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105 results on '"CREDAL SETS"'

1. A Comparative Analysis of Aggregation Rules for Coherent Lower Previsions

Author

Salamanca, Juan J., Montes, Ignacio, Miranda, Enrique, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Ansari, Jonathan, editor, Fuchs, Sebastian, editor, Trutschnig, Wolfgang, editor, Lubiano, María Asunción, editor, Gil, María Ángeles, editor, Grzegorzewski, Przemyslaw, editor, and Hryniewicz, Olgierd, editor

Published
2024
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2. Aggregation of the Distortion Models Induced by the KL Divergence and Euclidean Distance

Author

Montes, Ignacio, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Ansari, Jonathan, editor, Fuchs, Sebastian, editor, Trutschnig, Wolfgang, editor, Lubiano, María Asunción, editor, Gil, María Ángeles, editor, Grzegorzewski, Przemyslaw, editor, and Hryniewicz, Olgierd, editor

Published
2024
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3. Semi-supervised Learning Guided by the Generalized Bayes Rule Under Soft Revision

Author

Dietrich, Stefan, Rodemann, Julian, Jansen, Christoph, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Ansari, Jonathan, editor, Fuchs, Sebastian, editor, Trutschnig, Wolfgang, editor, Lubiano, María Asunción, editor, Gil, María Ángeles, editor, Grzegorzewski, Przemyslaw, editor, and Hryniewicz, Olgierd, editor

Published
2024
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4. A Novel Bayes’ Theorem for Upper Probabilities

Author

Caprio, Michele, Sale, Yusuf, Hüllermeier, Eyke, Lee, Insup, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Cuzzolin, Fabio, editor, and Sultana, Maryam, editor

Published
2024
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6. Necessary and Possibly Optimal Items in Selecting Problems

Author

Destercke, Sébastien, Guillaume, Romain, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Ciucci, Davide, editor, Couso, Inés, editor, Medina, Jesús, editor, Ślęzak, Dominik, editor, Petturiti, Davide, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2022
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7. Centroids of Credal Sets: A Comparative Study

Author

Miranda, Enrique, Montes, Ignacio, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Vejnarová, Jiřina, editor, and Wilson, Nic, editor

Published
2021
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8. Nonlinear desirability theory.

Author

Miranda, Enrique and Zaffalon, Marco

Subjects
*NONLINEAR theories, *EXPECTED utility, *SET theory, *REWARD (Psychology), *PRICES, *FOUNDING, *DECISION theory
Abstract

Desirability can be understood as an extension of Anscombe and Aumann's Bayesian decision theory to sets of expected utilities. At the core of desirability lies an assumption of linearity of the scale in which rewards are measured. It is a traditional assumption used to derive the expected utility model, which clashes with a general representation of rational decision making, though. Allais has, in particular, pointed this out in 1953 with his famous paradox. We note that the utility scale plays the role of a closure operator when we regard desirability as a logical theory. This observation enables us to extend desirability to the nonlinear case by letting the utility scale be represented via a general closure operator. The new theory directly expresses rewards in actual nonlinear currency (money), much in Savage's spirit, while arguably weakening the founding assumptions to a minimum. We characterise the main properties of the new theory both from the perspective of sets of gambles and of their lower and upper prices (previsions). We show how Allais paradox finds a solution in the new theory, and discuss the role of sets of probabilities in the theory. [ABSTRACT FROM AUTHOR]

Published
2023
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9. A Study of the Set of Probability Measures Compatible with Comparative Judgements

Author

Erreygers, Alexander, Miranda, Enrique, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Lesot, Marie-Jeanne, editor, Vieira, Susana, editor, Reformat, Marek Z., editor, Carvalho, João Paulo, editor, Wilbik, Anna, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2020
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10. Metrical Approach to Measuring Uncertainty

Author

Bronevich, Andrey G., Rozenberg, Igor N., Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Lesot, Marie-Jeanne, editor, Vieira, Susana, editor, Reformat, Marek Z., editor, Carvalho, João Paulo, editor, Wilbik, Anna, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2020
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11. Imprecise Probabilities

