Ryszard Szwarc

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This study examines the notion of inconsistency in pairwise comparisons for providing an axiomatization for it. It also proposes two inconsistency indicators for pairwise comparisons. The primary motivation for the inconsistency reduction is expressed by a computer industry concept " garbage in, garbage out ". The quality of the output depends on the(More)
Let µ denote a symmetric probability measure on [−1, 1] and let (p n) be the corresponding orthogonal polynomials normalized such that p n (1) = 1. We prove that the normalized Turán determinant ∆ n (x)/(1 − x 2), where ∆ n = p 2 n − p n−1 p n+1 , is a Turán determinant of order n − 1 for orthogonal polynomials with respect to (1 − x 2)dµ(x). We use this to(More)
Chain sequences are positive sequences fa n g of the form a n ¼ g n ð1 À g nÀ1 Þ for a nonnegative sequence fg n g: This concept has been introduced by Wall in connection with continued fractions. These sequences are very useful in determining the support of orthogonality measure for orthogonal polynomials. Equivalently, they can be used for localizing(More)
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