IEEE TFS: Abstracts of Published Papers, vol. 1, no. 2
Neural networks that learn from fuzzy if-then rules
An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples.
A possibilistic approach to clustering
The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples
Fuzzy inference based on families of alpha -level sets
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.
An improved synthesis method for multilayered neural networks using
An improved synthesis method for the multilayered neural network (NN) as function approximator is proposed. The method offers a translation mechanism that maps the qualitative knowledge into a multilayered NN structure. Qualitative knowledge is expressed in the form of representative points, which can be linguistically described as, 'when x is around x/sub i/, then y/sub i/ is around y'. Synthesis equations for the translation mechanism are provided. After the direct synthesis of the initial NN, the NN is tuned by backpropagation (BP), using the training data. The direct synthesis decreases the burden on BP and contributes to improved learning efficiency, accuracy, and stability. It is demonstrated that the translation mechanism is also useful for incremental modeling, i.e., increasing the number of neurons, or representative points, based on the results of BP.
A quadratic programming approach in estimating similarity relations
The problem of estimating how similar N objects are when they are compared with each other is investigated, using comparative judgments of all possible pairs of the N objects as data. The pairwise comparisons focus on the similarity relations instead of the relative importance of each object. A quadratic programming model is also proposed. It processes the similarity-based pairwise comparisons and determines the similarity relations among the N objects. The model has linear constraints; therefore it can be solved easily by transferring it into a system of linear equations.
Stable adaptive fuzzy control of nonlinear systems
A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded is developed. The specific formula for the bounds is provided, so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the Duffing chaotic system to track a trajectory. The simulation results show that the controller worked without using any fuzzy control rules, and that after fuzzy control rules were incorporated the adaptation speed became much faster. It is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control.
Comparison of Yager's level set method for fuzzy logic control with
Mamdani's and Larsen's methods
A new fuzzy reasoning method for fuzzy control recently proposed by R. Yager is investigated. A comparison with the most useful fuzzy control schemes, for a first-order with time delay process, is carried out. The results obtained show that Yager's method is superior from the point of view of both computational burden and control system behavior.
These abstracts are posted in order to accelerate dissemination of evolving Fuzzy Systems information. The abstracts are from papers published in the IEEE Transactions on Fuzzy Systems (TFS).
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