Author

Bradley, Seamus, Birta, Louis G., Series Editor, Crosbie, Roy E., Advisory Editor, Jakeman, Tony, Advisory Editor, Lehmann, Axel, Advisory Editor, Robinson, Stewart, Advisory Editor, Tolk, Andreas, Advisory Editor, Zeigler, Bernard P., Advisory Editor, Beisbart, Claus, editor, and Saam, Nicole J., editor

Published
2019
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12. An Imprecise Probability Approach for Abstract Argumentation Based on Credal Sets

Author

Morveli-Espinoza, Mariela, Nieves, Juan Carlos, Tacla, Cesar Augusto, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Kern-Isberner, Gabriele, editor, and Ognjanović, Zoran, editor

Published
2019
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13. Credal C4.5 with Refinement of Parameters

Author

Mantas, Carlos J., Abellán, Joaquín, Castellano, Javier G., Cano, José R., Moral, Serafín, Barbosa, Simone Diniz Junqueira, Series Editor, Chen, Phoebe, Series Editor, Filipe, Joaquim, Series Editor, Kotenko, Igor, Series Editor, Sivalingam, Krishna M., Series Editor, Washio, Takashi, Series Editor, Yuan, Junsong, Series Editor, Zhou, Lizhu, Series Editor, Medina, Jesús, editor, Ojeda-Aciego, Manuel, editor, Verdegay, José Luis, editor, Perfilieva, Irina, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2018
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14. Imprecise Sampling Models for Modelling Unobserved Heterogeneity? Basic Ideas of a Credal Likelihood Concept

Author

Augustin, Thomas, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Ciucci, Davide, editor, Pasi, Gabriella, editor, and Vantaggi, Barbara, editor

Published
2018
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15. Uncertainty-based information measures on the approximate non-parametric predictive inference model.

Author

Moral-García, Serafín and Abellán, Joaquín

Subjects
*PREDICTION models, *INFORMATION measurement, *UNCERTAINTY
Abstract

The Non-Parametric Predictive Inference Model for Multinomial Data (NPI-M) is an imprecise probabilities model used to represent the available information about a categorical variable. It presents some advantages over another imprecise probabilities model frequently used in the literature called Imprecise Dirichlet Model (IDM), which assumes previous knowledge about the data through a parameter. The Approximate Non-Parametric Predictive Inference Model for Multinomial Data (A-NPI-M) is a model similar to the NPI-M that can be expressed by reachable sets of probability intervals, is easier to manage, and is non-parametric. As a novelty, in this work, we analyze the main properties of A-NPI-M credal sets, comparing them with the properties of credal sets associated with the IDM. Moreover, we present procedures to calculate the most important uncertainty measures on A-NPI-M credal sets. Those procedures represent useful tools to make the A-NPI-M very suitable to be used in practical applications. [ABSTRACT FROM AUTHOR]

Published
2021
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16. Graphoid properties of concepts of independence for sets of probabilities.

Author

Cozman, Fabio Gagliardi

Subjects
*INDEPENDENCE (Mathematics), *PROBABILITY measures, *PROBABILITY theory, *CONDITIONAL probability, *CONCEPTS
Abstract

We examine several concepts of independence associated with (1) credal sets, understood as sets of probability measures, (2) sets of full conditional probabilities, (3) sets of lexicographic probabilities, and (4) sets of desirable gambles. Concepts of independence are evaluated with respect to the graphoid properties they satisfy, as these properties capture important abstract features of "independence". We emphasize the analysis of sets of probability measures as this is a popular formalism, looking at versions of epistemic, confirmational, and type-5 independence that are based on regular conditioning, as well as complete and strong independence. We then examine analogous concepts of independence for sets of full conditional probabilities, sets of lexicographic probabilities, and sets of desirable gambles. [ABSTRACT FROM AUTHOR]

Published
2021
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17. Credal sets representable by reachable probability intervals and belief functions.

Author

Moral-García, Serafín and Abellán, Joaquín

Subjects
*DEMPSTER-Shafer theory
Abstract

Belief functions and reachable probability intervals are theories based on imprecise probabilities that generalize classical probability theory. On the one hand, belief functions have been commonly used to deal with uncertainty and in the combination of information provided by different sources. On the other hand, reachable probability intervals have high expressive power, are easy to manage, and can be efficiently computed. Belief functions are not generalizations of reachable probability intervals, and the converse is also not verified. In this work, we study under which conditions a reachable set of probability intervals is associated with a belief function, as well as the properties that a belief function has to satisfy to be representable by a reachable set of probability intervals. [ABSTRACT FROM AUTHOR]

Published
2021
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18. The joy of Probabilistic Answer Set Programming: Semantics, complexity, expressivity, inference.

