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Some New Results on Possibilistic Measurement
, 1993
"... Further results on possibilistic measurement [5, 8, 9] are presented, including the introduction of possibilistic histograms, their interpretation as fuzzy numbers, and their continuous approximations. 1 Possibilistic Measurement Joslyn has presented a measurement method for possibility distributio ..."
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Cited by 8 (8 self)
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Further results on possibilistic measurement [5, 8, 9] are presented, including the introduction of possibilistic histograms, their interpretation as fuzzy numbers, and their continuous approximations. 1 Possibilistic Measurement Joslyn has presented a measurement method for possibility distributions [5, 8, 9]. The procedure is based on the observations of possibly nondisjoint intervals. From these set statistics an empirical random set can be derived. Under reasonable consistency requirements, its onepoint coverage function is a possibility distribution, from which a consonant (possibilistic) random set can in turn be derived. Given a finite universe\Omega := f! i g; 1 i n, the function m: 2\Omega 7! [0; 1] is an evidence function (otherwise known as a basic probability assignment) when m(;) = 0 and P A`\Omega m(A) = 1. Denote a random set generated from an evidence function as S := fh A j ; m j i : m j ? 0g, where h \Delta i is a vector, A j `\Omega ; m j := m(A j ), an...
An ObjectOriented Architecture for Possibilistic Models
 in: Proc. 1994 Conf. ComputerAided Systems Technology
, 1994
"... . An architecture for the implementation of possibilistic models in an objectoriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilist ..."
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Cited by 4 (4 self)
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. An architecture for the implementation of possibilistic models in an objectoriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilistic processes are specified. Supplementary methodsincluding the fast Mobius transform, the maximum entropy and Bayesian approximations of random sets, distribution operators, compatibility measures, consonant approximations, frequency conversions, and possibilistic normalization and measurement methodsare also introduced. Empirical results to be investigated are also described. 1 Introduction Possibility theory [4] is an alternative information theory to that based on probability. Although possibility theory is logically independent of probability theory, they are related: both arise in DempsterShafer evidence theory as fuzzy measures defined on random sets; and their distributions a...
Distributional Representations Of Random Interval Measurements
, 1997
"... : The measurement of setvalued and interval data is considered. Their random interval mathematical representations are introduced. The conditions for distributional (probabilistic and possibilistic) representations and conversions to and among them are established. Some properties of empirical ran ..."
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Cited by 3 (3 self)
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: The measurement of setvalued and interval data is considered. Their random interval mathematical representations are introduced. The conditions for distributional (probabilistic and possibilistic) representations and conversions to and among them are established. Some properties of empirical random sets and possibilistic histograms related to strong probabilistic compatibility are described. Finally, the nature of probability distributions which are strongly stochastically compatible with a given possibility distribution, and the derivation of frequency distributions from empirical random sets, are discussed. 3.1 INTRODUCTION Possibility theory (de Cooman et al., 1995) is an alternative information theory to that based on probability. Although possibility theory is logically independent of probability theory, they are related: both arise in DempsterShafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. So possibility theory i...
Possibilistic Measurement and Set Statistics
, 1992
"... Setbased statistics are necessary to generate possibility distributions from measured data. Methods by which physical measurements can generate statistical data on real intervals are considered, including trials from multiple heterogeneous measurement devices rather than a single instrument at mult ..."
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Cited by 1 (1 self)
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Setbased statistics are necessary to generate possibility distributions from measured data. Methods by which physical measurements can generate statistical data on real intervals are considered, including trials from multiple heterogeneous measurement devices rather than a single instrument at multiple times; classes of consistent intervals constructed from statistical data around a common point focus or interval core; and consonant intervals constructed from statistical data.
Qualitative ModelBased Diagnosis Using Possibility Theory
 Proc. 1994 Goddard Conf. on Space Applications of AI
, 1994
"... The potential for the use of possibility theory in the qualitative modelbased diagnosis of spacecraft systems is described. The first sections of the paper briefly introduce the ModelBased Diagnostic (mbd) approach to spacecraft fault diagnosis; Qualitative Modeling (qm) methodologies; and the con ..."
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Cited by 1 (1 self)
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The potential for the use of possibility theory in the qualitative modelbased diagnosis of spacecraft systems is described. The first sections of the paper briefly introduce the ModelBased Diagnostic (mbd) approach to spacecraft fault diagnosis; Qualitative Modeling (qm) methodologies; and the concepts of possibilistic modeling in the context of Generalized Information Theory (git). Then the necessary conditions for the applicability of possibilistic methods to qualitative mbd, and a number of potential directions for such an application, are described. Possibility theory is being developed as an alternative to traditional theories of uncertainty. While possibility is logically independent of probability theory, they are related: both arise in DempsterShafer evidence theory as fuzzy measures defined on random sets; and their distributions are fuzzy sets. Together these fields comprise the new field of Generalized Information Theory. Possibilistic processes, which generalize interva...
Strong Probabilistic Compatibility of Possibilistic Histograms
 in: Proc. 1995 Int. Symposium on Uncertainty Modeling and Analysis
, 1995
"... Some properties of empirical random sets and possibilistic histograms related to strong probabilistic compatibility are described. We will discuss possibilistic histograms and the possibility of occurence, the nature of probability distributions which are strongly stochastically compatible with a gi ..."
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Cited by 1 (1 self)
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Some properties of empirical random sets and possibilistic histograms related to strong probabilistic compatibility are described. We will discuss possibilistic histograms and the possibility of occurence, the nature of probability distributions which are strongly stochastically compatible with a given possibility distribution, and the derivation of frequency distributions from empirical random sets. 1 Introduction Possibility theory [3] is an alternative information theory to that based on probability. Although possibility theory is logically independent of probability theory, they are related: both arise in DempsterShafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. So possibility theory is a component of a broader Generalized Information Theory (git), which includes all of these fields [12]. Zadeh's concept of probabilisticpossibilistic consistency [16] is an example of the kind of principle which can be brought to bear on...
International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems c ○ World Scientific Publishing Company Normalizing possibility distributions using tnorms
"... A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given tnorm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common tnorms. For a given fuzzy subset µ, the correspo ..."
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A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given tnorm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common tnorms. For a given fuzzy subset µ, the corresponding normalized fuzzy subset ˆµ can be viewed as the distribution of µ conditioned on the (degree of) existence of its elements with maximal membership. From this view point we investigate the less specific normal fuzzy subset of X among the most similar fuzzy subsets to µ and the normal fuzzy subset generating the same fuzzy Tpreorder as µ.
Aggregation and Completion in Probability and Possibility Theory
, 1994
"... this paper some new ideas about the mathematical relations between probability and possibility are presented in the context of random set theory. Although some of these results are already known, I believe that the concepts of complete random sets and distributions, and numerical and structural aggr ..."
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this paper some new ideas about the mathematical relations between probability and possibility are presented in the context of random set theory. Although some of these results are already known, I believe that the concepts of complete random sets and distributions, and numerical and structural aggregation functions on them, provide a broad, consistent context not only in which to place probability and possibility, but also to consider new forms of measures and distributions which have yet to be studied. Below is a synoptic summary of the mathematical ideas to be presented in the full paper. 2 General Random Sets and Distributions