Power law cumulative frequency (P) versus event size (l) distributions P > or =l) approximately l(-alpha) are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scale...

The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow \gamma^*/{Z^{0}}^*$ in leading logarithmic approximation $O(\alpha^6 L^6)$ extending known up $O(\alpha^2 L^2)$ analytic form. We use method of massive on-shell operator matrix elements and present radiators both Mellin-$N$ momentum fraction $z$-space. Numerical results presented various e...

The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow \gamma^*/{Z^{0}}^*$ in leading logarithmic approximation $O(\alpha^6 L^6)$ extending known up $O(\alpha^2 L^2)$ analytic form. We use method of massive on-shell operator matrix elements and present radiators both Mellin-$N$ momentum fraction $z$-space. Numerical results presented various e...

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cu...

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This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...

This paper introduces a new concept within shadow segmentation for usage in shadow removal and augmentation through construction of an alpha overlay shadow model. Previously, an image was considered to consist of shadow and non-shadow regions. We construct a model that accounts for sunlit, umbra and penumbra regions. The model is based on theories about color constancy, daylight, and the geomet...

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of homogenous Decision Making Units (DMUs) with multiple inputs and multiple outputs. These factors may be evaluated in fuzzy or stochastic environment. Hence, the classic structures of DEA model may be changed where in two fold fuzzy stochastic environment. For instances, linearity, feasibility a...