Author

Cozman, Fabio Gagliardi and Mauá, Denis Deratani

Subjects
*SELF-expression, *ALGORITHMS, *JOY, *LOGIC programming, *SEMANTICS
Abstract

Probabilistic Answer Set Programming (PASP) combines rules, facts, and independent probabilistic facts. We argue that a very useful modeling paradigm is obtained by adopting a particular semantics for PASP, where one associates a credal set with each consistent program. We examine the basic properties of PASP under this credal semantics, in particular presenting novel results on its complexity and its expressivity, and we introduce an inference algorithm to compute (upper) probabilities given a program. [ABSTRACT FROM AUTHOR]

Published
2020
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19. Tractable inference in credal sentential decision diagrams.

Author

Mattei, Lilith, Antonucci, Alessandro, Mauá, Denis Deratani, Facchini, Alessandro, and Villanueva Llerena, Julissa

Subjects
*ALGORITHMS, *CHARTS, diagrams, etc., *LOGIC circuits, *CIRCUIT complexity, *BOOLEAN functions, *LINEAR programming
Abstract

Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually "learned" from a set of observations. This leads to overconfident and prior-dependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams , a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (so-called credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models. These allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables; (ii) the lower and upper conditional probabilities for the state of a single variable given an observation; (iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable , as all the three algorithms, based on bottom-up traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. The first algorithm is always exact, while the remaining two might induce a conservative (outer) approximation in the case of multiply connected circuits. A semantics for this approximation together with an auxiliary algorithm able to decide whether or not the result is exact is also provided together with a brute-force characterization of the exact inference in these cases. For a first empirical validation, we consider a simple application based on noisy seven-segment display images. The credal models are observed to properly distinguish between easy and hard-to-detect instances and outperform other generative models not able to cope with logical constraints. [ABSTRACT FROM AUTHOR]

Published
2020
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20. A comparison of random forest based algorithms: random credal random forest versus oblique random forest.

Author

Mantas, Carlos J., Castellano, Javier G., Moral-García, Serafín, and Abellán, Joaquín

Subjects
*RANDOM forest algorithms, *DECISION trees, *PROCESS optimization
Abstract

Random forest (RF) is an ensemble learning method, and it is considered a reference due to its excellent performance. Several improvements in RF have been published. A kind of improvement for the RF algorithm is based on the use of multivariate decision trees with local optimization process (oblique RF). Another type of improvement is to provide additional diversity for the univariate decision trees by means of the use of imprecise probabilities (random credal random forest, RCRF). The aim of this work is to compare experimentally these improvements of the RF algorithm. It is shown that the improvement in RF with the use of additional diversity and imprecise probabilities achieves better results than the use of RF with multivariate decision trees. [ABSTRACT FROM AUTHOR]

Published
2019
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22. Multilabel Prediction with Probability Sets: The Hamming Loss Case

Author

Destercke, Sebastien, Junqueira Barbosa, Simone Diniz, editor, Chen, Phoebe, editor, Cuzzocrea, Alfredo, editor, Du, Xiaoyong, editor, Filipe, Joaquim, editor, Kara, Orhun, editor, Kotenko, Igor, editor, Sivalingam, Krishna M., editor, Ślęzak, Dominik, editor, Washio, Takashi, editor, Yang, Xiaokang, editor, Laurent, Anne, editor, Strauss, Olivier, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2014
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23. Decision Making with Hierarchical Credal Sets

Author

Antonucci, Alessandro, Karlsson, Alexander, Sundgren, David, Junqueira Barbosa, Simone Diniz, editor, Chen, Phoebe, editor, Cuzzocrea, Alfredo, editor, Du, Xiaoyong, editor, Filipe, Joaquim, editor, Kara, Orhun, editor, Kotenko, Igor, editor, Sivalingam, Krishna M., editor, Ślęzak, Dominik, editor, Washio, Takashi, editor, Yang, Xiaokang, editor, Laurent, Anne, editor, Strauss, Oliver, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2014
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24. Evidential Combination Operators for Entrapment Prediction in Advanced Driver Assistance Systems

