890 research outputs found

    An analysis of possible applications of fuzzy set theory to the actuarial credibility theory

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    In this work, we review the basic concepts of actuarial credibility theory from the point of view of introducing applications of the fuzzy set-theoretic method. We show how the concept of actuarial credibility can be modeled through the fuzzy set membership functions and how fuzzy set methods, especially fuzzy pattern recognition, can provide an alternative tool for estimating credibility

    Quantum image classification using principal component analysis

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    We present a novel quantum algorithm for classification of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. In order to apply the algorithm we present a new quantum representation of grayscale images.Comment: 9 page

    Cauchy's functional equation and extensions: Goldie's equation and inequality, the Go{\l}\k{a}b-Schinzel equation and Beurling's equation

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    The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its counterpart in Beurling regular variation, together with the related Go{\l}\k{a}b-Schinzel equation.Comment: Companion paper to: Additivity, subadditivity and linearity: automatic continuity and quantifier weakenin
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