In real-world scenarios, time series forecasting often demands timeliness, making research on model backbones a perennially hot topic. To meet these performance demands, we propose a novel backbone from the perspective of information fusion. Introducing the Basic Probability Assignment (BPA) Module and the Time Evidence Fusion Network (TEFN), based on evidence theory, allows us to achieve superior performance. On the other hand, the perspective of multi-source information fusion effectively improves the accuracy of forecasting. Due to the fact that BPA is generated by fuzzy theory, TEFN also has considerable interpretability. In real data experiments, the TEFN partially achieved state-of-the-art, with low errors comparable to PatchTST, and operating efficiency surpass performance models such as Dlinear. Meanwhile, TEFN has high robustness and small error fluctuations in the random hyperparameter selection. TEFN is not a model that achieves the ultimate in single aspect, but a model that balances performance, accuracy, stability, and interpretability.

One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent, incomplete, or uncertain, making the problem of evidence fusion highly non-trivial. In this paper, we propose a new model for measuring degrees of beliefs based on possibly inconsistent, incomplete, and uncertain evidence, by combining tools from Dempster-Shafer Theory and Topological Models of Evidence. Our belief model is more general than the aforementioned approaches in two important ways: (1) it can reproduce them when appropriate constraints are imposed, and, more notably, (2) it is flexible enough to compute beliefs according to various standards that represent agents' evidential demands. The latter novelty allows the users of our model to employ it to compute an agent's (possibly) distinct degrees of belief, based on the same evidence, in situations when, e.g, the agent prioritizes avoiding false negatives and when it prioritizes avoiding false positives. Finally, we show that computing degrees of belief with this model is #P-complete in general.

Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M\"obius transform, but also based on the $(\max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently it was shown that Yager's negator plays a crucial role in the definition of pd-independent linear negators: any linear negator is a function of Yager's negator. Here, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. We show that any pd-independent negator is non-involutive, and any nontrivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pddependent negators that generates an involutive negation of probability distributions. Keywords: Probability distribution, contracting negation, involutive negation 1. Introduction The concept of the negation of a probability distribution (pd) was introduced by Yager [1].

Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster-Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negation. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager's and uniform negators. Keywords: Probability distribution, Negation, Dempster-Shafer theory 1. Introduction The concept of negation of probability distribution (pd) was recently introduced by Yager [18].

The process of information fusion needs to deal with a large number of uncertain information with multi-source, heterogeneity, inaccuracy, unreliability, and incompleteness. In practical engineering applications, Dempster-Shafer evidence theory is widely used in multi-source information fusion owing to its effectiveness in data fusion. Information sources have an important impact on multi-source information fusion in an environment of complex, unstable, uncertain, and incomplete characteristics. To address multi-source information fusion problem, this paper considers the situation of uncertain information modeling from the closed world to the open world assumption and studies the generation of basic probability assignment (BPA) with incomplete information. In this paper, a new method is proposed to generate generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open world assumption. The proposed method can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing. Finally, a series of comprehensive experiments basing on the UCI data sets are used to verify the rationality and superiority of the proposed method.

Transfer learning is a popular practice in deep neural networks, but fine-tuning of large number of parameters is a hard task due to the complex wiring of neurons between splitting layers and imbalance distributions of data in pretrained and transferred domains. The reconstruction of the original wiring for the target domain is a heavy burden due to the size of interconnections across neurons. We propose a distributed scheme that tunes the convolutional filters individually while backpropagates them jointly by means of basic probability assignment. Some of the most recent advances in evidence theory show that in a vast variety of the imbalanced regimes, optimizing of some proper objective functions derived from contingency matrices prevents biases towards high-prior class distributions. Therefore, the original filters get gradually transferred based on individual contributions to overall performance of the target domain. This largely reduces the expected complexity of transfer learning whilst highly improves precision. Our experiments on standard benchmarks and scenarios confirm the consistent improvement of our distributed deep transfer learning strategy.

Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making based on BPA is still an open issue in Dempster-Shafer evidence theory. In this paper, a novel approach of transforming basic probability assignments to probabilities is proposed based on Deng entropy which is a new measure for the uncertainty of BPA. The principle of the proposed method is to minimize the difference of uncertainties involving in the given BPA and obtained probability distribution. Numerical examples are given to show the proposed approach.

This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart.

This paper presents an efficient adaptation and application of the Dempster-Shafer theory of evidence, one that can be used effectively in a massively parallel hierarchical system for visual pattern perception. It describes the techniques used, and shows in an extended example how they serve to improve the system's performance as it applies a multiple-level set of processes.