Fuzzy neural networks for control of dynamic systems

This thesis provides a unified and comprehensive treatment of the fuzzy neural networks as the intelligent controllers. This work has been motivated by a need to develop the solid control methodologies capable of coping with the complexity, the nonlinearity, the interactions, and the time variance of the processes under control. In addition, the dynamic behavior of such processes is strongly influenced by the disturbances and the noise, and such processes are characterized by a large degree of uncertainty. Therefore, it is important to integrate an intelligent component to increase the control system ability to extract the functional relationships from the process and to change such relationships to improve the control precision, that is, to display the learning and the reasoning abilities. The objective of this thesis was to develop a self-organizing learning controller for above processes by using a combination of the fuzzy logic and the neural networks. An on-line, direct fuzzy neural controller using the process input-output measurement data and the reference model with both structural and parameter tuning has been developed to fulfill the above objective. A number of practical issues were considered. This includes the dynamic construction of the controller in order to alleviate the bias/variance dilemma, the universal approximation property, and the requirements of the locality and the linearity in the parameters. Several important issues in the intelligent control were also considered such as the overall control scheme, the requirement of the persistency of excitation and the bounded learning rates of the controller for the overall closed loop stability. Other important issues considered in this thesis include the dependence of the generalization ability and the optimization methods on the data distribution, and the requirements for the on-line learning and the feedback structure of the controller. Fuzzy inference specific issues such as the influence of the choice of the defuzzification method, T-norm operator and the membership function on the overall performance of the controller were also discussed. In addition, the e-completeness requirement and the use of the fuzzy similarity measure were also investigated. Main emphasis of the thesis has been on the applications to the real-world problems such as the industrial process control. The applicability of the proposed method has been demonstrated through the empirical studies on several real-world control problems of industrial complexity. This includes the temperature and the number-average molecular weight control in the continuous stirred tank polymerization reactor, and the torsional vibration, the eccentricity, the hardness and the thickness control in the cold rolling mills. Compared to the traditional linear controllers and the dynamically constructed neural network, the proposed fuzzy neural controller shows the highest promise as an effective approach to such nonlinear multi-variable control problems with the strong influence of the disturbances and the noise on the dynamic process behavior. In addition, the applicability of the proposed method beyond the strictly control area has also been investigated, in particular to the data mining and the knowledge elicitation. When compared to the decision tree method and the pruned neural network method for the data mining, the proposed fuzzy neural network is able to achieve a comparable accuracy with a more compact set of rules. In addition, the performance of the proposed fuzzy neural network is much better for the classes with the low occurrences in the data set compared to the decision tree method. Thus, the proposed fuzzy neural network may be very useful in situations where the important information is contained in a small fraction of the available data.

Fuzzy concepts and formal methods

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the information systems problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.

Citation based journal rankings : an application of fuzzy measures

Here we investigate the use of fuzzy measures and averaging aggregation functions for understanding the behavior and tendencies of decision-makers in an ordinal classification problem. Using the Aotools package to approximate the data, we classify each journal based on aggregation of the ISI Web of knowledge indices and discuss the results.

Fuzzy well-being in Pacific Asia

This paper develops a framework that uses fuzzy-set theory to measure human well-being. Fuzzy sets allow for gradual transition from one state to another while also allowing one to incorporate rules and goals, and hence are more appropriate for measuring outcomes that are ambiguous. Such ambiguity is an inherent characteristic of cross-country achieved well-being assessments. This framework is used to provide a fuzzy representation of the well known Human Development Index (HDI) and its three components. Fuzzy HDI estimates for 14 Pacific Asian countries are provided and compared with non-fuzzy estimates. Quite large differences in rankings emerge. The paper concludes by suggesting that fuzzy measures should be used more widely to measure achieved well-being outcomes.

Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Mart´ınez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale.We find that the key of computational techniques
based on linguistic 2-tuples is to set suitable numerical scale with
the purpose of making transformations between linguistic 2-tuples
and numerical values. By defining the concept of the transitive
calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

Modeling and control of flatness in cold rolling mill using fuzzy petri nets

Today, having a good flatness control in steel industry is essential to ensure an overall product quality, productivity and successful processing. Flatness error, given as difference between measured strip flatness and target curve, can be minimized by modifying roll gap with various control functions. In most practical systems, knowing the definition of the model in order to have an acceptable control is essential. In this paper, a fuzzy Petri net method for modeling and control of flatness in cold rolling mill is developed. The method combines the concepts of Petri net and fuzzy control theories. It focuses on the fuzzy decision making problems of the fuzzy rule tree structures. The method is able to detect and recover possible errors that can occur in the fuzzy rule of the knowledge-based system. The method is implemented and simulated. The results show that its error is less than that of a PI conventional controller.

Fuzzy entropy from weak fuzzy subsethood measures

In this paper, we propose a new construction method for fuzzy and weak fuzzy subsethood measures based on the aggregation of implication operators. We study the desired properties of the implication operators in order to construct these measures. We also show the relationship between fuzzy entropy and weak fuzzy subsethood measures constructed by our method.

Potential applications of discrete-event simulation and fuzzy rule-based systems to structural reliability and availability

This chapter discusses and illustrates some potential applications of discrete-event simulation (DES) techniques in structural reliability and availability analysis, emphasizing the convenience of using probabilistic approaches in modern building and civil engineering practices. After reviewing existing literature on the topic, some advantages of probabilistic techniques over analytical ones are highlighted. Then, we introduce a general framework for performing structural reliability and availability analysis through DES. Our methodology proposes the use of statistical distributions and techniques – such as survival analysis – to model component-level reliability. Then, using failure- and repair-time distributions and information about the structural logical topology (which allows determination of the structural state from their components’ state), structural reliability, and availability information can be inferred. Two numerical examples illustrate some potential applications of the proposed methodology to achieving more reliable and structural designs. Finally, an alternative approach to model uncertainty at component level is also introduced as ongoing work. This new approach is based on the use of fuzzy rule-based systems and it allows the introduction of experts’ opinions and evaluations in our methodology.

A construction method of Atanassov’s intuitionistic fuzzy sets for image processing

In this work we introduce a new construction method of Atanassov's intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency.

A multiple population genetic algorithm and its application in fuzzy controller

Genetic Algorithm is an important optimization technique, though its application in Fuzzy system is usually limited by problems like local optimal and premature convergence. With an aim to improve the performance of simple Genetic Algorithm, we propose a multi-population genetic algorithm MP-GA which uses two populations collaborating with each other, and apply it to fuzzy controller design to optimize its control rules. The simulation results of Inverted Pendulum demonstrate the effectiveness of this proposed method.

Selecting the individual numerical scale and prioritization method in the analytic hierarchy process : a 2-tuple fuzzy linguistic approach

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection.

Backward modelling and look-ahead fuzzy energy management controller for a parallel hybrid vehicle

This paper focuses on a parallel hybrid electric vehicle. It first develops a model for the vehicle using the backward-looking approach where the flow of energy starts from wheels and spreads towards engine and electric motor. Next, a fuzzy logic-based strategy is developed to control the operation of the vehicle. The objectives of the controller include managing the energy flow from engine and electric motor, controlling transmission ratio, adjusting speed, and sustaining battery's state of charge. The controller examines current vehicle speed, demand torque, slope difference, state of charge of battery, and engine and electric motor rotation speeds. Then, it determines the best values for continuous variable transmission ratio, speed, and torque. A slope window scheme is also developed to take into account the look-ahead slope information and determine the best vehicle speed for better fuel economy. The developed model and control strategy are simulated. The simulation results are presented and discussed. It is shown that the use of the proposed fuzzy controller reduces fuel consumption.