AHP and uncertainty theories for decision making using the ER-MCDA methodology

International audienceIn this paper, we present the ER-MCDA methodology for multi-criteria decision-making based on imperfect information coming from more or less reliable and conflicting sources. The Analytic Hierarchy Process (AHP), Fuzzy Sets, Possibility and Belief Functions theories are combined to take a decision based on imprecise and uncertain evaluations of quantitative, qualitative criteria. Classical aggregation of criteria is replaced by a two-step fusion process using advanced fusion rules based on the Dezert-Smarandache Theory (DSmT) that allows to make a difference between importance, reliability and uncertainty of information sources and contents

Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected Works), Vol. 4

The fourth volume on Advances and Applications of Dezert-Smarandache Theory (DSmT) for information fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics. The contributions (see List of Articles published in this book, at the end of the volume) have been published or presented after disseminating the third volume (2009, http://fs.unm.edu/DSmT-book3.pdf) in international conferences, seminars, workshops and journals. First Part of this book presents the theoretical advancement of DSmT, dealing with Belief functions, conditioning and deconditioning, Analytic Hierarchy Process, Decision Making, Multi-Criteria, evidence theory, combination rule, evidence distance, conflicting belief, sources of evidences with different importance and reliabilities, importance of sources, pignistic probability transformation, Qualitative reasoning under uncertainty, Imprecise belief structures, 2-Tuple linguistic label, Electre Tri Method, hierarchical proportional redistribution, basic belief assignment, subjective probability measure, Smarandache codification, neutrosophic logic, Evidence theory, outranking methods, Dempster-Shafer Theory, Bayes fusion rule, frequentist probability, mean square error, controlling factor, optimal assignment solution, data association, Transferable Belief Model, and others. More applications of DSmT have emerged in the past years since the apparition of the third book of DSmT 2009. Subsequently, the second part of this volume is about applications of DSmT in correlation with Electronic Support Measures, belief function, sensor networks, Ground Moving Target and Multiple target tracking, Vehicle-Born Improvised Explosive Device, Belief Interacting Multiple Model filter, seismic and acoustic sensor, Support Vector Machines, Alarm classification, ability of human visual system, Uncertainty Representation and Reasoning Evaluation Framework, Threat Assessment, Handwritten Signature Verification, Automatic Aircraft Recognition, Dynamic Data-Driven Application System, adjustment of secure communication trust analysis, and so on. Finally, the third part presents a List of References related with DSmT published or presented along the years since its inception in 2004, chronologically ordered

Sur la décombinaison de fonctions de croyance

International audienceThe evidence combination is a kind of decision-level information fusion in the theory of belief functions. Given two basic belief assignments (BBAs) originated from different sources, one can combine them using some combination rule, e.g., Dempster's rule to expect a better decision result. If one only has a combined BBA, how to determine the original two BBAs to combine? This can be considered as a defusion of information. This is useful, e.g., one can analyze the difference or dissimilarity between two different information sources based on the BBAs obtained using evidence decombination. Therefore, in this paper, we research on such a defusion in the theory of belief functions. We find that it is a well-posed problem if one original BBA and the combined BBA are both available, and it is an under-determined problem if both BBAs to combine are unknown. We propose an optimization-based approach for the evidence decombination according to the criteria of divergence maximization. Numerical examples are provided illustrate and verify our proposed decombination approach, which is expected to be used in applications such the difference analysis between information sources in information fusion systems when the original BBAs are discarded, and performance evaluation of combination rules

Generalized Ordered Propositions Fusion Based on Belief Entropy

A set of ordered propositions describe the different intensities of a characteristic of an object, the intensities increase or decrease gradually. A basic support function is a set of truth-values of ordered propositions, it includes the determinate part and indeterminate part. The indeterminate part of a basic support function indicates uncertainty about all ordered propositions. In this paper, we propose generalized ordered propositions by extending the basic support function for power set of ordered propositions. We also present the entropy which is a measure of uncertainty of a basic support function based on belief entropy. The fusion method of generalized ordered proposition also be presented. The generalized ordered propositions will be degenerated as the classical ordered propositions in that when the truth-values of non-single subsets of ordered propositions are zero. Some numerical examples are used to illustrate the efficiency of generalized ordered propositions and their fusion

Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected works), Vol. 2

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang

Decision Maps for Distributed Scenario-Based Multi-Criteria Decision Support

This thesis presents the Decision Map approach to support decision-makers facing complex uncertain problems that defy standardised solutions. First, scenarios are generated in a distributed manner: the reasoning processes can be adapted to the problem at hand whilst respecting constraints in time and availability of experts. Second, by integrating scenarios and MCDA, this approach facilitates robust decision-making respecting multiple criteria in a transparent well-structured manner

Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well