Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

Synergies between machine learning and reasoning - An introduction by the Kay R. Amel group

This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developed quite separately in the last four decades. First, some common concerns are identified and discussed such as the types of representation used, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then, the survey is organised in seven sections covering most of the territory where KRR and ML meet. We start with a section dealing with prototypical approaches from the literature on learning and reasoning: Inductive Logic Programming, Statistical Relational Learning, and Neurosymbolic AI, where ideas from rule-based reasoning are combined with ML. Then we focus on the use of various forms of background knowledge in learning, ranging from additional regularisation terms in loss functions, to the problem of aligning symbolic and vector space representations, or the use of knowledge graphs for learning. Then, the next section describes how KRR notions may benefit to learning tasks. For instance, constraints can be used as in declarative data mining for influencing the learned patterns; or semantic features are exploited in low-shot learning to compensate for the lack of data; or yet we can take advantage of analogies for learning purposes. Conversely, another section investigates how ML methods may serve KRR goals. For instance, one may learn special kinds of rules such as default rules, fuzzy rules or threshold rules, or special types of information such as constraints, or preferences. The section also covers formal concept analysis and rough sets-based methods. Yet another section reviews various interactions between Automated Reasoning and ML, such as the use of ML methods in SAT solving to make reasoning faster. Then a section deals with works related to model accountability, including explainability and interpretability, fairness and robustness. Finally, a section covers works on handling imperfect or incomplete data, including the problem of learning from uncertain or coarse data, the use of belief functions for regression, a revision-based view of the EM algorithm, the use of possibility theory in statistics, or the learning of imprecise models. This paper thus aims at a better mutual understanding of research in KRR and ML, and how they can cooperate. The paper is completed by an abundant bibliography

Decision making study: methods and applications of evidential reasoning and judgment analysis

Decision making study has been the multi-disciplinary research involving operations researchers, management scientists, statisticians, mathematical psychologists and economists as well as others. This study aims to investigate the theory and methodology of decision making research and apply them to different contexts in real cases. The study has reviewed the literature of Multiple Criteria Decision Making (MCDM), Evidential Reasoning (ER) approach, Naturalistic Decision Making (NDM) movement, Social Judgment Theory (SJT), and Adaptive Toolbox (AT) program. On the basis of these literatures, two methods, Evidence-based Trade-Off (EBTO) and Judgment Analysis with Heuristic Modelling (JA-HM), have been proposed and developed to accomplish decision making problems under different conditions. In the EBTO method, we propose a novel framework to aid people s decision making under uncertainty and imprecise goal. Under the framework, the imprecise goal is objectively modelled through an analytical structure, and is independent of the task requirement; the task requirement is specified by the trade-off strategy among criteria of the analytical structure through an importance weighting process, and is subject to the requirement change of a particular decision making task; the evidence available, that could contribute to the evaluation of general performance of the decision alternatives, are formulated with belief structures which are capable of capturing various format of uncertainties that arise from the absence of data, incomplete information and subjective judgments. The EBTO method was further applied in a case study of Soldier system decision making. The application has demonstrated that EBTO, as a tool, is able to provide a holistic analysis regarding the requirements of Soldier missions, the physical conditions of Soldiers, and the capability of their equipment and weapon systems, which is critical in domain. By drawing the cross-disciplinary literature from NDM and AT, the JA-HM extended the traditional Judgment Analysis (JA) method, through a number of novel methodological procedures, to account for the unique features of decision making tasks under extreme time pressure and dynamic shifting situations. These novel methodological procedures include, the notion of decision point to deconstruct the dynamic shifting situations in a way that decision problem could be identified and formulated; the classification of routine and non-routine problems, and associated data alignment process to enable meaningful decision data analysis across different decision makers (DMs); the notion of composite cue to account for the DMs iterative process of information perception and comprehension in dynamic task environment; the application of computational models of heuristics to account for the time constraints and process dynamics of DMs decision making process; and the application of cross-validation process to enable the methodological principle of competitive testing of decision models. The JA-HM was further applied in a case study of fire emergency decision making. The application has been the first behavioural test of the validity of the computational models of heuristics, in predicting the DMs decision making during fire emergency response. It has also been the first behavioural test of the validity of the non-compensatory heuristics in predicting the DMs decisions on ranking task. The findings identified extend the literature of AT and NDM, and have implications for the fire emergency decision making

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov