Workshop on Fuzzy Control Systems and Space Station Applications

The Workshop on Fuzzy Control Systems and Space Station Applications was held on 14-15 Nov. 1990. The workshop was co-sponsored by McDonnell Douglas Space Systems Company and NASA Ames Research Center. Proceedings of the workshop are presented

Classical Vs Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modelled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the "which way" experiments); they are, however, distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in Found. Phy

Robust techniques and applications in fuzzy clustering

This dissertation addresses issues central to frizzy classification. The issue of sensitivity to noise and outliers of least squares minimization based clustering techniques, such as Fuzzy c-Means (FCM) and its variants is addressed. In this work, two novel and robust clustering schemes are presented and analyzed in detail. They approach the problem of robustness from different perspectives. The first scheme scales down the FCM memberships of data points based on the distance of the points from the cluster centers. Scaling done on outliers reduces their membership in true clusters. This scheme, known as the Mega-clustering, defines a conceptual mega-cluster which is a collective cluster of all data points but views outliers and good points differently (as opposed to the concept of Dave\u27s Noise cluster). The scheme is presented and validated with experiments and similarities with Noise Clustering (NC) are also presented. The other scheme is based on the feasible solution algorithm that implements the Least Trimmed Squares (LTS) estimator. The LTS estimator is known to be resistant to noise and has a high breakdown point. The feasible solution approach also guarantees convergence of the solution set to a global optima. Experiments show the practicability of the proposed schemes in terms of computational requirements and in the attractiveness of their simplistic frameworks. The issue of validation of clustering results has often received less attention than clustering itself. Fuzzy and non-fuzzy cluster validation schemes are reviewed and a novel methodology for cluster validity using a test for random position hypothesis is developed. The random position hypothesis is tested against an alternative clustered hypothesis on every cluster produced by the partitioning algorithm. The Hopkins statistic is used as a basis to accept or reject the random position hypothesis, which is also the null hypothesis in this case. The Hopkins statistic is known to be a fair estimator of randomness in a data set. The concept is borrowed from the clustering tendency domain and its applicability to validating clusters is shown here. A unique feature selection procedure for use with large molecular conformational datasets with high dimensionality is also developed. The intelligent feature extraction scheme not only helps in reducing dimensionality of the feature space but also helps in eliminating contentious issues such as the ones associated with labeling of symmetric atoms in the molecule. The feature vector is converted to a proximity matrix, and is used as an input to the relational fuzzy clustering (FRC) algorithm with very promising results. Results are also validated using several cluster validity measures from literature. Another application of fuzzy clustering considered here is image segmentation. Image analysis on extremely noisy images is carried out as a precursor to the development of an automated real time condition state monitoring system for underground pipelines. A two-stage FCM with intelligent feature selection is implemented as the segmentation procedure and results on a test image are presented. A conceptual framework for automated condition state assessment is also developed

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

Modeling and Evaluation of Single Machine Flexibility Using Fuzzy Entropy and Genetic Algorithm Based Approach

International audienceFlexibility has long been recognized as a manufacturing capability that has the potential to impact mainly the competitive position of an organization. The entropy approach, which was extended from information theory, fell in handling problems with incomplete and uncertain data, because it depicts only the stochastic aspects included with measured observations. In order to get a global view, this work proposes a new approach based on fuzzy entropy concept. The development of the fuzzy model results in a set of nonlinear constrained problems to be solved using a metaheuristics method. The applicability of our approach is illustrated through a flexible manufacturing cell. By adopting such framework, both dimensions of uncertainty in system modeling, expressed by stochastic variability and imprecision, can be taken into consideration

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

Uncertainty balance principle

The objective of this paper is to present new and simple mathematical approach to deal with uncertainty transformation for fuzzy to random or random to fuzzy data. In particular we present a method to describe fuzzy (possibilistic) distribution in terms of a pair (or more) of related random (probabilistic) events, both fixed and variable. Our approach uses basic properties of both fuzzy and random distributions, and it assumes data is both possibilistic and probabilistic. We show that the data fuzziness can be viewed as a non uniqueness of related random events, and prove our Uncertainty Balance Principle. We also show how Zadeh’s fuzzy-random Consistency Principle can be given precise mathematical meaning. Various types of fuzzy distributions are examined and several numerical examples presented