Selection of parameters for a fuzzy logic controller

The fuzzy logic controller is reviewed and its parameter are explicitly identified. The problem of initial selection and subsequent adjustment of the parameters are discussed in detail by example.     

Buyer behavior adaptation based on a fuzzy logic controller and prediction techniques

The current form of Web provides numerous product resources available to users. Users can rely on intelligent agents for purchase actions. These actions are taken in specific environments such as Electronic Markets (EMs). In this paper, we study the interaction process between buyers and sellers and focus on the buyer side. Each buyer has the opportunity to interact with a number of sellers trying to buy the most appropriate products. This interaction can be modeled as a finite horizon Bargaining Game (BG). In this game, players have opposite goals concerning the product price. We adopt a number of techniques in the buyer side trying to give the appropriate level of efficiency in the buyer decision process. The buyer uses a prediction mechanism in combination with the use of Fuzzy Logic (FL) theory in order to be able to predict the upcoming seller proposal and, thus, understand the seller pricing policy. Based on this, he/she can adapt his/her behavior when trying to purchase products. The buyer adaptation mechanism produces the belief that the buyer has about the seller pricing policy and a parameter that indicates his/her own pricing policy which yields the buyer offers in the upcoming rounds. Moreover, the buyer is based on FL system that derives the appropriate actions at every round of the BG. Our results show that the combination of Fuzzy Logic (FL) with the above-mentioned techniques provides an efficient decision mechanism in the buyer side that in specific scenarios outperforms an optimal stopping model.     

Birkhoff variety theorem and fuzzy logic

An algebra with fuzzy equality is a set with operations on it that is equipped with similarity , i.e. a fuzzy equivalence relation, such that each operation f is compatible with . Described verbally, compatibility says that each f yields similar results if applied to pairwise similar arguments. On the one hand, algebras with fuzzy equalities are structures for the equational fragment of fuzzy logic. On the other hand, they are the formal counterpart to the intuitive idea of having functions that are not allowed to map similar objects to dissimilar ones. In this paper, we present a generalization of the well-known Birkhoffs variety theorem: a class of algebras with fuzzy equality is the class of all models of a fuzzy set of identities iff it is closed under suitably defined morphisms, substructures, and direct products. and Institute for Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic Mathematics Subject Classification (2000):03B52, 08B05     

Distributions in fuzzy logic

Probability distributions associated with several ‘ply’-operators are discussed. These exact distributions are compared with relevant Gaussian approximations.     

Design of fuzzy logic controllers based on generalized T-operators

Since Zadeh first proposed the basic principle of fuzzy logic controllers in 1968, the and operators have been popular in the design of fuzzy logic controllers. In this paper, the general concept of T-operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available. Then, by computer simulations, studies are made so as to determine the relations between the various T-operators and the performance of a fuzzy logic controller. It is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the T-operators.     

Probability distributions in fuzzy logic II

Probability distributions associated with several ‘iff’ ply operators are discussed. These exact distributions are compared with relevant normal approximants. Two possible applications are noted.     

Stable fuzzy logic design of point-to-point control for mechanical systems

An approach for the development of fuzzy point-to-point control laws for second-order mechanical systems is presented. Asymptotic stability of the resulting closed-loop system is proved using Lyapunov stability theory. Closed-loop performance and robustness are quantified in terms of the parameters of membership functions. As opposed to most existing fuzzy control laws, the closed-loop stability of the proposed controller does not depend on the knowledge of the entire dynamics. Moreover, the approach does not require the plant to be open-loop stable. The proposed approach is demonstrated on design and simulation study of a fuzzy controller for a two-link robotic arm.     

Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].     

Chaos synchronization using fuzzy logic controller

The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.     

