Showing papers on "Fuzzy number published in 1991"
TL;DR: The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data.
Abstract: The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed. >
3,237 citations
TL;DR: A general neural-network (connectionist) model for fuzzy logic control and decision systems is proposed, in the form of feedforward multilayer net, which avoids the rule-matching time of the inference engine in the traditional fuzzy logic system.
Abstract: A general neural-network (connectionist) model for fuzzy logic control and decision systems is proposed. This connectionist model, in the form of feedforward multilayer net, combines the idea of fuzzy logic controller and neural-network structure and learning abilities into an integrated neural-network-based fuzzy logic control and decision system. A fuzzy logic control decision network is constructed automatically by learning the training examples itself. By combining both unsupervised (self-organized) and supervised learning schemes, the learning speed converges much faster than the original backpropagation learning algorithm. The connectionist structure avoids the rule-matching time of the inference engine in the traditional fuzzy logic system. Two examples are presented to illustrate the performance and applicability of the proposed model. >
1,476 citations
TL;DR: A new fuzzy reasoning that can solve two problems of conventional fuzzy reasoning by combining an artificial neural network (NN) and fuzzy reasoning is proposed, capable of automatic determination of inference rules and adjustment according to the time-variant reasoning environment because of the use of NN in fuzzy reasoning.
594 citations
TL;DR: It is shown from two examples that the successive identification method of a fuzzy model is very useful for modeling complex systems.
485 citations
Proceedings Article•
14 Jul 1991TL;DR: It is concluded that the proposedl new fuzzy inference system can not only incorporate prior knowledge about the original system but also fine-tune the membership functions of the fuzzy rules as the training data set varies.
Abstract: We propose a new approach to build a, fuzzy inference system of which the parameters can be updated to achieve a desired input-output mapping. The structure of the proposed fuzzy inference system is called generalized neural networks, and its learning procedure (rules to update parameters) is basically composed of a gradient descent algorithm and Kalman filter algorithm. Specifically, we first introduce the concept of generalized neural networks (GNN's) and develop a gradient-descent-based supervised learning procedure to update the GNN's parameters. Secondly, we observe that if the overall output of a GNN is a linear combination of some of its parameters, then these parameters can be identified by one-time application of Kalman filter algorithm to minimize the squared error, According to the simulation results, it is concluded that the proposedl new fuzzy inference system can not only incorporate prior knowledge about the original system but also fine-tune the membership functions of the fuzzy rules as the training data set varies.
426 citations
TL;DR: The hierarchical fuzzy control algorithm developed in this paper is applied to control the feedwater flow to a steam generator of a power plant and results show that the hierarchical fuzzy controller yields superior performance over the conventional PID controller.
Abstract: In a conventional rule based fuzzy control system, the rules are of the following form: if (condition) then (action), and all rules are essentially in a random order. The number of rules increases exponentially as the number of the system variables, on which the fuzzy rules are based, is increased. In this paper, the rules are structured in a hierarchical way so that the total number of rules will be a linear function of the system variables. The hierarchical fuzzy control algorithm developed in this paper is applied to control the feedwater flow to a steam generator of a power plant. The simulation results show that the hierarchical fuzzy controller yields superior performance over the conventional PID controller.
378 citations
TL;DR: The T-operators are extended to the conventional fuzzy reasoning methods which are based on the min and max operators and provide both a general and a flexible method for the design of fuzzy logic controllers and, more generally, for the modelling of any decision-making process.
364 citations
TL;DR: It is shown that, if there is a certain relation between two measurable functions, then the Choquet integral is additive for these two functions.
360 citations
TL;DR: The relations between the similarity-based interpretation of the role of conditional possibility distributions and the approximate inferential procedures of Baldwin are discussed and a straightforward extension of the theory to the case where the similarity scale is symbolic rather than numeric is described.
279 citations
TL;DR: This second part of an overview of fuzzy set-based methods for approximate reasoning is devoted to deductive approaches dealing with knowledge bases made of a collection of symbolic expressions to which numerical weigths are attached.
TL;DR: The concepts of fuzzy continuity, product and quotient spaces are presented, and their fundamental properties are obtained in fuzzifying topology.
TL;DR: A new approach using fuzzy dynamic programming is proposed for the unit commitment of a power system, in which the hourly loads, the cost, and system security are all expressed in fuzzy set notations is developed.
Abstract: A new approach using fuzzy dynamic programming is proposed for the unit commitment of a power system. A characteristic feature of the approach is that the errors in the forecast hourly loads can be taken into account by using fuzzy set notations, making the approach superior to the conventional dynamic programming method which assumes that the hourly loads are exactly known and there exist no errors in the forecast loads. To reach an optimal commitment strategy under the fuzzy environment, a fuzzy dynamic programming model in which the hourly loads, the cost, and system security are all expressed in fuzzy set notations is developed. The effectiveness of the approach is demonstrated by the unit commitment of the Taiwan power system, which contains six nuclear units, 48 thermal units, and 44 hydro units. >
TL;DR: The results support that the class of weak t-norms having the Exchange Property seems to be a good model of the conjunction (or equivalently, of intersection) operator in fuzzy set theory.