Author

Karlsson, Alexander, Dahlbom, Anders, Zhong, Hui, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Kobsa, Alfred, editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Tanaka, Yuzuru, editor, Wahlster, Wolfgang, editor, Siekmann, Jörg, editor, Andreasen, Troels, editor, Christiansen, Henning, editor, Cubero, Juan-Carlos, editor, and Raś, Zbigniew W., editor

Published
2014
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25. Extreme Points of the Credal Sets Generated by Elementary Comparative Probabilities

Author

Miranda, Enrique, Destercke, Sébastien, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, and van der Gaag, Linda C., editor

Published
2013
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28. Independence and 2-Monotonicity: Nice to Have, Hard to Keep

Author

Destercke, Sebastien, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, and Liu, Weiru, editor

Published
2011
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31. Credal Sets Approximation by Lower Probabilities: Application to Credal Networks

Author

Antonucci, Alessandro, Cuzzolin, Fabio, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Hüllermeier, Eyke, editor, Kruse, Rudolf, editor, and Hoffmann, Frank, editor

Published
2010
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32. Extreme Points of the Core of Possibility Measures and Maxitive p-Boxes.

Author

Montes, Ignacio and Miranda, Enrique

Subjects
*EPISTEMIC logic, *DEMPSTER-Shafer theory, *PROBABILITY measures, *CUMULATIVE distribution function, *VARIATE difference method
Abstract

Under an epistemic interpretation, an upper probability can be regarded as equivalent to the set of probability measures it dominates, sometimes referred to as its core. In this paper, we study the properties of the number of extreme points of the core of a possibility measure, and investigate in detail those associated with (uni- and bi-)variate p-boxes, that model the imprecise information about a cumulative distribution function. [ABSTRACT FROM AUTHOR]

Published
2018
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33. An Experimental Study about Simple Decision Trees for Bagging Ensemble on Datasets with Classification Noise

Author

Abellán, Joaquín, Masegosa, Andrés R., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Sossai, Claudio, editor, and Chemello, Gaetano, editor

Published
2009
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34. Pari-mutuel probabilities as an uncertainty model.

Author

Montes, Ignacio, Miranda, Enrique, and Destercke, Sébastien

Subjects
*PROBABILITY theory, *UNCERTAINTY (Information theory), *MATHEMATICAL models, *SET theory, *MATHEMATICAL functions
Abstract

Highlights • We prove some properties of the Pari Mutuel Model as a coherent lower (and upper) probability. • We show that a Pari Mutuel Model is a particular case of a probability interval. • We give the maximal number of extreme points of the credal set associated with a Pari Mutuel Model and we give the form of those extreme points. • We give sufficient and necessary conditions for the Pari Mutuel Model to induce a belief function. • We show how to merge information given in terms of Pari Mutuel Models. Abstract The pari-mutuel model is a betting scheme that has its origins in horse racing, and that has been applied in a number of contexts, mostly economics. In this paper, we consider the set of probability measures compatible with a pari-mutuel model, characterize its extreme points, and investigate the properties of the associated lower and upper probabilities. We show that the pari-mutuel model can be embedded within the theory of probability intervals, and prove necessary and sufficient conditions for it to be a belief function or a minitive measure. In addition, we also investigate the combination of different pari-mutuel models and their definition on product spaces. [ABSTRACT FROM AUTHOR]

Published
2019
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36. A power-flow emulator approach for resilience assessment of repairable power grids subject to weather-induced failures and data deficiency.

