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This study provides a proof that the limit of a distance-based inconsistency reduction process is a matrix induced by the vector of geometric means of rows when a distance-based inconsistent pairwise comparisons matrix is transformed into a consistent PC matrix by stepwise inconsistency reduction in triads. The distance-based inconsistency indicator was defined by Koczkodaj (1993) for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof) and finally completed in 2010. However, there was no interpretation provided for the limit of convergence despite its considerable importance. This study also demonstrates that the vector of geometric means and the right principal eigenvector are linearly independent for the pairwise comparisons matrix size greater than three, although both vectors are identical (when normalized) for a consistent PC matrix of any size.
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Content available remote On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
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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 quality of the input.
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Content available remote A context aware framework for product based software certification
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In this paper, we propose a proof of concept context aware framework to facilitate product based software certification. The framework provides an applied environment for software certification by integrating tools such as Eclipse, Jena, OntoStudio, Protégé, Equinox, EMMA, log4j, RCP, JUnit, Jfeature and Apache Ant. It was developed within the Open Service Gateway initiative (OSGi) environment and is managed by a collection of automation scripts. The framework is intended for the certification of software which is developed with high level languages. We also propose a product based software certification process that is structured on component based certification principles and integrates current methodologies such as Integrated Component Maturity Model (ICMM), PECA framework (Plan the evaluation, Establish criteria, Collect data and Analyze data) and Goal Question Metric (GQM). Although the certification process is product based, the process also tries to be aligned with ISO JTC1 SC7, ISO IEC 25000, ISO 15939, ISO IEC 14598 and ISO 9126 standards. The general core of this certification process is composed of elements from a number of known software certification models. We tried to gather the benefits of other software certification models into a single model. At first every component is evaluated independently and then a global certificate level is computed which depends on the evaluation status of very component. The described software certification process addresses areas of the software certification which are known as magic steps.
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Content available remote Classifying Visual Objects with the Consistency-Driven Pairwise Comparisons Method
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The classification of the various image features or visual objects can be carried out by the consistency-driven pairwise comparisons method based on their relative importance. A key issue in the proposed approach is a weight-based synthesis for combining various image features. When compared with the traditional experience-based linear assignment method, the proposed approach is more effective and easy to communicate.
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This study demonstrates how a government procurement process could be improved by the pairwise comparisons method. A case study, related to assessment of project proposals is used for demonstration purpose. The project proposals were requested by a Canadian government agency to assess the environmental and public safety hazards of abandoned mines. However, the presented model is applicable (with easy-to-implement modifications) to any other case of government procurement.
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Random but visually nice shapes are often needed for cognitive experiments and processes. This study describes a heuristic for generating random but nice shapes. We call them placated shapes. These shapes are produced by applying the Gaussian blur to randomly generated polygons. Subsequently, the threshold is set to transform pixels to black and white from different shades of gray. This transformation produces placated shapes for easier estimation of areas. Randomly generated placated shapes are used for testing the accuracy of cognitive processes by pairwise comparisons. They can also be used in many other areas such as computer games or software testing. Such shapes could also be used for camouflaging heavy army equipment.
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The key issue of this study is synthesis of medical images and expert knowledge for early detection of a medical condition, such as stroke or cancer. Such synthesis is a missing link for making decisions during the diagnostic process. Knowledge mining in image databases can be enhanced by computing the relative importance of image features using pairwise comparisons. Computed weights can be systematically used for synthesis of various image features present in the same or different images.
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A medical knowledge-driven diagnostic process can be supported by AI methods as presented here by an Asperger Syndrome case study. Two methods: consistency-driven pairwise comparisons (CDPC) and automatic understanding (AU) are presented in this study. Deficiencies of a data-driven model for the medical diagnostic p rocess and clinical reasoning are also discussed.
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This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty’s Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only representation of PC. This study should be regarded as an interpretation and clarification of past investigations of PC. In addition, this article is a reflection on general PC research at a higher level of abstraction: the philosophy of science. It delves into the foundations and implications of pairwise comparisons. Some results of this study are based on a recently published work by Koczkodaj and Szwarc. Finally, open problems have also been reported for future research.
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