TL;DR: It is argued that the previous method of solving for x, based on the extension principle and regular fuzzy arithmetic, should be abandoned since it too often fails to produce a solution.
18 Nov 1991
TL;DR: A supervised neural network classifier using a combination of min-max hyperboxes and fuzzy logic is described in this paper, where the degree to which an input pattern belongs to a class is determined by the membership function of the winning hyperbox.
Abstract: A supervised neural network classifier using a combination of min-max hyperboxes and fuzzy logic is described A min-max hyperbox and its membership function define a fuzzy set Each class in the neural network is a collection of labeled hyperboxes (fuzzy sets) The degree to which an input pattern belongs to a class is determined by the membership function of the winning hyperbox Using multiple hyperbox fuzzy sets to form classes allows arbitrary numbers and shapes of classes and their respective class boundaries The min-max classification learning procedure requires only a single pass through the data and allows online learning The author describes how the fuzzy min-max classifier is implemented as a neural network, explains how min-max classes are produced, and provides two examples of operation >
TL;DR: In this article, a fuzzy model for power system operation is presented, where uncertainty in loads and generations are modeled as fuzzy numbers and system behavior under known (while uncertain) injections is dealt with by a DC fuzzy power flow model.
Abstract: A fuzzy model for power system operation is presented. Uncertainties in loads and generations are modeled as fuzzy numbers. System behavior under known (while uncertain) injections is dealt with by a DC fuzzy power flow model. System optimal (while uncertain) operation is calculated with linear programming procedures in which the problem nature and structure allow some efficient techniques such as Dantzig-Wolfe decomposition and dual simplex to be used. Among the results, one obtains a fuzzy cost value for system operation and possibility distributions for branch power flows and power generations. Some risk analysis is possible, as system robustness and exposure indices can be derived and hedging policies can be investigated. >
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TL;DR: New models based on fuzzy shortest paths are presented and a general algorithm based on dynamic programming is given to solve the new models and the analysis concepts developed are discussed in terms of general fuzzy mathematical programming.
TL;DR: An introduction to the theory of fuzzy binary relations and some related concepts is presented, including major classes of fuzzy orderings defined and classified with respect to the duality relation.
TL;DR: The regularity and the spread are defined for describing the algebraic properties of extended fuzzy numbers and A − A = θ, which is a natural extension from the nonfuzzy field, is proved.
TL;DR: It is shown that the fuzzy quadratic equation, with real fuzzy number coefficients, always has a (new) solution and the previous solution based on the extension principle is a subset of the new solution.
TL;DR: 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.
TL;DR: Fuzzy-set logic is used to account for imprecision and uncertainty in data while employing event-tree analysis and permits an analysis of the qualitative evaluation of the event tree to gain the quantitative results.
Abstract: A method is presented for dealing with event-tree analysis under uncertainty. Fuzzy-set logic is used to account for imprecision and uncertainty in data while employing event-tree analysis. The fuzzy event-tree logic allows the use of verbal statements for the probabilities and consequences, such as very high, moderate, and low probability. The technique permits an analysis of the qualitative evaluation of the event tree to gain the quantitative results. The application of fuzzy event trees is further demonstrated by using a set of event trees for an electric power protection system to assess the viability of the method in complex situations. >
TL;DR: The problem of aggregating n fuzzy sets F1, F2,.., Fn on a set ω is viewed as one of merging the opinions of n individuals that rate objects belonging to ω, and a number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative, mainly technical, or facultative.
TL;DR: The role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty and the role of equations in diverse fields of applications making use of an ample framework of general systems theory are studied.
TL;DR: An overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice and detailed accounts of categorical approaches using a closed structure to capture the fuzzy and connective are given.
TL;DR: The presented fuzzy clustering problem uses the distance between observations and location parameter vectors, which is based on the L1-norm, instead of the inner product induced norm used in classical fuzzy ISODATA.
08 Jul 1991
TL;DR: A contribution to the theoretical development of fuzzy neural network theory is presented and a few methods of how these neurons change themselves during learning to improve their performance are given.
Abstract: A contribution to the theoretical development of fuzzy neural network theory is presented. Three types of fuzzy neuron models are proposed. Neuron I is described by logical equations of 'if-then' rules; its inputs are either fuzzy sets or crisp values. Neuron II, with numerical inputs, and neuron III, with fuzzy inputs, are considered to be simple extensions of non-fuzzy neurons. A few methods of how these neurons change themselves during learning to improve their performance are also given. The application of the non-fuzzy neural network approach to fuzzy information processing is briefly discussed. >
TL;DR: A fuzzy logic control scheme to enhance the overall stability of a multi-machine power system and is easy to implement, and requires a low amount of computation because of its simple control rules, and required data.
TL;DR: In this paper, the concept of fuzzy success/failure (state) is introduced to represent the system structure, the performance and other considerations (e.g. cost), and the transition from fuzzy success to fuzzy failure is viewed as a fuzzy event.