Robot fingers to tune TV amplifiers using fuzzy logic

This paper contains the definition and the resolution of the problem of tuning electronic amplifiers of aerials for VHF, UHF and SHF signals, in terms of a control problem with fuzzy sets and fuzzy rules. An industrial prototype of a specific robotic system to tune the amplifiers automatically is described briefly. This prototype has been made in collaboration with the manufacturer of this amplifiers Televés S.A. The robot is driven with a fuzzy controller based on the fuzzy sets and fuzzy rules found for the tuning problem.     

A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

Implication in fuzzy logic

Intermediate truth values and the order relation “as true as” are interpreted. The material implication A → B quantifies the degree by which “B is at least as true as A.” Axioms for the → operator lead to a representation of → by the pseudo-Lukasiewicz model. A canonical scale for the truth value of a fuzzy proposition is selected such that the → operator is the Lukasiewicz operator and the negation is the classical 1−. operator. The mathematical structure of some conjunction and disjunction operators related to → are derived.     

Bilattices for deductions in multi-valued logic

In this exploratory paper we propose a framework for the deduction apparatus of multi-valued logics based on the idea that a deduction apparatus has to be a tool to manage information on truth values and not directly truth values of the formulas. This is obtained by embedding the algebraic structure V defined by the set of truth values into a bilattice B. The intended interpretation is that the elements of B are pieces of information on the elements of V. The resulting formalisms are particularized in the framework of fuzzy logic programming. Since we see fuzzy control as a chapter of multi-valued logic programming, this suggests a new and powerful approach to fuzzy control based on positive and negative conditions.     

Application of fuzzy control to a road tunnel ventilation system

This paper deals with the serious problems of ventilation system in a large road tunnel. Higher visibility and lower concentration of carbon monoxide are the key issues concerning the ventilation system. Prior to designing the fuzzy control model, a configuration layout of the ventilation system including sensing, control and traffic prediction as well is conceptually constructed. Based on the layout that offers assignments of sensors and control elements, a fuzzy logic control model is developed. Membership functions of sensor errors and control increments are physically submitted in order to set up the fuzzy logic rules. Timing and spacing filtering in terms of weighting approaches is employed in the fuzzy logic rules. A dynamic equation describing the concentration of air pollution is also given so as to cooperate with the fuzzy logic rules and to play roles in the computer simulation. The result of computer simulation involving five cases indicates that a multi-level scheme is able to solve the engineering problems.     

Instance-specific multi-objective parameter tuning based on fuzzy logic

Finding good parameter values for meta-heuristics is known as the parameter setting problem. A new parameter tuning strategy, called IPTS, is proposed that is a novel instance-specific method to take the trade-off between solution quality and computational time into consideration. Two important steps in the method are an a priori statistical analysis to identify the factors that determine heuristic performance in both quality and time for a specific type of problem, and the transformation of these insights into a fuzzy inference system rule base which aims to return parameter values on the Pareto-front with respect to a decision maker’s preference.Applied to the symmetric Travelling Salesman Problem and the meta-heuristic Guided Local Search, the approach is consistently faster than a traditional non-instance-specific parameter tuning strategy without significantly affecting solution quality; optimised for speed, computational times are shown to be on average 20 times faster while producing solutions of similar quality. A number of interesting areas for further research are discussed.     

Autonomous control of complex systems: robotic applications

One of the biggest challenges of any control paradigm is being able to handle large complex systems under unforeseen uncertainties. A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques cannot easily handle the problem. Soft computing, a collection of fuzzy logic, neuro-computing, genetic algorithms and genetic programming, has proven to be a powerful tool for adding autonomy to many complex systems. For such systems the size soft computing control architecture will be nearly infinite. Examples of complex systems are power networks, national air traffic control system, an integrated manufacturing plant, etc. In this paper a new rule base reduction approach is suggested to manage large inference engines. Notions of rule hierarchy and sensor data fusion are introduced and combined to achieve desirable goals. New paradigms using soft computing approaches are utilized to design autonomous controllers for a number of robotic applications at the ACE Center are also presented briefly.