Showing papers on "Membership function published in 1993"
01 Jan 1993
TL;DR: The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets, and the concept of probabilities is absolutely different from that of sets.
Abstract: As is well-known in recent years, there are two kinds of uncertainities, randomness and fuzziness, which can be both dealt with from a mathematical point of view. We know the concept of probabilities with respect to randomness and also that of fuzzy sets with respect to fuzziness. This fact tempts us to discuss fuzzy sets in comparison with probabilities. However, such a direct comparison must fail. The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets. We have to notice that the concept of probabilities is absolutely different from that of sets. To discuss our problem in detail, let us consider probabilities for the time being. There are a number of interpretations for probabilities: classical probabilities (originated by Laplace); measure theoretical probabilities (by Kolmogorov); subjective probabilities in Bayesian statistics; probabilities as logics and so on.
889 citations
TL;DR: Algorithms which enable forecasting attainable periods are developed which look valid and applicable to further analyses of other questions and items on questionnaires and using these methods simultaneously as well as the traditional Delphi method may prove a really effective result.
640 citations
TL;DR: This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged and a brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented.
Abstract: In an earlier companion paper (56) a supervised learning neural network pattern classifier called the fuzzy min- max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core that is constructed from a min point and a max point. The min-max points are determined using the fuzzy min-max learning algorithm, an expansion-contraction process that refines the author's earlier Fuzzy Adaptive Reso- nance Theory neural network (50). The fuzzy min-max clustering neural network stabilizes into pattern clusters in only a few passes through a data set; it can be reduced to hard cluster boundaries that are easily examined without sacrificing the fuzzy boundaries; it provides the ability to incorporate new data and add new clusters without retraining; and it inherently provides degree of membership information that is extremely useful in higher level decision making and information processing. This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged. A brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented. The fuzzy min- max clustering neural network will be explained in detail and examples of its clustering performance will be given. The paper will conclude with a description of problems that need to be addressed and a list of some potential applications.
541 citations
TL;DR: This work describes six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc, and gives an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical.
Abstract: An important subject in fuzzy control theory is tuning of a fuzzy controller. If one wants to tune a fuzzy controller, one can focus on the choice of rules, membership functions, number of input and output fuzzy sets and their degree of overlapping, implication, and connection operations, and defuzzification method. All these choices are closely related and in no way independent of each other. We describe six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc. Further, we give an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical. We illustrate this by several examples.
284 citations
28 Mar 1993
TL;DR: The authors address some classical misunderstandings between fuzzy sets and probabilities, and consider probabilistic interpretations of membership functions that may help in membership function assessment.
Abstract: One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets The literature pertaining to this debate is surveyed The authors address some classical misunderstandings between fuzzy sets and probabilities They consider probabilistic interpretations of membership functions that may help in membership function assessment Nonprobabilistic interpretations of fuzzy sets are identified The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed >
250 citations
01 Jul 1993
TL;DR: An approach is described that utilizes fuzzy sets to develop a fuzzy qualitative simulation algorithm that allows a semiquantitative extension to qualitative simulation, providing three significant advantages over existing techniques.
Abstract: An approach is described that utilizes fuzzy sets to develop a fuzzy qualitative simulation algorithm that allows a semiquantitative extension to qualitative simulation, providing three significant advantages over existing techniques. Firstly, it allows a more detailed description of physical variables, through an arbitrary, but finite, discretisation of the quantity space. The adoption of fuzzy sets also allows common-sense knowledge to be represented in defining values through the use of graded membership, enabling the subjective element in system modelling to be incorporated and reasoned with in a formal way. Secondly, the fuzzy quantity space allows more detailed description of functional relationships in that both strength and sign information can be represented by fuzzy relations holding against two or multivariables. Thirdly, the quantity space allows ordering information on rates of change to be used to compute temporal durations of the state and the possible transitions. Thus, an ordering of the evolution of the states and the associated temporal durations are obtained. This knowledge is used to develop an effective temporal filter that significantly reduces the number of spurious behaviors. >
224 citations
28 Mar 1993
TL;DR: The fuzzy error backpropagation algorithm, a special learning algorithm inspired by the standard BP-procedure for multivariable neural networks, is able to learn the fuzzy sets of the fuzzy neural network.
Abstract: A kind of neural network architecture designed for control tasks is presented. It is called the fuzzy neural network. The structure of the network can be interpreted in terms of a fuzzy controller. It has a three-layered architecture and uses fuzzy sets as its weights. The fuzzy error backpropagation algorithm, a special learning algorithm inspired by the standard BP-procedure for multivariable neural networks, is able to learn the fuzzy sets. The extended version that is presented is also able to learn fuzzy-if-then rules by reducing the number of nodes in the hidden layer of the network. The network does not learn from examples, but by evaluating a special fuzzy error measure. >
127 citations
TL;DR: Some criteria for selecting a fuzzy subspace to be subdivided are proposed and compared with each other by computer simulations and the proposed method is also compared with other fuzzy classification methods.
