the details of how to transform the technical trading heuristics into nonlinear dynamic equations. First, we define fuzzy sets to represent the fuzzy terms in the technical trading rules; second, we translate each technical trading heuristic into a group of fuzzy IF-THEN rules; third, we combine the fuzzy IF-THEN rules in a group into a fuzzy system; and finally, the linear combination of these fuzzy systems is used as the excess demand function in the price dynamic equation. We transform a wide variety of technical trading rules into fuzzy systems, including moving average rules, support and resistance rules, trend line rules, big buyer, big seller and manipulator rules, band and stop rules, and volume and relative strength rules. Simulation results show that the price dynamics driven by these technical trading rules are complex and chaotic, and some common phenomena in real stock prices such as jumps, trending and self-fulfilling appear naturally.In Part II of the paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give parameter ranges for the price series to change from divergence to chaos and to oscillation. We prove that the price dynamical model has an infinite number of equilibriums, but all these equilibriums are unstable. We demonstrate the short-term predictability of the price volatility and derive the detailed formulas of the Lyapunov exponent as functions of the model parameters. We show that although the price is chaotic, the volatility converges to some constant very quickly at the rate of the Lyapunov exponent. We extract the formula relating the converged volatility to the model parameters based on Monte-Carlo simulations. We explore the circumstances under which the returns are uncorrelated and illustrate in details of how the correlation index changes with the model parameters. Finally, we plot the strange attractor and the return distribution of the chaotic price series to illustrate the complex structure and the fat-tailed distribution of the returns.In Part III of the paper, we apply the price dynamical model with big buyers and big sellers developed in Part I of this paper to the daily closing prices of the top 20 banking and real estate stocks listed in the Hong Kong Stock Exchange. The basic idea is to estimate the strength parameters of the big buyers and the big sellers in the model and make buy/sell decisions based on these parameter estimates. We propose two trading strategies: (i) Follow-the-Big-Buyer which buys when big buyer begins to appear and there is no sign of big sellers, holds the stock as long as the big buyer is still there, and sells the stock once the big buyer disappears; and (ii) Ride-the-Mood which buys as soon as the big buyer strength begins to surpass the big seller strength, and sells the stock once the opposite happens. Based on the testing over 245 two-year intervals uniformly distributed across the seven years from 03-July-2007 to 02-July-2014 which includes a variety of scenarios, the net profits would increase 67% or 120% on average if an investor switched from the benchmark Buy-and-Hold strategy to the Follow-the-Big-Buyer or Ride-the-Mood strategies during this period, respectively.

Research on Fuzzy Control of Mine Ventilation Based on Embedded Systems

Taking embedded processor as the core control unit, the paper designs the fan monitoring system software and hardware to achieve the fan working condition detection and real-time control. For the control algorithm, the paper analyzes the fuzzy control system theory and composition, and then combined with tunnel ventilation particularity, introduce feed-forward model to predict the incremental acquisition of pollutants to reduce lag, combined with the system feedback value and the set value, by calculate of two independent computing fuzzy controller, and ultimately determine the number of units increase or decrease in the tunnel jet fans start and stop. Through simulation analysis, the introduction of a feed-forward signal, it can more effectively improve the capability of the system impact of interference.

Optimal design of interval type 2 fuzzy controllers based on a simple tuning algorithm

Evolutionary algorithms are one of the most common choices reported in the literature for the tuning of fuzzy logic controllers based on either type-1 or type-2 fuzzy systems. An alternative to evolutionary algorithms is the simple tuning algorithm (STA-FLC), which is a methodology designed to improve the response of type-1 fuzzy logic controllers in a practical, intuitive and simple ways. This paper presents an extension of the simple tuning algorithm for fuzzy logic controllers based on the theory of type-2 fuzzy systems by using a parallel model implementation, it also includes a mechanism to calculate the feedback gain, new integral criteria parameters, and the effect of the AND/OR operator combinations on the fuzzy rules to improve the algorithm applicability and performance. All these improvements are demonstrated with experiments applied to different types of plants.

