This work advances and substantiates the thesis that the resolution of this crisis lies in the domain of possibility theory, specifically in the axiomatic approach developed in Bychkovs article. Unlike numerous attempts to fix Dempster rule, this approach builds from scratch a logically consistent and mathematically rigorous foundation for working with uncertainty, using the dualistic apparatus of possibility and necessity measures. The aim of this work is to demonstrate that possibility theory is not merely an alternative, but provides a fundamental resolution to DST paradoxes. A comparative analysis of three paradigms will be conducted probabilistic, evidential, and possibilistic. Using a classic medical diagnostic dilemma as an example, it will be shown how possibility theory allows for correct processing of contradictory data, avoiding the logical traps of DST and bringing formal reasoning closer to the logic of natural intelligence.

General Type-2 (GT2) Fuzzy Logic Systems (FLSs) are perfect candidates to quantify uncertainty, which is crucial for informed decisions in high-risk tasks, as they are powerful tools in representing uncertainty. In this paper, we travel back in time to provide a new look at GT2-FLSs by adopting Zadeh's (Z) GT2 Fuzzy Set (FS) definition, intending to learn GT2-FLSs that are capable of achieving reliable High-Quality Prediction Intervals (HQ-PI) alongside precision. By integrating Z-GT2-FS with the \(\alpha\)-plane representation, we show that the design flexibility of GT2-FLS is increased as it takes away the dependency of the secondary membership function from the primary membership function. After detailing the construction of Z-GT2-FLSs, we provide solutions to challenges while learning from high-dimensional data: the curse of dimensionality, and integrating Deep Learning (DL) optimizers. We develop a DL framework for learning dual-focused Z-GT2-FLSs with high performances. Our study includes statistical analyses, highlighting that the Z-GT2-FLS not only exhibits high-precision performance but also produces HQ-PIs in comparison to its GT2 and IT2 fuzzy counterparts which have more learnable parameters. The results show that the Z-GT2-FLS has a huge potential in uncertainty quantification.

Fault tree analysis is a vital method of assessing safety risks. It helps to identify potential causes of accidents, assess their likelihood and severity, and suggest preventive measures. Quantitative analysis of fault trees is often done via the dependability metrics that compute the system's failure behaviour over time. However, the lack of precise data is a major obstacle to quantitative analysis, and so to reliability analysis. Fuzzy logic is a popular framework for dealing with ambiguous values and has applications in many domains. A number of fuzzy approaches have been proposed to fault tree analysis, but -- to the best of our knowledge -- none of them provide rigorous definitions or algorithms for computing fuzzy unreliability values. In this paper, we define a rigorous framework for fuzzy unreliability values. In addition, we provide a bottom-up algorithm to efficiently calculate fuzzy reliability for a system. The algorithm incorporates the concept of $\alpha$-cuts method. That is, performing binary algebraic operations on intervals on horizontally discretised $\alpha$-cut representations of fuzzy numbers. The method preserves the nonlinearity of fuzzy unreliability. Finally, we illustrate the results obtained from two case studies.

Maji et al. introduced in 2002 a method of parametric decision making using soft sets as tools and representing their tabular form as a binary matrix. In cases, however, where some or all of the parameters used for the characterization of the elements of the universal set are of fuzzy texture, their method does not give always the best decision making solution. In order to tackle this problem, we modified in earlier works the method of Maji et al. by replacing the binary elements in the tabular form of the corresponding soft set either by grey numbers or by triangular fuzzy numbers. In this work, in order to tackle more efficiently cases in which the decision maker has doubts about the correctness of the fuzzy/qualitative characterizations assigned to some or all of the elements of the universal set, we replace the binary elements of the tabular form by neutrosophic triplets. Our new, neutrosophic decision making method is illustrated by an application concerning the choice of a new player by a soccer club.

Pre-trained large language models have recently achieved ground-breaking performance in a wide variety of language understanding tasks. However, the same model can not be applied to multimodal behavior understanding tasks (e.g., video sentiment/humor detection) unless non-verbal features (e.g., acoustic and visual) can be integrated with language. Jointly modeling multiple modalities significantly increases the model complexity, and makes the training process data-hungry. While an enormous amount of text data is available via the web, collecting large-scale multimodal behavioral video datasets is extremely expensive, both in terms of time and money. In this paper, we investigate whether large language models alone can successfully incorporate non-verbal information when they are presented in textual form. We present a way to convert the acoustic and visual information into corresponding textual descriptions and concatenate them with the spoken text. We feed this augmented input to a pre-trained BERT model and fine-tune it on three downstream multimodal tasks: sentiment, humor, and sarcasm detection. Our approach, TextMI, significantly reduces model complexity, adds interpretability to the model's decision, and can be applied for a diverse set of tasks while achieving superior (multimodal sarcasm detection) or near SOTA (multimodal sentiment analysis and multimodal humor detection) performance. We propose TextMI as a general, competitive baseline for multimodal behavioral analysis tasks, particularly in a low-resource setting.

Humans are sophisticated at reading interlocutors' emotions from multimodal signals, such as speech contents, voice tones and facial expressions. However, machines might struggle to understand various emotions due to the difficulty of effectively decoding emotions from the complex interactions between multimodal signals. In this paper, we propose a multimodal emotion analysis framework, InterMulti, to capture complex multimodal interactions from different views and identify emotions from multimodal signals. Our proposed framework decomposes signals of different modalities into three kinds of multimodal interaction representations, including a modality-full interaction representation, a modality-shared interaction representation, and three modality-specific interaction representations. Additionally, to balance the contribution of different modalities and learn a more informative latent interaction representation, we developed a novel Text-dominated Hierarchical High-order Fusion(THHF) module. THHF module reasonably integrates the above three kinds of representations into a comprehensive multimodal interaction representation. Extensive experimental results on widely used datasets, (i.e.) MOSEI, MOSI and IEMOCAP, demonstrate that our method outperforms the state-of-the-art.

The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kind of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations.

The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's extension principle for determining the degree of membership of a function of fuzzy numbers is corrected for this generalization. An analogue of the concept of mean value is also suggested. The use of partially ordered values in cognitive maps with comparison of expert assessments is considered.

Fusion technique is a key research topic in multimodal sentiment analysis. The recent attention-based fusion demonstrates advances over simple operation-based fusion. However, these fusion works adopt single-scale, i.e., token-level or utterance-level, unimodal representation. Such single-scale fusion is suboptimal because that different modality should be aligned with different granularities. This paper proposes a fusion model named ScaleVLAD to gather multi-Scale representation from text, video, and audio with shared Vectors of Locally Aggregated Descriptors to improve unaligned multimodal sentiment analysis. These shared vectors can be regarded as shared topics to align different modalities. In addition, we propose a self-supervised shifted clustering loss to keep the fused feature differentiation among samples. The backbones are three Transformer encoders corresponding to three modalities, and the aggregated features generated from the fusion module are feed to a Transformer plus a full connection to finish task predictions. Experiments on three popular sentiment analysis benchmarks, IEMOCAP, MOSI, and MOSEI, demonstrate significant gains over baselines.

Google is paying tribute Tuesday to the computer scientist who created the mathematical framework "fuzzy logic." On this day in 1964, Zadeh submitted the paper "Fuzzy Sets," which laid out the concept of "fuzzy logic." The logo featured on Google.com "The theory he presented offered an alternative to the rigid'black and white' parameters of traditional logic and instead allowed for more ambiguous or'fuzzy' boundaries that more closely mimic the way humans see the world," reads a biography of Zadeh by Google. The theory has been used in various tech applications, including anti-skid algorithms for cars.