111 citations
TL;DR: This paper test some widely used fuzzy implication operators with respect to the recently introduced Smets-Magrez axioms and presents a unified generalization of Zadeh's compositional rule of inference.
110 citations
TL;DR: The approach developed and illustrated enables a decision maker's beliefs regarding the shape and range of the possibility distribution of the model to be reflected more systematically, and consequently should yield more reliable and realistic results from fuzzy regression.
28 Mar 1993
TL;DR: The authors derive the gradient descent optimization equations for Takagi-Sugeno fuzzy rule bases with symmetric and asymmetric triangular membership functions, minimum and multiplication operators, and constant and affine output functions.
Abstract: The authors derive the gradient descent optimization equations for Takagi-Sugeno fuzzy rule bases with symmetric and asymmetric triangular membership functions, minimum and multiplication operators, and constant and affine output functions. A new type of affine output Takagi-Sugeno rules called centered Takagi-Sugeno rules is proposed. It makes it possible to avoid a class of local minima. The gradient descent method is systematically tested for the approximation of a one-input, one-output analytical function including a discontinuity and a high curvature point, and for the approximation of a two-input function. >
TL;DR: A fuzzy importance index is proposed to demonstrate the contribution of a basic event to the safety improvement of the top event in a fuzzy environment.
TL;DR: A fuzzy-inference method in which fuzzy sets are defined by the families of their alpha -level sets, based on the resolution identity theorem, has the following advantages over conventional methods: it provides fast inference operations and requires less memory capacity; it easily interfaces with two-valued logic.
Abstract: A fuzzy-inference method in which fuzzy sets are defined by the families of their alpha -level sets, based on the resolution identity theorem, is proposed. It has the following advantages over conventional methods: (1) it studies the characteristics of fuzzy inference, in particular the input-output relations of fuzzy inference; (2) it provides fast inference operations and requires less memory capacity; (3) it easily interfaces with two-valued logic; and (4) it effectively matches with systems that include fuzzy-set operations based on the extension principle. Fuzzy sets defined by the families of their alpha -level sets are compared with those defined by membership functions in terms of processing time and required memory capacity in fuzzy logic operations. The fuzzy inference method is then derived, and important propositions of fuzzy-inference operations are proved. Some examples of inference by the proposed method are presented, and fuzzy-inference characteristics and computational efficiency for alpha -level-set-based fuzzy inference are considered. >
TL;DR: Some applications of the fuzzy statistical test are demonstrated and the fuzzy hypothesis that two population means are nearly equal is tested by the proposed procedure.
28 Mar 1993
TL;DR: The empirical results show that the edge detector based on fuzzy if-then rules is generally more applicable to a wider class of images ranging from clear to very vague images.
Abstract: An edge detection approach based on fuzzy if-then rules is presented. This method avoids the difficulties of selecting parameter values in most of the edge detectors when no information about the images is known in advance. Combining all the if-then rules generates a set of potential edge pixels. The membership value of being an edge point for each pixel is assigned by a membership function. The pseudocentroid of a set of potential edge points is used as the threshold for the decision of selecting a real set of edge pixels. Comparison studies with the gradient, Laplacian, and Laplacian of Gaussian edge detectors having fixed parameters are provided. The empirical results show that the edge detector based on fuzzy if-then rules is generally more applicable to a wider class of images ranging from clear to very vague images. >
01 Aug 1993-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: This work shows how a number of the classic aggregation methods fall out as special cases of this very general formulation based upon the use of fuzzy subsets to model the criteria and a form of the fuzzy integral to connect these two to obtain the overall decision function.
Abstract: The central focus of this work is to provide a general formulation for the aggregation of multi-criteria. This formulation is based upon the use of fuzzy subsets to model the criteria and the use of fuzzy measures to capture the interrelationship between criteria. A form of the fuzzy integral is used to connect these two to obtain the overall decision function. We are particularly interested here in the formulations obtained under different assumptions about the nature of the underlying fuzzy measure. We show how a number of the classic aggregation methods fall out as special cases of this very general formulation.
TL;DR: It is shown that there are many cases for which the FWA, and all other published methods, will give wrong results, and an alternative approach is suggested which will work in all cases.
TL;DR: The Optimal Fuel Shuffling System (OFSS) was developed for the optimal design of pressurized water reactor (PWR) fuel loading patterns and was demonstrated and validated for cycle 1 of the Kori-1 PWR.
Abstract: The Optimal Fuel Shuffling System (OFSS) was developed for the optimal design of pressurized water reactor (PWR) fuel loading patterns. An optimal loading pattern is defined in which the local power peaking factor is lower than a predetermined value during one cycle and the effective multiplication factor is maximized to extract the maximum energy. The OFSS is a hybrid system in which a rule-based system, fuzzy logic, and an artificial neural network (ANN) are connected with each other. The rule-based system classifies loading patterns into two types by using several heuristic rules and a fuzzy rule. The fuzzy rule is introduced to achieve a more effective and faster search. Its membership function is automatically updated in accordance with the prediction results. The ANN predicts core parameters for the patterns generated from the rule-based system. A back propagation network is used for fast prediction of the core parameters. The ANN and fuzzy logic can be used to improve the capabilities of existing algorithms. The OFSS was demonstrated and validated for cycle 1 of the Kori-1 PWR.
