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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...
Possibilistic Semantics and Measurement Methods in Complex Systems
 in: Proc. 2nd Int. Symposium on Uncertainty Modeling and Analysis, ed. Bilal Ayyub
, 1993
"... Possibility theory is a new mathematical theory for the representation of uncertainty. It is related to, but distinct from, probability theory, DempsterShafer evidence theory, and fuzzy set theory. It has been applied almost exclusively to knowledgebased engineering systems, with measurements take ..."
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Cited by 6 (6 self)
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Possibility theory is a new mathematical theory for the representation of uncertainty. It is related to, but distinct from, probability theory, DempsterShafer evidence theory, and fuzzy set theory. It has been applied almost exclusively to knowledgebased engineering systems, with measurements taken from subjective evaluations. Toward the end of developing a strictly possibilistic semantics of natural systems, the following will be considered: the semantics of possibility statements in relation to modal logic, natural language, and mathematical possibility theory; a strong consistency relation for probability and possibility; the basis for the application of possibility theory to complex systems; and physical measurement procedures for possibility. 1 Introduction Possibility theory, as a new method for the representation of uncertainty, is similar to, and yet distinct from, probability theory. Together with other new mathematical theories of uncertainty (fuzzy sets, fuzzy measures, D...
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...
On Possibilistic Automata
 in: Lecture Notes in Computer Science
, 1993
"... . General automata are considered with respect to normalization over semirings. Possibilistic automata are defined as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochastic automata where stochastic (+=\Theta) semirings are replaced by possibilistic (=) semirings; but ..."
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Cited by 3 (3 self)
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. General automata are considered with respect to normalization over semirings. Possibilistic automata are defined as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochastic automata where stochastic (+=\Theta) semirings are replaced by possibilistic (=) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata) or may not be (resulting in fuzzy automata proper). While possibilistic automata are direct generalizations of nondeterministic automata, stochastic automata are not. Some properties of possibilistic automata are considered, and the identity of possibilistic automata strongly consistent with stochastic automata is shown. 1 Introduction Fuzzy automata were introduced and examined in the late 1960's in a series of papers by Santos [20], Santos and Wee [22], and Wee and Fu [25]. Their most commonly considered form is the pessimistic maxmin fuzzy automata, a system e A : =\Omega Q; A; F; ¯ ...
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...
CAST Extensions to DASME to Support Generalized Information Theory
, 1996
"... . The Data Analysis and System Modeling Environment (dasme) is a computerassisted modeling environment, currently under development at NASA's Goddard Space Flight Center, designed to support groundbased mission operations with a mixed discrete/continuous modeling capability. This paper describes p ..."
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Cited by 1 (1 self)
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. The Data Analysis and System Modeling Environment (dasme) is a computerassisted modeling environment, currently under development at NASA's Goddard Space Flight Center, designed to support groundbased mission operations with a mixed discrete/continuous modeling capability. This paper describes planned castbased extensions to dasme to support a broader range of systems theoretical computing models, and in particular models utilizing concepts from Generalized Information Theory (git) such as fuzzy systems, possibilistic measurement, and possibilistic processes. Support for modelbased diagnostics and trend analysis of spacecraft systems is targetted. 1 Introduction This paper describes a software systems development project ongoing in the Software and Automation Systems Branch (Code 522) of NASA's Goddard Space Flight Center in Greenbelt, Maryland. Code 522's rolewithin the overall Goddard mission of Earth and space science research with earthorbiting satellites is to condu...