Author

Rocchetta, Roberto, Zio, Enrico, and Patelli, Edoardo

Subjects
*ELECTRIC power distribution grids, *PREDICATE calculus, *STOCHASTIC models, *EMULATION software, *SENSITIVITY analysis
Abstract

A generalised uncertainty quantification framework for resilience assessment of weather-coupled, repairable power grids is presented. The framework can be used to efficiently quantify both epistemic and aleatory uncertainty affecting grid-related and weather-related factors. The power grid simulator has been specifically designed to model interactions between severe weather conditions and grid dynamic states and behaviours, such as weather-induced failures or delays in components replacements. A resilience index is computed by adopting a novel algorithm which exploits a vectorised emulator of the power-flow solver to reduce the computational efforts. The resilience stochastic modelling framework is embedded into a non-intrusive generalised stochastic framework, which enables the analyst to quantify the effect of parameters imprecision. A modified version of the IEEE 24 nodes reliability test system has been used as representative case study. The surrogate-based model and the Power-Flow-based model are compared, and the results show similar accuracy but enhanced efficiency of the former. Global sensitivity of the resilience index to increasing imprecision in parameters of the probabilistic model has been analysed. The relevance of specific weather/grid uncertain factors is highlighted by global sensitivity analysis and the importance of dealing with imprecision in the information clearly emerges. [ABSTRACT FROM AUTHOR]

Published
2018
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37. Some Characteristics of Credal Sets and Their Application to Analysis of Polls Results.

Author

Bronevich, Andrey G. and Spiridenkova, Natalia S.

Subjects
PROBABILITY theory, PUBLIC opinion polls, VOTING, SET theory, MATHEMATICAL models of uncertainty, MATHEMATICAL models
Abstract

In the theory of imprecise probabilities there are well established functionals for measuring uncertainty. Meanwhile, when we try to apply them to real problems they have a lack of meaningful interpretation. In this investigation we propose some characteristics of credal sets that seem to be useful for analyzing polls results. [ABSTRACT FROM AUTHOR]

Published
2017
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38. Evenly convex credal sets.

Author

Cozman, Fabio Gagliardi

Subjects
*AXIOMS, *CONVEX sets, *PROBABILITY theory, *INTERSECTION theory, *ARCHIMEDEAN property
Abstract

Abstract An evenly convex credal set is a set of probability measures that is evenly convex; that is, a set that is an arbitrary intersection of open halfspaces. An evenly convex credal set can for instance encode preference judgments through strict and non-strict inequalities such as P (A) > 1 / 2 and P (A) ≤ 2 / 3. This paper presents an axiomatization of evenly convex sets from preferences, where we introduce a new (and very weak) Archimedean condition. We examine the duality between preference orderings and credal sets; we also consider assessments of almost preference and natural extensions. We then discuss regular conditioning, a concept that is closely related to evenly convex sets. Highlights • A set of axioms is presented for evenly convex credal sets. • An evenly convex set is an intersection of arbitrarily many open halfspaces; a credal set is a set of probability measures. • Axioms show how preference orderings can be represented by evenly convex credal sets. • Axioms include irreflexivity, transitivity, cancellation, monotonicity, and a new Archimedean condition. • Paper discusses duality, natural extensions, regular conditioning. [ABSTRACT FROM AUTHOR]

Published
2018
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39. Compositional models for credal sets.

Author

Vejnarová, Jiřina

Subjects
*PROBABILITY theory, *MATHEMATICAL models, *SET theory, *SYSTEMS theory, *MATHEMATICS
Abstract

We present the composition operator, already known from probability, possibility, evidence and valuation-based systems theories, for credal sets. We prove that the proposed definition preserves all the properties enabling us to design compositional models in a way analogous to those in the above-mentioned theories. A special kind of compositional models, the so-called perfect sequences of credal sets, is studied in more detail and (among others) its relationship to perfect sequences of probability distributions is revealed. The theoretical results are illustrated by numerous simple examples. [ABSTRACT FROM AUTHOR]

Published
2017
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40. Software project risk analysis based on extended influence diagrams.

Author

Ruiping Yuan, Bingwu Liu, and Jiansheng Zhang

Abstract

An extended influence diagram is proposed according to the characteristics of software project risks. Sub-model nodes are added to the topology level while credal sets are used in the parameter level to present imprecise probabilities. Then, software project risk influence diagrams are defined. Finally, an example is given to illustrate the process of risk analysis using extended influence diagrams. Case results indicate that extended influence diagrams are easy to be built and they performs well in predicting software project risks. [ABSTRACT FROM PUBLISHER]

Published
2012
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41. Extreme points of the credal sets generated by comparative probabilities.

