For deterministic feedback, we additionally present a gap-independent algorithm that identifies a Condorcet winning team withinO(nklog(k)+k5)duels.

Discrete fuzzy numbers, and in particular those defined over a finite chain $L_n = \{0, \ldots, n\}$, have been effectively employed to represent linguistic information within the framework of fuzzy systems. Research on total (admissible) orderings of such types of fuzzy subsets, and specifically those belonging to the set $\mathcal{D}_1^{L_n\rightarrow Y_m}$ consisting of discrete fuzzy numbers $A$ whose support is a closed subinterval of the finite chain $L_n = \{0, 1, \ldots, n\}$ and whose membership values $A(x)$, for $x \in L_n$, belong to the set $Y_m = \{ 0 = y_1 < y_2 < \cdots < y_{m-1} < y_m = 1 \}$, has facilitated the development of new methods for constructing logical connectives, based on a bijective function, called $\textit{pos function}$, that determines the position of each $A \in \mathcal{D}_1^{L_n\rightarrow Y_m}$. For this reason, in this work we revisit the problem by introducing algorithms that exploit the combinatorial structure of total (admissible) orders to compute the $\textit{pos}$ function and its inverse with exactness. The proposed approach achieves a complexity of $\mathcal{O}(n^{2} m \log n)$, which is quadratic in the size of the underlying chain ($n$) and linear in the number of membership levels ($m$). The key point is that the dominant factor is $m$, ensuring scalability with respect to the granularity of membership values. The results demonstrate that this formulation substantially reduces computational cost and enables the efficient implementation of algebraic operations -- such as aggregation and implication -- on the set of discrete fuzzy numbers.

Thus, attempts to closely match the recorded scores may lead to over-fitting and impair generalization performance.

Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and hyperspectral images, there is still no consensus on the most suitable vector ordering for constructing morphological operators. This paper addresses this issue by examining a reduced ordering approximating the Condorcet ranking derived from a set of vector orderings. Inspired by voting problems, the Condorcet ordering ranks elements from most to least voted, with voters representing different orderings. In this paper, we develop a machine learning approach that learns a reduced ordering that approximates the Condorcet ordering. Preliminary computational experiments confirm the effectiveness of learning the reduced mapping to define vector-valued morphological operators for color images.

--This paper addresses the problem of robot navigation in mixed geometric/semantic 3D environments. Given a hierarchical representation of the environment, the objective is to navigate from a start position to a goal, while satisfying task-specific safety constraints and minimizing computational cost. We introduce Hierarchical Class-ordered A* (HCOA*), an algorithm that leverages the environment's hierarchy for efficient and safe path-planning in mixed geometric/semantic graphs. We use a total order over the semantic classes and prove theoretical performance guarantees for the algorithm. We propose three approaches for higher-layer node classification based on the semantics of the lowest layer: a Graph Neural Network method, a k-Nearest Neighbors method, and a Majority-Class method. We evaluate HCOA* in simulations on two 3D Scene Graphs, comparing it to the state-of-the-art and assessing the performance of each classification approach. Results show that HCOA* reduces the computational time of navigation by up to 50%, while maintaining near-optimal performance across a wide range of scenarios. S robotic sensing technologies advance, enabling robots to perceive vast and diverse information, two fundamental questions arise: What information from this extensive data stream is most important for a given task? Hierarchical semantic environment representations, such as 3D Scene Graphs (3DSGs) [1]-[3], provide rich and structured abstractions that mirror human-like reasoning, thus facilitating the selection and organization of information.