Patent•
09 Sep 1993
TL;DR: In this paper, a fuzzy microcontroller is used to determine the ratio of a reference barcode element with respect to a reference membership function, which is then fuzzified by determining the distance of the crisp input from the center of the membership function.
Abstract: An arrangement (apparatus and method) using fuzzy logic for determining the ratios of barcode elements with respect to a reference barcode element. A barcode interface outputs width data for the reference barcode element and the other barcode elements of the barcode pattern in accordance with a predetermined barcode format. A latch array latches the width data of the reference barcode element and supplies the reference width data and a divided value of the reference width data to a fuzzy microcontroller as center and width data for a fuzzy membership function, respectively. The latch array also latches the barcode element width data from the barcode interface, divides the barcode element width data by a set of predetermined ratios, and outputs the quotient data to the fuzzy microcontroller. Each quotient data corresponding to one of the ratios is fuzzified by determining the distance of the crisp input from the center of the membership function and linearly complementing the distance with respect to the width of the membership function. The quotient data that has the highest membership value is deemed to correspond to the winning ratio. The fuzzy microcontroller uses rule-based logic that enables code recognition of the barcode scanner on the basis of successive determined ratios, as well as control of external devices in response to the determined ratios.
TL;DR: This paper proposes a recursive parameter tuning algorithm for the identification of fuzzy relational model for an unknown dynamic system and constructs a control input fuzzy set inducing a desired output fuzzy set for the control purpose.
TL;DR: W: C. Rauszer, editor, Banach Center Publications, volume 22, pages 135-150, 1993.
Abstract: W: C. Rauszer, editor, Banach Center Publications, volume 22, pages 135-150. Polish Academy of Sciences, Warsaw, Poland, 1993
TL;DR: Here more general conditions are given for both the function ƒ and the manner in which the fuzzy numbers {μi} are combined so that this simple method for computing induced membership may be used.
Patent•
18 Jun 1993TL;DR: In this paper, a method and apparatus in a system comprising cordless telecommunication utilize fuzzy-logic to evaluate at least two radio communication parameters when making a handoff decision, or to produce basic data on which a handover decision can be made.
Abstract: A method and apparatus in a system comprising cordless telecommunication utilize fuzzy-logic to evaluate at least two radio communication parameters when making a handoff decision, or to produce basic data on which a handoff decision can be made. The parameters are assigned membership to at least two input data sets, each having its own membership function. The parameters are divided into groups and a rule table of fuzzy-condition statements is formed. The fuzzy-condition statements are executed and the consequences weighted to a crisp-value which is used in conjunction with handoff. The inventive apparatus includes a fuzzy-processing unit for grouping parameters and executing rules, a unit for determining the crisp-values, for instance the average value, maximum value and/or the minimum value of rule consequences, and an evaluating unit which uses the crisp-values in conjunction with establishing a candidate list or in making a handoff decision.
TL;DR: An alternative procedure is presented which allows for the use of any convex and normalized fuzzy set to assess the contribution of each alternative to some overall objective, according to a set of criteria.
TL;DR: It is shown that the well known formulae of fuzzy set operations such as the max-mm operations, the bounded sum-difference operations, and the probability sum-product operations are consequences of the definition under three different correlations of the fuzzy sets.
TL;DR: The fuzzy integrals of fuzzy mappings are defined, the fuzzy integral of fuzzy-valued functions is obtained, and the properties and convergence theorems are obtained.
TL;DR: The use of nonlinear membership functions in fuzzy linear programming problems are considered to show that the corresponding solution to be obtained can be derived from a parallel linear model, making use of a similar procedure to that of post-optimal analysis in classical linear programming.
28 Mar 1993
TL;DR: The parameters of the input and output fuzzy membership functions for fuzzy if-then min-max inferencing may be adapted using supervised learning applied to training data and the overall performance of the fuzzy system can be improved by this adaptive pruning.
Abstract: The parameters of the input and output fuzzy membership functions for fuzzy if-then min-max inferencing may be adapted using supervised learning applied to training data. Under the assumption that the inference surface is in some sense smooth, the process of adaptation can reveal overdetermination of the fuzzy system in two ways. First, if two membership functions come sufficiently close to each other, they can be fused into a single membership function. Second, annihilation occurs when a membership function becomes sufficiently narrow. In both cases, the number of if-then rules is reduced. In certain cases, the overall performance of the fuzzy system can be improved by this adaptive pruning. The process of membership function fusion and annihilation is illustrated with two examples. >
TL;DR: It is shown that in the case of fuzzy linear programming problems, whether or not a fuzzy optimal solution has been found by using linear membership functions modeling the constraints, possible further changes of those membership functions do not affect the former optimal solution.