作者：
L.A. ZadehProfessor in the Graduate School and Director
Berkeley Initiative in Soft Computing (BISC) Computer Science Division and the Electronics Research Laboratory Department of Electrical Engineering and Computer Science University of California Berkeley CA USA
A good fuzzy classifier for a three-class arrhythmia problem is analyzed "a posteriori", in order to estimate the importance of the ECG features for the final system performance. A set of fuzzy rules is auto...
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A good fuzzy classifier for a three-class arrhythmia problem is analyzed "a posteriori", in order to estimate the importance of the ECG features for the final system performance. A set of fuzzy rules is automatically built on forty MIT-BIH database's files, using fourteen ECG measures to characterize each beat. The implemented fuzzy model correctly classifies 92% of normal beats, 80% of PVBs and 56% of SVPBs of the test set. The information contained in the fuzzy model is then quantified and the gain in information, derived from application of the fuzzy rules along a given input dimension, is measured. Only three ECG features (QRS width, PR segment and prematurity degree) seem to carry the main responsibility for the correct classification of the three arrhythmic classes. The uninformative character of ECG measures with lowest information gain is confirmed by the almost unaltered-when not improved-performance of the classifier when these features are removed from the input vector.
A granular fuzzy set theory is modeled on fuzzy sets whose membership functions are defined on sets of sets (granules). The grade is interpreted literally; for example, that the grade of x is 1/2 means one half of the...
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A granular fuzzy set theory is modeled on fuzzy sets whose membership functions are defined on sets of sets (granules). The grade is interpreted literally; for example, that the grade of x is 1/2 means one half of the granule x belongs to the fuzzy set. By taking the union of these subgranules, one get a crisp set representation of a fuzzy set. In other words, a granular fuzzy set is a fuzzy set that has a crisp set representation. A measure theory based on such granular fuzzy sets is developed. The measure theory of crisp sets is imported to fuzzy sets via their crisp representations. Using such a notion, a belief function can be shown to be the inner probability of a probability theory of fuzzy sets.
作者：
L.A. ZadehBerkeley Initiative in Soft Computing (BISC)
Graduate School Berkeley Initiative in Soft Computing (BISC) Computer Science Division and the Electronics Research Laboratory Department of EECS University of California Berkeley CA USA
The proposed restructuring of fuzzy logic (FL) is centred on two basic issues: (a) identification of the principal facets of FL and its core concepts; and (b) introduction of the concept of the generalization group an...
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The proposed restructuring of fuzzy logic (FL) is centred on two basic issues: (a) identification of the principal facets of FL and its core concepts; and (b) introduction of the concept of the generalization group and its employment for generation of rules of inference or, equivalently, rules of constraint propagation. The proposed restructuring has three objectives. First, to clarify and solidify the foundations of fuzzy logic; second to make more transparent the links between fuzzy logic and other methodologies; and third, to suggest alternative ways for further development of fuzzy logic and its applications.
作者：
L.A. ZadehBerkeley Initiative in Soft Computing (BISC)
Computer Science Division and the Electronics Research Laboratory Department of Electrical Engineering and Computer Science University of California Berkeley CA USA
Recognition systems of one kind or another have been around for a long time. But what we are beginning to see today are recognition systems that are capable of performing tasks that could not be done in the past. The ...
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Recognition systems of one kind or another have been around for a long time. But what we are beginning to see today are recognition systems that are capable of performing tasks that could not be done in the past. The quantum jump in the capabilities of today's recognition systems reflect three converging developments: (a) major advances in sensor technology; (b) major advances in sensor data processing technology; and (c) the use of softcomputing techniques to infer a conclusion from observed data.
The paper investigates techniques for comparing two fuzzy graphs. Fuzzy graphs are attracting attention because they not only allow easy interpretation but in addition finding regions of interest or tolerating missing...
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The paper investigates techniques for comparing two fuzzy graphs. Fuzzy graphs are attracting attention because they not only allow easy interpretation but in addition finding regions of interest or tolerating missing attributes can be done computationally in a very efficient manner. This is of great interest in numerous applications such as intelligent data analysis, meta-modeling and others. Two ways of comparing fuzzy graphs are presented.
作者：
Lotfi A. ZadehProfessor Emeritus and Director
Berkeley Initiative in Soft Computing (BISC) Computer Science Division Department of EECS University of California Berkeley CA 94720-1776.
The essence of softcomputing is that, unlike the traditional, hard computing, it is aimed at an accommodation with the pervasive imprecision of the real world. Thus, the guiding principle of softcomputing is: `...ex...
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The essence of softcomputing is that, unlike the traditional, hard computing, it is aimed at an accommodation with the pervasive imprecision of the real world. Thus, the guiding principle of softcomputing is: `...exploit the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness, low solution cost and better rapport with reality'. In the final analysis, the role model for softcomputing is the human mind. softcomputing is not a single methodology. Rather, it is a partnership. The principal partners at this juncture are fuzzy logic, neuro-computing and probabilistic reasoning, with the latter subsuming genetic algorithms, chaotic systems, belief networks and parts of learning theory. In coming years, the ubiquity of intelligent systems is certain to have a profound impact on the ways in which man-made intelligent systems are conceived, designed, manufactured, employed and interacted with. It is within this perspective that the basic issues relating to softcomputing and intelligent systems are addressed in this paper.
The notion of fuzzy is context dependent, so for each context very often there is a fuzzy theory. Present papers use the notion of neighborhood systems to unify them. A neighborhood system is an association that assig...
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The notion of fuzzy is context dependent, so for each context very often there is a fuzzy theory. Present papers use the notion of neighborhood systems to unify them. A neighborhood system is an association that assigns to each datum a list of data (a neighborhood). Rough sets and topological spaces are special cases. A "real world" fuzzy set should allow small amount of perturbation, so it should have an elastic membership function. Mathematically, such an elastic membership function can be expressed by a highly structured subset of membership function space. Structured sets can be singletons, equivalence classes, neighborhoods, or their fuzzified versions. This paper proposed that fuzzy sets should be abstractly defined by such structures and are termed soft sets (sofsets). Based on such structures, W-sofset, F-sofset, P-sofset, B-sofset, C-sofset, N-sofset, FP-sofset, and FF-sofsets have been identified. In this sequence, a predecessor is always a special case of a successor. Each type represents some implicit form of classical fuzzy theory. It is hoped that such a unified view will provide a useful set theory for softcomputing.
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