Fuzzy sets, fuzzy algebra, and fuzzy statistics

Kandel, Abraham; Byatt, W.J.

doi:10.1109/proc.1978.11171

Cited by 176 publications

(46 citation statements)

References 185 publications

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“…ƒF o ƒ is actually the median of 2n -1 terms {F(u 1 ), F(u 2 ) … F(u n ), g({u 1 }),…, g({u 1 ,…, u n -1 })}(see for instance Kandel and Byatt, 1978;Dubois and Prade, 1980a), as opposed to the convex combination of sets view, which yields average values. Sugeno integrals are the basis for defining possibility and necessity of fuzzy events.…”

Section: Extending Usual Functionsmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

139

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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Section: Extending Usual Functionsmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

139

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“…The membership function [93] describes the strength of our belief that an element x is a member of the set A, and is denoted by uA(x) . lf p,,(x) = l, we are certain x is in A; if ju",(x) = O, we are certain that x is not in A.…”

Section: Fuzzy Set Methodsmentioning

confidence: 99%

Nonlinear image restoration using a segmentation-oriented expert system

Jeong

Beex

ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing

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“…The key idea in the fuzzy set theory is the definition of vagueness [6]. In the probability theory there is no such concept.…”

Section: Toleration Of Vaguenessmentioning

confidence: 99%

“…The Axiomatic 'Inadequacy' of Probability: Kandel and Byatt [6] claim that the laws of probability are not realistic since human beings do not conform to them. Kosko [9] claims that the conditional probability theory lacks an adequate axiomatic foundation.…”

Section: Promotion Of Emulationmentioning

confidence: 99%

AwarePen - Classification Probability and Fuzziness in a Context Aware Application

Berchtold¹,

Riedel²,

Beigl³

et al.

Ubiquitous Intelligence and Computing

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Abstract. Fuzzy inference has been proven a candidate technology for context recognition systems. In comparison to probability theory, its advantage is its more natural mapping of phenomena of the real world as context. This paper reports on our experience with building and using monolithic fuzzy-based systems (a TSK-FIS) to recognize real-world events and to classify these events into several categories. It will also report on some drawbacks of this approach that we have found. To overcome these drawbacks a novel concept is proposed in this paper. The concept incorporates fuzzy-based approaches with probabilistic methods, and separates the monolithic fuzzy-based system into several modules. The core advantage of the concept lays in the separation of detection complexity into distinct modules, each of them using fuzzy-based inference for context classification. Separation of detection functionality is supported by an automatic process using transition probabilities between context classifiers to optimize detection quality for the resulting detection system. This way our approach incorporates the advantages of fuzzy-based and probabilistic systems. This paper will show results of experiments of an existing system using a monolithic FIS approach, and reports on advantages when using a modular approach.

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Fuzzy sets, fuzzy algebra, and fuzzy statistics

Cited by 176 publications

References 185 publications

Fuzzy Sets: History and Basic Notions

Fuzzy Sets: History and Basic Notions

Nonlinear image restoration using a segmentation-oriented expert system

AwarePen - Classification Probability and Fuzziness in a Context Aware Application

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