Vector valued information measures and integration with respect to fuzzy vector capacities

[EN] Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities. Bartle-Dunford-Schwartz integration (for the additive case) and Choquet type integration (for the non-additive case) are considered, showing that these formalisms can be used to define and develop vector-valued impact measures. Examples related to existing bibliometric tools as well as to new measuring indices are given.The authors would like to thank both Prof. Dr. Olvido Delgado and the referee for their valuable comments and suggestions which helped to prepare the manuscript. The first author gratefully acknowledges the support of the Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2016-77054-C2-1-P.Sánchez Pérez, EA.; Szwedek, R. (2019). Vector valued information measures and integration with respect to fuzzy vector capacities. Fuzzy Sets and Systems. 355:1-25. https://doi.org/10.1016/j.fss.2018.05.004S12535

Vector-valued impact measures and generation of specific indexes for research assessment

A mathematical structure for defining multi-valued bibliometric indices is provided with the aim of measuring the impact of general sources of information others than articles and journals-for example, repositories of datasets. The aim of the model is to use several scalar indices at the same time for giving a measure of the impact of a given source of information, that is, we construct vector valued indices. We use the properties of these vector valued indices in order to give a global answer to the problem of finding the optimal scalar index for measuring a particular aspect of the impact of an information source, depending on the criterion we want to fix for the evaluation of this impact. The main restrictions of our model are (1) it uses finite sets of scalar impact indices (altmetrics), and (2) these indices are assumed to be additive. The optimization procedure for finding the best tool for a fixed criterion is also presented. 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The use of fuzzy relations in the assessment of information resources producers' performance

Abstract. The producers assessment problem has many important practical instances: it is an abstract model for intelligent systems evaluating e.g. the quality of computer software repositories, web resources, social networking services, and digital libraries. Each producer's performance is determined according not only to the overall quality of the items he/she outputted, but also to the number of such items (which may be different for each agent). Recent theoretical results indicate that the use of aggregation operators in the process of ranking and evaluation producers may not necessarily lead to fair and plausible outcomes. Therefore, to overcome some weaknesses of the most often applied approach, in this preliminary study we encourage the use of a fuzzy preference relation-based setting and indicate why it may provide better control over the assessment process

Universal Prediction

In this thesis I investigate the theoretical possibility of a universal method of prediction. A prediction method is universal if it is always able to learn from data: if it is always able to extrapolate given data about past observations to maximally successful predictions about future observations. The context of this investigation is the broader philosophical question into the possibility of a formal specification of inductive or scientific reasoning, a question that also relates to modern-day speculation about a fully automatized data-driven science. I investigate, in particular, a proposed definition of a universal prediction method that goes back to Solomonoff (1964) and Levin (1970). This definition marks the birth of the theory of Kolmogorov complexity, and has a direct line to the information-theoretic approach in modern machine learning. Solomonoff's work was inspired by Carnap's program of inductive logic, and the more precise definition due to Levin can be seen as an explicit attempt to escape the diagonal argument that Putnam (1963) famously launched against the feasibility of Carnap's program. The Solomonoff-Levin definition essentially aims at a mixture of all possible prediction algorithms. An alternative interpretation is that the definition formalizes the idea that learning from data is equivalent to compressing data. In this guise, the definition is often presented as an implementation and even as a justification of Occam's razor, the principle that we should look for simple explanations. The conclusions of my investigation are negative. I show that the Solomonoff-Levin definition fails to unite two necessary conditions to count as a universal prediction method, as turns out be entailed by Putnam's original argument after all; and I argue that this indeed shows that no definition can. Moreover, I show that the suggested justification of Occam's razor does not work, and I argue that the relevant notion of simplicity as compressibility is already problematic itself

Universal Prediction

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ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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