Identification of Nonlinear System Based on Fuzzy Model with Enhanced Gradient Search

Theidentification and modeling theory of nonlinear systems has always been challengingto researchers. Fuzzy system due to its languagedescriptive way similar to human brain and deal with qualitative informationintelligently proves better choice for nonlinear system modeling over last fewdecades. The fuzzy system theory itself also has nonlinear characteristics thereforewhen establishing the fuzzy model of nonlinear system; it should be able towell describe the nonlinear characteristics. Takagi-Sugeno (TS) fuzzy systemsare not only suitable for modeling the nonlinear system due to combination ofthe good performance with the simple linear expressions, but also useful todesign the fuzzy controller. This paper proposed a new optimization algorithm namedas Enhanced Gradient Search (EGS) for identification of nonlinear system basedon TS fuzzy system. In proposed EGS, parameters of membership functions aretrained adaptively so as to calculate the gradient of cost function which isnecessary for minimizing the error. Using gradient information of costfunction, EGS applies in an innovative way such that it keeps and updates thebest search results at every training step during the optimization process. Theapplicability of EGS for TS fuzzy model shows splendid performance especially inmodeling of nonlinear system.

Inventory Information Management of Logistics Supply Chain

The supply chain information management of logistics has become an important method to enhance its competitiveness. The inventory information management and application of the logistics supply is researched based on grey clustering decision-making methods. The inventory theory and methods are studied firstly, and the fuzzy mathematics and grey system theory are used to solve the classification problem. The electronic industry logistics supply chain is taken as the example, the inventory information management problem is solved. The inventory information management theory is improved in this paper, and it can more accurately reflect the market situation, it provides the reference for the classification of inventory information management in logistics supply chain.

Review paper: A Briefing to Grey Systems Theory

Abstract Grey systems theory, probability theory, fuzzy systems theory and rough set theory are known as four uncertain systems scientific methodologies. After thirty years of development, grey systems theory has formed its own disciplinary framework, whose content includes grey philosophy, grey mathematics, processing and technology systems of grey information, as well as grey systems engineering. However, as a developing area of scientific activities, a lot of theoretical contents are still imperfect and awaiting further studies. The purpose of this paper is to acquaint the readers with the development history, the main content and the major challenges of grey system theory. It is our hope that this paper could play the role of attracting the attention of the international academic community to the theory so that the development of this theory could be further promoted.

A novel cost function based on decomposing least‐square support vector machine for Takagi–Sugeno fuzzy system identification

This study develops and illustrates a novel cost function which is the combination of these terms constituted of decomposing least square-support vector machine (LS-SVM) and error terms for the identification of Takagi-Sugeno (T-S) fuzzy system based only on measured data without any prior knowledge. The proposed method combines the advantages of fuzzy system theory and some ideas from LS-SVM. Firstly, Gustafson-Kessel clustering algorithm is applied to split training data into R clustering subsets. Likewise, LS-SVM is also decomposed into R terms and consequent parameters a k for T-S fuzzy system corresponding to these terms obtained by decomposing LS-SVM are combined with the error terms to form the new total cost function. Following that, this constrained optimisation problem based on the total cost function can be solved by applying the Lagrange technique. The resulting fuzzy system generated by this method has the following distinct features: (i) the obtained new cost function can be regarded as a structural risk instead of empirical risk; (ii) although incorporating LS-SVM concept into the cost function of T-S fuzzy model, it is shown that the computation process cannot only avoid the selection of kernel function, but also merely use the scalar product for original input space to further reduce the calculation greatly; and (iii) as seen in the proposed novel cost function, the approach can well guarantee the performance of both local-regression models and global model. Finally, the viability and superiority of the method are verified by simulation.

Coalgebras for Fuzzy Transition Systems

This paper studies a coalgebraic theory of fuzzy transition systems. Main conclusions include: the functor FA for deterministic fuzzy transition systems and the functor (P∘F)A for nondeterministic fuzzy transition systems preserve weak pullbacks, and the functor FA has a final coalgebra under some restricted conditions. Moreover, we show how to get a concrete (fuzzy) bisimulation from a coalgebraic bisimulation.