Showing papers on "Fuzzy set published in 1995"

Neuro-fuzzy modeling and control

Abstract: Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called adaptive-network-based fuzzy inference system (ANFIS), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed. >

A k-nearest neighbor classification rule based on Dempster-Shafer theory

Abstract: In this paper, the problem of classifying an unseen pattern on the basis of its nearest neighbors in a recorded data set is addressed from the point of view of Dempster-Shafer theory. Each neighbor of a sample to be classified is considered as an item of evidence that supports certain hypotheses regarding the class membership of that pattern. The degree of support is defined as a function of the distance between the two vectors. The evidence of the k nearest neighbors is then pooled by means of Dempster's rule of combination. This approach provides a global treatment of such issues as ambiguity and distance rejection, and imperfect knowledge regarding the class membership of training patterns. The effectiveness of this classification scheme as compared to the voting and distance-weighted k-NN procedures is demonstrated using several sets of simulated and real-world data. >

Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms

Abstract: This paper examines the applicability of genetic algorithms (GA's) in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions; however, the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology. When GA's have been used to develop both, it has been done serially, e.g., design the membership functions and then use them in the design of the rule set. This, however, means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently. GA's are fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. This new method has been applied to two problems, a cart controller and a truck controller. Beyond the development of these controllers, we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules. >

Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological, and Engineering Systems

Abstract: From the Publisher: This book presents in a systematic and comprehensive manner themodeling of uncertainty, vagueness, or imprecision, alias "fuzziness," in just about any field of science and engineering. It delivers a usable methodology for modeling in the absence of real-time feedback. The book includes a short introduction to fuzzy logic containing basic definitions of fuzzy set theory and fuzzy rule systems. It describes methods for the assessment of rule systems, systems with discrete response sets, for modeling time series, for exact physical systems, examines verification and redundancy issues, and investigates rule response functions. Definitions and propositions, some of which have not been published elsewhere, are provided; numerous examples as well as references to more elaborate case studies are also given. Fuzzy rule-based modeling has the potential to revolutionize fields such as hydrology because it can handle uncertainty in modeling problems too complex to be approached by a stochastic analysis. There is also excellent potential for handling large-scale systems such as regionalization or highly non-linear problems such as unsaturated groundwater pollution.

Combining multiple neural networks by fuzzy integral for robust classification

Abstract: In the area of artificial neural networks, the concept of combining multiple networks has been proposed as a new direction for the development of highly reliable neural network systems. The authors propose a method for multinetwork combination based on the fuzzy integral. This technique nonlinearly combines objective evidence, in the form of a fuzzy membership function, with subjective evaluation of the worth of the individual neural networks with respect to the decision. The experimental results with the recognition problem of on-line handwriting characters confirm the superiority of the presented method to the other voting techniques. >

Fuzzy Measures and Integrals

Abstract: Chapter 5 was concerned with the theory of fuzzy sets as a mathematical model to describe vague concepts, and as an extension of ordinary set theory. In a similar spirit, this chapter is about an extension of additive measures, in particular probability measures, to a more general class of non-additive set functions.

A sensor-based navigation for a mobile robot using fuzzy logic and reinforcement learning

Abstract: The proposed navigator consists of an avoidance behavior and goal-seeking behavior. Two behaviors are independently designed at the design stage and then combined them by a behavior selector at the running stage. A behavior selector using a bistable switching function chooses a behavior at each action step so that the mobile robot can go for the goal position without colliding with obstacles. Fuzzy logic maps the input fuzzy sets representing the mobile robot's state space determined by sensor readings to the output fuzzy sets representing the mobile robot's action space. Fuzzy rule bases are built through the reinforcement learning which requires simple evaluation data rather than thousands of input-output training data. Since the fuzzy rules for each behavior are learned through a reinforcement learning method, the fuzzy rule bases can be easily constructed for more complex environments. In order to find the mobile robot's present state, ultrasonic sensors mounted at the mobile robot are used. The effectiveness of the proposed method is verified by a series of simulations. >

Imprecision in Engineering Design

Abstract: The decisions with the greatest importance and potential cost (if wrong) are made early in the engineering design process. A method for representing and manipulating imprecise and vague information in design is described, particularly focused on the preliminary phase when the (fuzzy) imprecision and uncertainty in the descriptions of the design artifact are high. The preferences of designers and customers are captured with fuzzy sets. Formal methods for including noise, trade-off strategies and design iteration are included. Increasing the information available to a designer will reduce the risk of making design decisions incorrectly. Providing (fuzzy) set-based information to engineers can facilitate concurrency in design.