Author

Miranda, Enrique and Destercke, Sébastien

Subjects
*SET theory, *PROBABILITY theory, *COMPARATIVE studies, *COMPUTATIONAL complexity, *ALGORITHMS, *UNCERTAINTY
Abstract

When using convex probability sets (or, equivalently, lower previsions) as uncertainty models, identifying extreme points can help simplifying various computations or the use of some algorithms. In general, sets induced by specific models such as possibility distributions, linear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this paper, we study extreme points of another specific model: comparative probability orderings between the singletons of a finite space. We characterize these extreme points by means of a graphical representation of the comparative model, and use them to study the properties of the lower probability induced by this set. By doing so, we show that 2-monotone capacities are not informative enough to handle this type of comparisons without a loss of information. In addition, we connect comparative probabilities with other uncertainty models, such as imprecise probability masses. [ABSTRACT FROM AUTHOR]

Published
2015
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42. Ensembles of decision trees based on imprecise probabilities and uncertainty measures.

Author

Abellán, Joaquín

Subjects
*DECISION trees, *PROBABILITY theory, *UNCERTAINTY (Information theory), *INFORMATION measurement, *COMPARATIVE studies, *MATHEMATICAL variables
Abstract

Abstract: In this paper, we present an experimental comparison among different strategies for combining decision trees built by means of imprecise probabilities and uncertainty measures. It has been proven that the combination or fusion of the information obtained from several classifiers can improve the final process of the classification. We use previously developed schemes, known as Bagging and Boosting, along with a new one based on the variation of the root node via the information rank of each feature of the class variable. To this end, we applied two different approaches to deal with missing data and continuous variables. We use a set of tests on the performance of the methods analyzed here, to show that, with the appropriate approach, the Boosting scheme constitutes an excellent way to combine this type of decision tree. It should be noted that it provides good results, even compared with a standard Random Forest classifier, a successful procedure very commonly used in the literature. [Copyright &y& Elsevier]

Published
2013
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43. Equivalence relations among dominance concepts on probability intervals and general credal sets.

Author

Abellán, Joaquín

Subjects
*PROBABILITY theory, *DECISION making, *SET theory, *STATISTICAL correlation, *MATHEMATICAL combinations
Abstract

Probability intervals constitute a useful tool for representing uncertain knowledge. They present high computational efficiency. If a set of probability intervals is used to represent the available information, the concept of dominance can play an important role in the decision-taking process. In this paper, we present the equivalence relations among three dominance concepts when the set of probability intervals used is obtained from a general credal set or from a reachable set of probability intervals; these are the two models of imprecise probabilities, the first being more general than the second. These three concepts of dominance present the common characteristic of having been used in the final process of a classifier. [ABSTRACT FROM AUTHOR]

Published
2012
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44. Uncertainty measures on probability intervals from the imprecise Dirichlet model.

Author

Abellán, J.

Subjects
*MATHEMATICAL models, *DISTRIBUTION (Probability theory), *CONVEX sets, *SET theory, *SIMULATION methods & models, *SYSTEMS theory
Abstract

When we use a mathematical model to represent information, we can obtain a closed and convex set of probability distributions, also called a credal set. This type of representation involves two types of uncertainty called conflict (or randomness) and non-specificity, respectively. The imprecise Dirichlet model (IDM) allows us to carry out inference about the probability distribution of a categorical variable obtaining a Set of a special type of credal set (probability intervals). In this paper, we shall present tools for obtaining the uncertainty functions on probability intervals obtained with the IDM, which can enable these functions in any application of this model to be calculated. [ABSTRACT FROM AUTHOR]

Published
2006
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45. Measures of divergence on credal sets

Author

Abellán, Joaquín and Gómez, Manuel

Subjects
*MATHEMATICAL logic, *SET theory, *MATHEMATICAL variables, *PROBABILITY theory
Abstract

Abstract: When there is uncertainty about the values of a variable, it is possible to have different pieces of information about it. This can be due to the fact that they represent the points of view of different agents and these agents have followed different criteria when codify the pieces of information by means of numbers. The aim of this paper is to provide tools for the comparison of these representations. This is done in the framework of imprecise probabilities, more concretely the credal set theory is used. The reason is that credal sets are very general, including as particular cases possibility theory, probability theory and belief functions. So it can serve as basis to compare the representations of information obtained by following these formalisms. The measures used for comparison are: inconsistency measure, inclusion index and informative distance. [Copyright &y& Elsevier]

Published
2006
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46. AN ALGORITHM TO COMPUTE THE UPPER ENTROPY FOR ORDER-2 CAPACITIES.

