Defuzzification: criteria and classification

Leekwijck, Werner Van; Kerre, Etienne

doi:10.1016/s0165-0114(97)00337-0

Cited by 649 publications

(306 citation statements)

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“…Possibility theory and defuzzification Possibilistic mean values can be defined using Choquet integrals with respect to possibility and necessity measures [65,37], and come close to defuzzification methods [134]. A fuzzy interval is a fuzzy set of reals whose membership function is unimodal and upper-semi continuous.…”

Section: Probability-possibility Transformationsmentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

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This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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Section: Probability-possibility Transformationsmentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

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“…The quantitative score is obtained by the assessment of the upper bound of α-cut at 0.8. This α-cut value was chosen by the experts by considering the correspondence between the membership level and the fractile of a probability distribution [36][37] and the analysis of defuzzification methods that provide real values [38]. Indeed, the experts wanted to select the defuzzification value that corresponded to a value between a "mean probable" and "probable",…”

Section: Possibility Expression Of Imperfect Assessmentsmentioning

confidence: 99%

A dam assessment support system based on physical measurements, sensory evaluations and expert judgements

Curt¹,

Talon²,

Mauris

2011

Measurement

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In engineering system control, human beings can play various key roles, in particular concerning measurement, global assessment and decision. This paper focuses on methods that allow the representation and aggregation of heterogeneous data (sensory evaluations, physical measurements, outputs of mathematical models, etc.) used in a global dam assessment process.It is acknowledged that in such complex systems many of the variables involved are evaluated with uncertainty. We propose a possibility theory-based approach to deal with all the different uncertain pieces of information and propagate them in aggregation models for global dam assessment. Finally, decision-making and communication applications relating to dam safety are presented.

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“…We know a number of defuzzification procedures from the literature (Van Leekwijck & Kerre, 1999). Continuous, linear functionals on R give a class of defuzzification functionals .…”

Section: Defuzzification Functionalsmentioning

confidence: 99%

“…In the course of this operation to a membership function representing a classical fuzzy set a real number is attached. We know a number of defuzzification procedures from the literature, such as: FOM (first of maximum), LOM (last of maximum), MOM (middle of maximum), RCOM (random choice of maximum), COG (center of gravity), and others which were extensively discussed by the authors of (Van Leekwijck & Kerre, 1999). They have classified the most widely used defuzzification techniques into different groups, and examined the prototypes of each group with respect to the defuzzification criteria.…”

Section: Approximation Of Defuzzification Functionalsmentioning

confidence: 99%