Fuzzy sets engineering

Abstract: From the Publisher: The phenomenon of fuzzy sets amplified by their numerousapplications has triggered a significant amount of interest among research communities as well as practitioners in many areas including engineering, ecology, economics, administration, and business. What is the role of fuzzy sets? When should they be used? Why do they work? What are good design practices? This book presents the genuine essence of engineering of fuzzy sets. It includes sound theory, a general methodological framework, efficient algorithms, and detailed validation schemes. Fuzzy Sets Engineering presents discussions in a top-down fashion, with general methodology followed by specific domains which rely strongly on the methodological foundations. Based on this methodological framework, the book then provides a careful, in-depth exposure to very diversified areas. Numerous application-driven examples are offered. Text discusses general modelling methodology of fuzzy sets then describes useful ideas of neurocomputations. Self-contained chapters allow readers to customize their reading by selecting any of these essential design topics: fuzzy controller, fuzzy control, or information processing with recurrent systems such as fuzzy flip-flops or fuzzy Petri nets. Topics can be investigated in a variety of orders. This versatile format makes this an ideal textbook or reference source for both novices and experienced individuals.

A new algorithm for identifying fuzzy measures and its application to pattern recognition

Abstract: We present a new algorithm for identifying fuzzy measures, which is a kind of gradient algorithm with constraints. Its performance is superior to the one of previous attempts, and we show its efficiency to a problem of pattern recognition using Choquet integral. >

Overview and literature survey of fuzzy set theory in power systems

Abstract: Increasing interest has been seen in applying fuzzy set theory to power systems problems from the number of publications on this topic. As a relatively new research topic a need is felt to pay more attention to the understanding of the basic principles of the theory and the identification of problems suitable for solving by this method. This paper presents a survey of publications on applications of fuzzy set theory to power systems and the basic procedures for fuzzy set based methods to solve specific power systems problems. Simple numerical examples are used to show the practical procedures of problem formulation and solution. Theses examples are: generator maintenance scheduling, dynamic programming, and power system stabiliser. >

Similarity in fuzzy reasoning

Abstract: Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis for fuzzy sets, to the framework of GL-monoids that can be understood as a generalization of MV-algebras. Residuation is a basic concept in GL-monoids and many proofs can be formulated in a simple and clear way instead of using special properties of the unit interval.

Fuzzy Sets and Fuzzy Decision-Making

Abstract: The Basics of Fuzzy Set Theory Fuzzy Phenomena and Fuzzy Concepts Naive Thoughts of Fuzzy Sets Definition of Fuzzy Sets Basic Operations of Fuzzy Sets The Resolution Theorem A Representation Theorem Extension Principles References Factor Spaces What are "Factors"? The State Space of Factors Relations and Operations Between Factors Axiomatic Definition of Factor Spaces Describing Concepts in a Factor Space References The Basics of Fuzzy Decision-Making Feedback Extension and Its Applications Feedback Ranks and Degrees of Coincidence Equivalence Between Sufficient Factors and Coincident Factors How to Improve the Precision of a Feedback Extension Representation of the Intention of a Concept Basic Forms of Fuzzy Decision-Making Limitations of the Weighted Average Formula References Determination of Membership Functions A General Method for Determining Membership Functions The Three-Phase Method The Incremental Method The Multiphase Fuzzy Statistical Method The Method of Comparisons The Absolute Comparison Method The Set-Valued Statistical Iteration Method Ordering by Precedence Relations The Relative Comparison Method and the Mean Pair-Wise Comparison Method References Multifactorial Analysis Background of the Problem Multifactorial Functions Axiomatic Definition of Additive Standard Multifactorial Functions Properties of ASMm-funcs Generations of ASMm-funcs Applications of ASMm-funcs in Fuzzy Decision-Making A General Model of Multifactorial Decision-Making References Variable Weights Analysis Defining the Problem An Empirical Variable Weight Formula Principles of Variable Weights References Multifactorial Decision-Making with Multiple Objectives Background and Models Multifactorial Evaluation The Multifactorial Evaluation Approach to the Classification of Quality Incomplete Multifactorial Evaluation Multi-Level Multifactorial Evaluation An Application of Multifactorial Evaluation in Textile Engineering References Set-Valued Statistics and Degree Analysis Fuzzy Statistics and Random Sets The Falling Shadow of Random Sets Set-Valued Statistics Degree Analysis Random and Set-Valued Experiments A Mathematical Model for Employee Evaluation References Refinements of Fuzzy Operators The Axiomatic Structure of Zadeh's Operators Common Fuzzy Operators Generalized Fuzzy Operators The Strength of Fuzzy Operators "AND" and "OR" Fuzzy Operators Based on the Falling Shadow Theory References Multifactorial Decision Based on Theory of Evidence A Brief Introduction to Theory of Evidence Composition of Belief Measures Multifactorial Evaluation Based on the Theory of Evidence Two Special Types of Composition Functions The Maximum Principle for Multiple Object Evaluations References

