A pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

In this work we shall give a pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

Relational Hidden Variables and Non-Locality

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic

Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality

Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is `possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy's paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurence of Hardy's paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy's paradox is not true more generally: we find a new `proof without inequalities' in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality

Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

Land cover classification using fuzzy rules and aggregation of contextual information through evidence theory

Land cover classification using multispectral satellite image is a very challenging task with numerous practical applications. We propose a multi-stage classifier that involves fuzzy rule extraction from the training data and then generation of a possibilistic label vector for each pixel using the fuzzy rule base. To exploit the spatial correlation of land cover types we propose four different information aggregation methods which use the possibilistic class label of a pixel and those of its eight spatial neighbors for making the final classification decision. Three of the aggregation methods use Dempster-Shafer theory of evidence while the remaining one is modeled after the fuzzy k-NN rule. The proposed methods are tested with two benchmark seven channel satellite images and the results are found to be quite satisfactory. They are also compared with a Markov random field (MRF) model-based contextual classification method and found to perform consistently better.Comment: 14 pages, 2 figure

Analysis of fuzzy clustering and a generic fuzzy rule-based image segmentation technique

Many fuzzy clustering based techniques when applied to image segmentation do not incorporate spatial relationships of the pixels, while fuzzy rule-based image segmentation techniques are generally application dependent. Also for most of these techniques, the structure of the membership functions is predefined and parameters have to either automatically or manually derived. This paper addresses some of these issues by introducing a new generic fuzzy rule based image segmentation (GFRIS) technique, which is both application independent and can incorporate the spatial relationships of the pixels as well. A qualitative comparison is presented between the segmentation results obtained using this method and the popular fuzzy c-means (FCM) and possibilistic c-means (PCM) algorithms using an empirical discrepancy method. The results demonstrate this approach exhibits significant improvements over these popular fuzzy clustering algorithms for a wide range of differing image types