This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.

Fuzzy numbers are commonly represented with fuzzy sets. Their objective is to better represent imprecise data. However, operations on fuzzy numbers are not as straightforward as maths on crisp numbers. Commonly, the Zadeh's extension rule is applied to elaborate a result. This can produce two problems: (1) high computational complexity and (2) for some fuzzy sets and some operations the results is not a fuzzy set with the same features (eg. multiplication of two triangular fuzzy sets does not produce a triangular fuzzy set). One more problem is the fuzzy spread -- fuzziness of the result increases with the number of operations. These facts can severely limit the application field of fuzzy numbers. In this paper we would like to revisite this problem with a different kind of fuzzy numbers -- extensional fuzzy numbers. The paper defines operations on extensional fuzzy numbers and relational operators (=, >, >=, <, <=) for them. The proposed approach is illustrated with several applicational examples. The C++ implementation is available from a public GitHub repository.

We then annotated ten thousand WBC images with these attributes, resulting in 113k labels (11 attributes x 10.3k images). Annotating at this level of detail and scale is unprecedented, offering unique value to AI in pathology. Moreover, we conduct experiments to predict these attributes from cell images, and also demonstrate specific applications that can benefit from our detailed annotations.

Dust storms harm health and reduce visibility; quick detection from satellites is needed. We present a near real-time system that flags dust at the pixel level using multi-band images from NASA's Terra and Aqua (MODIS). A 3D convolutional network learns patterns across all 36 bands, plus split thermal bands, to separate dust from clouds and surface features. Simple normalization and local filling handle missing data. An improved version raises training speed by 21x and supports fast processing of full scenes. On 17 independent MODIS scenes, the model reaches about 0.92 accuracy with a mean squared error of 0.014. Maps show strong agreement in plume cores, with most misses along edges. These results show that joint band-and-space learning can provide timely dust alerts at global scale; using wider input windows or attention-based models may further sharpen edges.

Shape-morphing robots have shown benefits in industrial grasping. We propose form-flexible grippers for adaptive grasping. The design is based on the hybrid jamming and suction mechanism, which deforms to handle objects that vary significantly in size from the aperture, including both larger and smaller parts. Compared with traditional grippers, the gripper achieves self-closing to form an airtight seal. Under a vacuum, a wide range of grasping is realized through the passive morphing mechanism at the interface that harmonizes pressure and flow rate. This hybrid gripper showcases the capability to securely grasp an egg, as small as 54.5% of its aperture, while achieving a maximum load-to-mass ratio of 94.3.

Granular materials (GMs) are ubiquitous in daily life. Understanding their properties is also important, especially in agriculture and industry. However, existing works require dedicated measurement equipment and also need large human efforts to handle a large number of particles. In this paper, we introduce a method for estimating the relative values of particle size and density from the video of the interaction with GMs. It is trained on a visuo-haptic learning framework inspired by a contact model, which reveals the strong correlation between GM properties and the visual-haptic data during the probe-dragging in the GMs. After training, the network can map the visual modality well to the haptic signal and implicitly characterize the relative distribution of particle properties in its latent embeddings, as interpreted in that contact model. Therefore, we can analyze GM properties using the trained encoder, and only visual information is needed without extra sensory modalities and human efforts for labeling. The presented GM property estimator has been extensively validated via comparison and ablation experiments. The generalization capability has also been evaluated and a real-world application on the beach is also demonstrated. Experiment videos are available at \url{https://sites.google.com/view/gmwork/vhlearning} .

The proximity perception of objects in granular materials is significant, especially for applications like minesweeping. However, due to particles' opacity and complex properties, existing proximity sensors suffer from high costs from sophisticated hardware and high user-cost from unintuitive results. In this paper, we propose a simple yet effective proximity sensing system for underground stuff based on the haptic feedback of the sensor-granules interaction. We study and employ the unique characteristic of particles -- failure wedge zone, and combine the machine learning method -- Gaussian process regression, to identify the force signal changes induced by the proximity of objects, so as to achieve near-field perception. Furthermore, we design a novel trajectory to control the probe searching in granules for a wide range of perception. Also, our proximity sensing system can adaptively determine optimal parameters for robustness operation in different particles. Experiments demonstrate our system can perceive underground objects over 0.5 to 7 cm in advance among various materials.

In business process simulation, resource availability is typically modeled by assigning a calendar to each resource, e.g., Monday-Friday, 9:00-18:00. Resources are assumed to be always available during each time slot in their availability calendar. This assumption often becomes invalid due to interruptions, breaks, or time-sharing across processes. In other words, existing approaches fail to capture intermittent availability. Another limitation of existing approaches is that they either do not consider multitasking behavior, or if they do, they assume that resources always multitask (up to a maximum capacity) whenever available. However, studies have shown that the multitasking patterns vary across days. This paper introduces a probabilistic approach to model resource availability and multitasking behavior for business process simulation. In this approach, each time slot in a resource calendar has an associated availability probability and a multitasking probability per multitasking level. For example, a resource may be available on Fridays between 14:00-15:00 with 90\% probability, and given that they are performing one task during this slot, they may take on a second concurrent task with 60\% probability. We propose algorithms to discover probabilistic calendars and probabilistic multitasking capacities from event logs. An evaluation shows that, with these enhancements, simulation models discovered from event logs better replicate the distribution of activities and cycle times, relative to approaches with crisp calendars and monotasking assumptions.

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.