Author

ABELLÁN, JOAQUIN and MORAL, SERAFIN

Subjects
*ENTROPY (Information theory), *ALGORITHMS, *PROBABILITY theory, *MATHEMATICAL functions, *INFORMATION theory
Abstract

The upper entropy of a credal set is the maximum of the entropies of the probabilities belonging to it. Although there are algorithms for computing the upper entropy for the particular cases of credal sets associated to belief functions and probability intervals, there is none for a more general model. In this paper, we shall present an algorithm to obtain the upper entropy for order-2 capacities. Our algorithm is an extension of the one presented for belief functions, and proofs of correctness are provided. By using a counterexample, we shall also prove that this algorithm is not valid for general lower probabilities as it computes a value which is strictly greater than the maximum of entropy. [ABSTRACT FROM AUTHOR]

Published
2006

47. Additivity of uncertainty measures on credal sets.

Author

Abellán, Joaquín and Klir, George J.

Subjects
*PROBABILITY theory, *DISTRIBUTION (Probability theory), *CONVEX sets, *UNCERTAINTY (Information theory), *INDEPENDENCE (Mathematics)
Abstract

A general way of representing incomplete information is to use closed and convex sets of probability distributions, which are also called credal sets. Each credal set is associated with uncertainty, whose amount is quantified by an appropriate uncertainty measure. One of the requisite properties of uncertainty measures is the property of additivity, which is associated with the concept of independence. For credal sets, the concept of independence is not unique. This means that different definitions of independence lead to different definitions of additivity for uncertainty measures. In this paper, we compare the various definitions of independence, but our principal aim is to analyze those definitions that are employed in the most significant uncertainty measures established in the literature for credal sets. [ABSTRACT FROM AUTHOR]

Published
2005
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48. Difference of entropies as a non-specificity function on credal sets.

Author

Abellán, Joaquín and Moral ‡, Serafín

Subjects
*ALGORITHMS, *SYSTEMS engineering, *SYSTEMS theory, *ENTROPY (Information theory), *INFORMATION storage & retrieval systems
Abstract

This paper proposes the use of the maximum difference of entropies as a non-specificity measure for credal sets and studies its properties. The main advantage of the new measure is that it does not only take into account the absolute imprecision of the credal set, but also the position of the credal set with respect to the uniform distribution. The paper provides an algorithm to compute the most difficult part of the difference of entropies, the minimum of entropy. The algorithm computes the exact minimum of entropy for order-2 capacities and it is based on the branch and bound technique with some additional procedures to prune the search. [ABSTRACT FROM AUTHOR]

Published
2005
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49. A study of the set of probability measures compatible with comparative judgements

Author

Enrique Miranda and Alexander Erreygers

Subjects
Structure (mathematical logic), Technology and Engineering, Extreme points, Comparative probability, Computer science, 05 social sciences, Sets of desirable gambles, Space (mathematics), Comparative probabilities, 050105 experimental psychology, Article, Set (abstract data type), 03 medical and health sciences, 0302 clinical medicine, Mathematics and Statistics, Credal sets, Lower previsions, 0501 psychology and cognitive sciences, Extreme point, Representation (mathematics), Mathematical economics, 030217 neurology & neurosurgery, Probability measure
Abstract

We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to Walley’s behavioural theory of imprecise probabilities, and introduce a graphical representation that allows us to bound, and in some cases determine, the extreme points of the set of compatible measures. In doing this, we generalise some earlier work by Miranda and Destercke on elementary comparisons.

Published
2020

50. MAXIMUM OF ENTROPY FOR CREDAL SETS.

Author

Abellan, Joaquin and Moral, Serafin

Subjects
*SET theory, *FUZZY sets, *FUZZY systems, *PROBABILITY theory, *MATHEMATICS, *UNCERTAINTY (Information theory)
Abstract

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals. [ABSTRACT FROM AUTHOR]

Published
2003
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