Commutative POVMs and Fuzzy Observables

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.Comment: Contribution to the Pekka Lahti Festschrif

Three Dimensional Quantum Geometry and Deformed Poincare Symmetry

We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We generalize to the deformed case the construction of the flat Euclidean space as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra of functions becomes the non-commutative algebra of SU(2) distributions endowed with the convolution product. This construction gives the action of ISU(2) on the algebra and allows the determination of plane waves and coordinate functions. In particular, we show that: (i) plane waves have bounded momenta; (ii) to a given momentum are associated several SU(2) elements leading to an effective description of an element in the algebra in terms of several physical scalar fields; (iii) their product leads to a deformed addition rule of momenta consistent with the bound on the spectrum. We generalize to the non-commutative setting the local action for a scalar field. Finally, we obtain, using harmonic analysis, another useful description of the algebra as the direct sum of the algebra of matrices. The algebra of matrices inherits the action of ISU(2): rotations leave the order of the matrices invariant whereas translations change the order in a way we explicitly determine.Comment: latex, 37 page

Exploring fuzzy cognitive mapping for IS evaluation: A research note

Existing IS Evaluation (ISE) techniques tend to focus on modeling individuals, teams, organization, or systems, in relation to process and environmental boundaries. Whilst such approaches are noteworthy and of merit, they do not necessarily provide insights into those causal interdependencies that are inherent within decision-making task. As has been noted by the extant literature in the field, the ISE task is dependent upon many factors – the resulting outputs of which may be tangible or intangible. The implicit level of uncertainty associated with modeling such decision-making tasks and behaviors, are therefore difficult to comprehend and impart via wholly Quantitative and / or Qualitative analyses. The authors therefore present and propose supporting and on-going research into the application of Fuzzy Logic, in the guise of Fuzzy Cognitive Mapping (FCM) simulations, as a means to model tangible/intangible aspects of the ISE decision-making task. Such a Fuzzy Information Systems Evaluation (F-ISE) is shown via the application of the FCM technique, in terms of three models of investment appraisal that are aligned to an ISE task within a UK manufacturing organization. In doing so, it is anticipated that such a technique may be a useful addition to the plethora of ISE techniques available to both researcher and practitioner alike

Knowledge discovery for friction stir welding via data driven approaches: Part 2 – multiobjective modelling using fuzzy rule based systems

In this final part of this extensive study, a new systematic data-driven fuzzy modelling approach has been developed, taking into account both the modelling accuracy and its interpretability (transparency) as attributes. For the first time, a data-driven modelling framework has been proposed designed and implemented in order to model the intricate FSW behaviours relating to AA5083 aluminium alloy, consisting of the grain size, mechanical properties, as well as internal process properties. As a result, ‘Pareto-optimal’ predictive models have been successfully elicited which, through validations on real data for the aluminium alloy AA5083, have been shown to be accurate, transparent and generic despite the conservative number of data points used for model training and testing. Compared with analytically based methods, the proposed data-driven modelling approach provides a more effective way to construct prediction models for FSW when there is an apparent lack of fundamental process knowledge