Fuzzy finite element approach for the analysis of imprecisely defined systems

Abstract: Many engineering systems are too complex to be defined in precise mathematical terms. They often contain information and features that are vague, imprecise, qualitative, linguistic, or incomplete. The traditional deterministic and probabilistic techniques are not adequate to analyze such systems. This paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems. The development of the methodology starts from the basic concepts of fuzzy numbers of fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation, manipulation, and solution of the finite element equations. Simple stress analysis problems involving vaguely defined geometry, material properties, external loads, and boundary conditions are solved to establish and to illustrate the new procedure. The approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information. If complete data are known, the method handles the information similar to that of a probabilistic approach. The present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures.

Optimization of clustering criteria by reformulation

Abstract: Various hard, fuzzy and possibilistic clustering criteria (objective functions) are useful as bases for a variety of pattern recognition problems. At present, many of these criteria have customized individual optimization algorithms. Because of the specialized nature of these algorithms, experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time. This paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software. We prove that the original and reformulated versions of each criterion are fully equivalent. Finally, two numerical examples are given to illustrate reformulation. >

Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques

Abstract: This paper develops a new approach to building Sugeno-type models. The essential idea is to separate the premise identification from the consequence identification, while these are mutually related in the previous methods. A fuzzy discretization technique is suggested to determine the premise of the model, and an orthogonal estimator is provided to identify the consequence of the model. The orthogonal estimator can provide information about the model structure, or which terms to include in the model, and final parameter estimates in a very simple and efficient manner. The well-known gas furnace data of Box and Jenkins is used to illustrate the proposed modeling approach and to compare its performance with other statistical and fuzzy modeling approaches. It shows that the performance of the new approach compares favorably with these existing techniques.

Commutative, residuated 1—monoids

Abstract: The purpose of this paper is to outline a common framework for a diversity of monoidal structures which constitute the basis of various papers in fuzzy set theory. The most frequent structures we encounter in the literature are given by Hey ting algebras, MV-algebras and semigroup structures on the real unit interval (so-called t-norms ([27]). Heyting algebras appear in papers looking from an intuitionistic point of view at fuzzy set theory, MV-algebras form the base for a positivistic approach to fuzzy set theory (cf. Poincare's paradox and related topics in [15]), and finally t-norms are prefered by statisticians working with a probabilistic understanding of fuzzy set theory. All these monoidal structures have in common the following basic properties : Integrality, commutativity of the semigroup operation * and the existence of a binary operation which is adjoint to the given operation *. Therefore we claim that the structure of integral, commutative, residuated l-monoids forms the appropriate level of generality for our intension.

Optimal fuzzy inference for short-term load forecasting

Abstract: This paper proposes an optimal fuzzy inference method for short-term load forecasting. The proposed method constructs an optimal structure of the simplified fuzzy inference that minimizes model errors and the number of the membership functions to grasp nonlinear behavior of power system short-term loads. The model is identified by simulated annealing and the steepest descent method. The proposed method is demonstrated in examples.

Fuzzy rules extraction directly from numerical data for function approximation

Abstract: In our previous work (1993) we developed a method for extracting fuzzy rules directly from numerical input-output data for pattern classification. In this paper we extend the method to function approximation. For function approximation, first, the universe of discourse of an output variable is divided into multiple intervals, and each interval is treated as a class. Then the same as for pattern classification, using the input data for each interval, fuzzy rules are recursively defined by activation hyperboxes which show the existence region of the data for the interval and inhibition hyperboxes which inhibit the existence region of data for that interval. The approximation accuracy of the fuzzy system derived by this method is empirically studied using an operation learning application of a water purification plant. Additionally, we compare the approximation performance of the fuzzy system with the function approximation approach based on neural networks. >