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 non-disjoint intervals. From these set statistics an empirical random set can be derived. Under reasonable consistency requirements, its one-point 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 architecture for the implementation of possibilistic models in an object-oriented 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 methods---including 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 methods---are 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 Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions a...

: The measurement of set-valued 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 Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. So possibility theory i...

The potential for the use of possibility theory in the qualitative model-based diagnosis of spacecraft systems is described. The first sections of the paper briefly introduce the Model-Based 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...

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 Dempster-Shafer 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 probabilistic-possibilistic consistency [16] is an example of the kind of principle which can be brought to bear on...

Set-based 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.