Showing papers on "Fuzzy associative matrix published in 1994"
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01 Apr 1994
TL;DR: Fuzzy systems and fuzzy models the fuzzy world model fuzzy sets fuzzy logic approximate reasoning constructing a fuzzy system model case studies and advanced fuzzy system modelling techniques fuzzy database and objectbase operations.
Abstract: Fuzzy systems and fuzzy models the fuzzy world model fuzzy sets fuzzy logic approximate reasoning constructing a fuzzy system model case studies and advanced fuzzy system modelling techniques fuzzy database and objectbase operations N-dimensional fuzzy models adaptive fuzzy systems models fuzzy models with multiple experts hybrid fuzzy and neural co-operating systems model stability validation and performancce metrics production systems installation and maintenance.
510 citations
TL;DR: A new and general decision making method for evaluating weapon systems using fuzzy AHP based on entropy weight, which will derive the priority among the alternatives by the entropy weight through the use of interval arithmetic, α-cuts, and index of optimism to estimate the degree of satisfaction of the judgement.
288 citations
TL;DR: The new method employed to identify the rule relevant nodes before the rules are extracted makes FuNe I suitable for applications with large number of inputs, and optimization of the knowledge base in possible including the tuning of membership functions.
251 citations
TL;DR: A new algorithm for evaluating weapon systems by Analytical Hierarchy Process (AHP) based on fuzzy scales, which is a multiple criteria decision making approach in a fuzzy environment is proposed and applied to a weapon system evaluation and selection problem.
223 citations
TL;DR: This model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature, and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query.
220 citations
TL;DR: Formulas are derived which can calculate the number of input fuzzy sets, output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy, and it is revealed that the number is minimal when the maximum number of intersection between adjacentinput fuzzy sets is one.
209 citations
TL;DR: Fuzzy logic methods have been used successfully in many real-world applications, but the foundations of fuzzy logic remain under attack as mentioned in this paper, and almost all of the successful fuzzy logic applications are embedded controllers, while most of the theoretical papers on fuzzy methods deal with knowledge representation and reasoning.
Abstract: Fuzzy logic methods have been used successfully in many real-world applications, but the foundations of fuzzy logic remain under attack. Taken together, these two facts constitute a paradox. A second paradox is that almost all of the successful fuzzy logic applications are embedded controllers, while most of the theoretical papers on fuzzy methods deal with knowledge representation and reasoning. I hope to resolve these paradoxes by identifying which aspects of fuzzy logic render it useful in practice, and which aspects are inessential. My conclusions are based on a mathematical result, on a survey of literature on the use of fuzzy logic in heuristic control and in expert systems, and on practical experience in developing expert systems. >
207 citations
10 Aug 1994
TL;DR: This paper describes a generation method of rectangular fuzzy rules from numerical data for classification problems and formulates a rule selection problem for constructing a compact fuzzy classification system as a combinatorial optimization problem with two objectives: to minimize the number of selected fuzzy rules and to maximize theNumber of correctly classified patterns.
Abstract: This paper proposes a genetic-algorithm-based approach to the construction of fuzzy classification systems with rectangular fuzzy rules. In the proposed approach, compact fuzzy classification systems are automatically constructed from numerical data by selecting a small number of significant fuzzy rules using genetic algorithms. Since significant fuzzy rules are selected and unnecessary fuzzy rules are removed, the proposed approach can be viewed as a knowledge acquisition tool for classification problems. In this paper, we first describe a generation method of rectangular fuzzy rules from numerical data for classification problems. We next formulate a rule selection problem for constructing a compact fuzzy classification system as a combinatorial optimization problem with two objectives: to minimize the number of selected fuzzy rules and to maximize the number of correctly classified patterns. We then show how genetic algorithms are applied to the rule selection problem. Last, we illustrate the proposed approach by computer simulations on numerical examples and the iris data of Fisher.
195 citations
TL;DR: Algorithms for constructing fuzzy rules from input-output training data, which require only a single pass through the training set, are examined to produce a computationally efficient method of learning.
Abstract: Fuzzy inference systems and neural networks both provide mathematical systems for approximating continuous real-valued functions. Historically, fuzzy rule bases have been constructed by knowledge acquisition from experts while the weights on neural nets have been learned from data. This paper examines algorithms for constructing fuzzy rules from input-output training data. The antecedents of the rules are determined by a fuzzy decomposition of the input domains. The decomposition localizes the learning process, restricting the influence of each training example to a single rule. Fuzzy learning proceeds by determining entries in a fuzzy associative memory using the degree to which the training data matches the rule antecedents. After the training set has been processed, similarity to existing rules and interpolation are used to complete the rule base. Unlike the neural network algorithms, fuzzy learning algorithms require only a single pass through the training set. This produces a computationally efficient method of learning. The effectiveness of the fuzzy learning algorithms is compared with that of a feedforward neural network trained with back-propagation. >
157 citations
TL;DR: A representational model for the knowledge base (KB) of fuzzy production systems with rule chaining based on the Petri net formalism is developed and a process of "incremental reasoning" is developed that allows the KB to take information about previously unknown values into consideration as soon as such information becomes available.
Abstract: We develop a representational model for the knowledge base (KB) of fuzzy production systems with rule chaining based on the Petri net formalism. The model presents the execution of a KB following a data driven strategy based on the sup-min compositional rule of inference. In this connection, algorithms characterizing different situations have been described, including the case where the KB is characterized by complete information about all the input variables and the case where it is characterized by ignorance of some of these variables. For this last situation we develop a process of "incremental reasoning"; this process allows the KB to take information about previously unknown values into consideration as soon as such information becomes available. Furthermore, as compared to other solutions, the rule chaining mechanism we introduce is more flexible, and the description of the rules more generic. The computational complexity of these algorithms is O((C/2+M+N)R/sup 2/) for the "complete information" case and O((M+N)R/sup 2/) and O(2(M+N)R/sup 2/) for the other cases, where R is the number of fuzzy conditional statements of the KB, M and N the maximum number of antecedents and consequents in the rules and C the number of chaining transitions in the KB representation. >
145 citations
01 Jan 1994
TL;DR: A weighted fuzzy reasoning algorithm for handling medical diagnostic problems, where fuzzy set theory and fuzzy production rules are used for knowledge representation, which can perform fuzzy matching between the patient's symptom manifestations and the antecedent portions of fuzzyproduction rules to determine the presence of diseases.
Abstract: This paper presents a weighted fuzzy reasoning algorithm for handling medical diagnostic problems, where fuzzy set theory and fuzzy production rules are used for knowledge representation. The algorithm can perform fuzzy matching between the patient's symptom manifestations and the antecedent portions of fuzzy production rules to determine the presence of diseases, where the result is interpreted as a certainty level indicating the degree of certainty of the presence of the disease. Because the algorithm allows each symptom in medical diagnosis to have a different degree of importance, it is more flexible than the ones we presented in [3] and [4]. The algorithm can be executed very efficiently. If the knowledge base contains n fuzzy production rules and there are p symptoms, then the time complexity of the algorithm is O ( np ).
TL;DR: The necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated and the consequences of this separation are characterised.
TL;DR: It is argued that this technique can produce good approximate solutions by applying it to solve a fuzzy optimization problem by introducing fuzzy genetic algorithms to (approximately) solve fuzzy optimization problems.
26 Jun 1994
TL;DR: A design problem for a fuzzy regulator which consists of fuzzy state feedback laws is solved by extending the idea of modem control theory and the concept of a fuzzy observer, which estimates the states of fuzzy dynamic plants, is introduced.
