Model abstraction (MA) and event abstraction (EA) are means to reduce complexity of (discovered) models and event data. Imagine a process intelligence project that aims to analyze a model discovered from event data which is further abstracted, possibly multiple times, to reach optimality goals, e.g., reducing model size. So far, after discovering the model, there is no technique that enables the synchronized abstraction of the underlying event log. This results in loosing the grounding in the real-world behavior contained in the log and, in turn, restricts analysis insights. Hence, in this work, we provide the formal basis for synchronized model and event abstraction, i.e., we prove that abstracting a process model by MA and discovering a process model from an abstracted event log yields an equivalent process model. We prove the feasibility of our approach based on behavioral profile abstraction as non-order preserving MA technique, resulting in a novel EA technique.

Determining the reliability of evidence sources is a crucial topic in Dempster-Shafer theory (DST). Previous approaches have addressed high conflicts between evidence sources using discounting methods, but these methods may not ensure the high efficiency of classification models. In this paper, we consider the combination of DS theory and Intuitionistic Fuzzy Sets (IFS) and propose an algorithm for quantifying the reliability of evidence sources, called Fuzzy Reliability Index (FRI). The FRI algorithm is based on decision quantification rules derived from IFS, defining the contribution of different BPAs to correct decisions and deriving the evidential reliability from these contributions. The proposed method effectively enhances the rationality of reliability estimation for evidence sources, making it particularly suitable for classification decision problems in complex scenarios. Subsequent comparisons with DST-based algorithms and classical machine learning algorithms demonstrate the superiority and generalizability of the FRI algorithm. The FRI algorithm provides a new perspective for future decision probability conversion and reliability analysis of evidence sources.

In pattern recognition, handling uncertainty is a critical challenge that significantly affects decision-making and classification accuracy. Dempster-Shafer Theory (DST) is an effective reasoning framework for addressing uncertainty, and the Random Permutation Set (RPS) extends DST by additionally considering the internal order of elements, forming a more ordered extension of DST. However, there is a lack of a transformation method based on permutation order between RPS and DST, as well as a sequence-based probability transformation method for RPS. Moreover, the reliability of RPS sources remains an issue that requires attention. To address these challenges, this paper proposes an RPS transformation approach and a probability transformation method tailored for RPS. On this basis, a reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition. Experimental results demonstrate that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order relations between the input features. A particular min-cost-max-flow fractional matching problem, whose entropy regularized version can be approximated by an optimal transport (OT) optimization, leads to a transform which is efficient, differentiable, equivariant, parameterless and probabilistically interpretable. While the Sinkhorn OT solver has been adapted extensively in many contexts, we use it differently by minimizing the cost between a set of features to $itself$ and using the transport plan's $rows$ as the new representation. Empirically, the transform is highly effective and flexible in its use and consistently improves networks it is inserted into, in a variety of tasks and training schemes. We demonstrate state-of-the-art results in few-shot classification, unsupervised image clustering and person re-identification. Code is available at \url{github.com/DanielShalam/BPA}.

Developing a general information processing model in uncertain environments is fundamental for the advancement of explainable artificial intelligence. Dempster-Shafer theory of evidence is a well-known and effective reasoning method for representing epistemic uncertainty, which is closely related to subjective probability theory and possibility theory. Although they can be transformed to each other under some particular belief structures, there remains a lack of a clear and interpretable transformation process, as well as a unified approach for information processing. In this paper, we aim to address these issues from the perspectives of isopignistic belief functions and the hyper-cautious transferable belief model. Firstly, we propose an isopignistic transformation based on the belief evolution network. This transformation allows for the adjustment of the information granule while retaining the potential decision outcome. The isopignistic transformation is integrated with a hyper-cautious transferable belief model to establish a new canonical decomposition. This decomposition offers a reverse path between the possibility distribution and its isopignistic mass functions. The result of the canonical decomposition, called isopignistic function, is an identical information content distribution to reflect the propensity and relative commitment degree of the BPA. Furthermore, this paper introduces a method to reconstruct the basic belief assignment by adjusting the isopignistic function. It explores the advantages of this approach in modeling and handling uncertainty within the hyper-cautious transferable belief model. More general, this paper establishes a theoretical basis for building general models of artificial intelligence based on probability theory, Dempster-Shafer theory, and possibility theory. Introduction Dempster-Shafer (DS) theory of evidence, also known as belief function theory, is an effective artificial intelligence tool for modeling and handling uncertainty in partial knowledge environments.

Deep learning models for medical image segmentation can fail unexpectedly and spectacularly for pathological cases and images acquired at different centers than training images, with labeling errors that violate expert knowledge. Such errors undermine the trustworthiness of deep learning models for medical image segmentation. Mechanisms for detecting and correcting such failures are essential for safely translating this technology into clinics and are likely to be a requirement of future regulations on artificial intelligence (AI). In this work, we propose a trustworthy AI theoretical framework and a practical system that can augment any backbone AI system using a fallback method and a fail-safe mechanism based on Dempster-Shafer theory. Our approach relies on an actionable definition of trustworthy AI. Our method automatically discards the voxel-level labeling predicted by the backbone AI that violate expert knowledge and relies on a fallback for those voxels. We demonstrate the effectiveness of the proposed trustworthy AI approach on the largest reported annotated dataset of fetal MRI consisting of 540 manually annotated fetal brain 3D T2w MRIs from 13 centers. Our trustworthy AI method improves the robustness of a state-of-the-art backbone AI for fetal brain MRIs acquired across various centers and for fetuses with various brain abnormalities.

The amount of information we have to deal with day-by-day is large enough not to be able to handle it without specialized software tools. Ordinary events we face daily, from doctor's appointments to upcoming Zoom meetings, are compiled into a system with too many variables to track and manage efficiently. Therefore, at least, the use of a simple task management app is a must nowadays. In business, the stakes are much higher. The volumes of data that constant collaboration with clients generates are too big to efficiently process them manually.

Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed by Pincus to describe the irregularities of complex systems. The more irregular the time series, the greater the approximate entropy. The ApEn of the network represents the ability of a network to generate new nodes, or the possibility of undiscovered nodes. Through the association of network characteristics and basic probability assignment (BPA) , a measure of the uncertainty of BPA regarding completeness can be obtained. The main contribution of paper is to define the integrity of the basic probability assignment then the approximate entropy of the BPA is proposed to measure the uncertainty of the integrity of the BPA. The proposed method is based on the logical network structure to calculate the uncertainty of BPA in evidence theory. The uncertainty based on the proposed method represents the uncertainty of integrity of BPA and contributes to the identification of the credibility of BPA.

Although highly accurate automated diagnostic techniques for melanoma have been reported, the realization of a system capable of providing diagnostic evidence based on medical indices remains an open issue because of difficulties in obtaining reliable training data. In this paper, we propose bulk production augmentation (BPA) to generate high-quality, diverse pseudo-skin tumor images with the desired structural malignant features for additional training images from a limited number of labeled images. The proposed BPA acts as an effective data augmentation in constructing the feature detector for the atypical pigment network (APN), which is a key structure in melanoma diagnosis. Experiments show that training with images generated by our BPA largely boosts the APN detection performance by 20.0 percentage points in the area under the receiver operating characteristic curve, which is 11.5 to 13.7 points higher than that of conventional CycleGAN-based augmentations in AUC.