Abstract: Deals with design procedures for fuzzy regulators and fuzzy observers, which are the most important and basic concepts for fuzzy control system design. First, a design problem for a fuzzy regulator which consists of fuzzy state feedback laws is solved by extending the idea of modem control theory. Next, the concept of a fuzzy observer, which estimates the states of fuzzy dynamic plants, is introduced. Finally, a design algorithm for a fuzzy control system containing a fuzzy regulator and a fuzzy observer is constructed. The fuzzy regulator guarantees the stability of the fuzzy control system in accordance with the definition of stability in the sense of Lyapunov. The fuzzy observer guarantees that the estimation error for the states of the fuzzy dynamic plants converges to zero. The 'separate theorem', which guarantees that one should be able to design regulators and observers separately, cannot be applied to the case of the design of fuzzy regulators and fuzzy observers. >
TL;DR: The formulated mathematical programming problem which yields the max-min strategy can be reduced to the linear programming problem by making use of Sakawa's method, the variable transformations, and the relaxation procedure.
TL;DR: It is proved that the minimum of the fuzzy preinvex functions on the invex sets can be characterized by variational-like inequalities.
TL;DR: This paper presents the design of a fuzzy controller for managing cells generated by voice sources in asynchronous transfer mode (ATM) networks, an improved and intelligent implementation of the leaky bucket cell rate control mechanism extensively studied in the literature.
Abstract: This paper presents the design of a fuzzy controller for managing cells generated by voice sources in asynchronous transfer mode (ATM) networks. Typical voice cells, characterized by a high degree of burstiness, complicate any attempt to use classical control theory in the design of an ATM cell rate controller. The fuzzy control approach presented in this paper overcomes this limitation by appealing to the linguistic ability of fuzzy set theory and logic to handle the complexity. Specifically, the cell rate control problem is linguistically stated but treated mathematically via fuzzy set manipulation. In particular, the ATM voice cell controller being proposed is an improved and intelligent implementation of the leaky bucket cell rate control mechanism extensively studied in the literature. This intelligent implementation of the leaky bucket mechanism uses a channel utilization feedback via the QoS parameters to improve its performance. This ATM fuzzy controller takes the form of an organized set of linguistic rules quantitatively expressed and manipulated by means of fuzzy set theory and fuzzy logic. The fuzzy control rules are stored in fuzzy associative memory to permit parallel executions. >
TL;DR: By computer simulations based on a random subsampling technique, it is shown that the performance of fuzzy systems is comparable to that of neural networks and it is also shown that pre-specified conditions such as a fuzzy partition, initial fuzzy if-then rules and the number of iterations have a significant effect on theperformance of trained fuzzy systems.
TL;DR: There is no single generalization from binary logic to fuzzy logic that is clearly best or correct, and many self-consistent systems have been developed which reduce to 2-valued logic if all parameters are crisp.
Abstract: 30 Years after its introduction, fuzzy logic remains an area of active research. As can be seen from the examples given here, in most instances there is no single generalization from binary logic to fuzzy logic that is clearly best or correct. Many self-consistent systems have been developed which reduce to 2-valued logic if all parameters are crisp. The choice of a model depends at this point on how well each functions in practice. For medical expert systems, the theoretical framework of fuzzy logic provides a rich environment from which to choose. The adequacy of each approach is born out by the success of the model in practice. >
NEC1
TL;DR: The ability of each approach to interpolate sparse fuzzy if-then rules is examined by computer simulations and high fitting ability of approaches and high interpolating ability of those in the second category are demonstrated.
TL;DR: It is shown that the property of similarity is preserved when the sup-min compositional rule of inference is applied to similar values of fuzzy variables and fuzzy relations, which extends the results of Pappis (1991).
TL;DR: This paper uses a multilayer feedforward ANN with the criterions of three people, each with different characteristic, using the backpropagation algorithm and different structures to rank a set of fuzzy numbers which can be considered as utilities of decision problems with fuzzy environment, hence enabling the best choice.
TL;DR: A combined approach for discrete-time fuzzy model identification is proposed and a recursive identification algorithm based on the prediction-error method is derived for optimally resolving the numerical fuzzy relational equation by minimizing a quadratic performance index.
Abstract: A combined approach for discrete-time fuzzy model identification is proposed. By this approach, the identification is performed in two stages. First, the linguistic approach is utilized to obtain an approximate fuzzy relation from the sampled nonfuzzy input-output data. This approximate fuzzy relation is then used as the initial estimate for the second stage in which a more accurate fuzzy relation is determined by the approach of numerical resolution of fuzzy relational equation. A recursive identification algorithm based on the prediction-error method is derived for optimally resolving the numerical fuzzy relational equation by minimizing a quadratic performance index. This algorithm makes the proposed approach particularly attractive to online applications. Two numerical examples are provided to show the superiority of the combined approach over other methods. >
09 May 1994
TL;DR: A Markoov fuzzy process is constructed, which represents transitions of grades of fuzzy sets, with a transition possibility measure and a general state space, to solve fuzzy dynamic programming with optimal stopping times and with general state spaces and action spaces under fuzzy transitions.
Abstract: Abstract This paper constructs a Markoov fuzzy process, which represents transitions of grades of fuzzy sets, with a transition possibility measure and a general state space. We analyse Snell's optimal stopping problem for the process and we apply the results to solve fuzzy dynamic programming with optimal stopping times and with general state spaces and action spaces under fuzzy transitions.
TL;DR: The principles of threshold fuzzification and fuzzy rule-based threshold adaption are outlined, and the usefulness of fuzzy logic for man-machine interaction is pointed out.
TL;DR: It is argued that any continuous fuzzy expert system may be approximated by a neural net; and any continuous neural net (feedforward, multilayered) may be approximation by a fuzzy Expert system.
TL;DR: It is shown how the determination of the firing level of a neuron can be viewed as a measure of possibility between two fuzzy sets, the weights of connection and the input and a way to represent fuzzy production rules in a neural framework is suggested.
26 Jun 1994
TL;DR: This paper investigates the design of a fuzzy logic PID controller that uses a simplified design scheme that takes advantage of the properties of the fuzzy PI and PD controllers.
Abstract: This paper investigates the design of a fuzzy logic PID controller that uses a simplified design scheme. Fuzzy logic PD and PI controllers are effective for many control problems but lack the advantages of the fuzzy PID controller. Fuzzy controllers use a rule base to describe relationships between the input variables. Implementation of a detailed rule base, such as a PID controller, increases in complexity as the number of input variables grow and the ranges of operation for the variables become more defined. We propose a hybrid fuzzy PID controller which takes advantage of the properties of the fuzzy PI and PD controllers. The effectiveness of the PID fuzzy controller implementation is illustrated with an example. >
25 May 1994
TL;DR: In this paper, the authors show how the classical theory of T-norm and S-norms of fuzzy logic can be generalized to a theory of quantifiers and s-quantifiers, respectively.
Abstract: We show how the "classical" theory of T-norms and S-norms of fuzzy logic can be generalized to a theory of T-quantifiers and S-quantifiers, respectively. The key idea leading to this generalization is the fact that the (infinite) iteration of the two-valued conjunction and disjunction gives the two-valued all-quantifier and ex-quantifier, respectively. In the framework of fuzzy logic the same holds for min with respect to Inf and for max with respect to Sup. As a T-norm (S-norm) is commutative and associative, we can construct an all-/spl tau/-quantifier (an ex-/spl sigma/-quantifier) from a given T-norm /spl tau/ (S-norm /spl sigma/). These quantifiers are characterized by axioms (T-quantifiers and S-quantifiers). Furthermore we show that the generating procedure is "complete" with respect to arbitrary T-quantifiers (S-quantifiers) and uniquely reversible. >
TL;DR: A new morphology is proposed which uses fuzzy structuring elements and is internal on fuzzy sets, fully compatible with conventional morphology which uses binary structured elements, either on binary or on grey-tone sets.
Abstract: A new morphology is proposed which uses fuzzy structuring elements and is internal on fuzzy sets. It is fully compatible with conventional morphology which uses binary structuring elements, either on binary or on grey-tone sets. The properties of the two basic operations, fuzzy dilation and fuzzy erosion, are presented. An example showing the interest of fuzzy morphology to manipulate the uncertainty linked to spatial information is presented in multisource medical image data fusion.