Conflict is widespread in society, and trisecting an agent set is a crucial research direction in three-way conflict analysis. In practice, the varying risk preferences among decision-makers lead to diverse trisections of an agent set in similar circumstances. In this paper, we consider decision-makers’ risk preferences and propose novel models of three-way conflict. Initially, we divide a set of issues into two disjoint subsets and utilize information entropy to compute issues’ weights. Then, we design alliance measures regarding an individual issue through the transition probability function. Based on the issues’ weights and alliance measures, we propose alliance probabilities between two agents. Additionally, we present risk-preferred, risk-averse, and risk-neutral decisions with the relative utility function. Finally, we design an algorithm to derive rules for three-way conflict analysis and demonstrate how to utilize the proposed model for decision-making through an example.
Decision trees (DTRs) and decision rules are extensively examined and applied in various domains of computer science. The theory of DTRs and rules highlights several crucial inquiries, such as how the complexity of deterministic decision trees (DDTRs) and decision rule systems depends on the complexity of the set of attributes associated with the columns of the decision table (DT). In this research paper, we focus on the analysis of nondeterministic decision trees (NDTRs) as a substitute for decision rule systems. NDTRs can be seen as representations of decision rule systems. We examine classes of DTs featuring multi-valued decisions (known as multi-label DTs) that maintain closure under attribute removal (columns) and modifications to the sets of assigned decisions for rows. We examine the behavior of functions that describe the worst-case dependence of the minimum complexity of DDTRs and NDTRs on the complexity of the set of attributes associated with the columns of tables belonging to a closed class (CC) of DTs closed under the above two operations. We enumerate all possible types of behavior exhibited by these functions.
Hyperbolic embedding has advantages for hierarchically category images, hence it has been applied in few-shot learning and achieved significant results. However, treating all samples equally may not ensure that the learned hyperbolic embedding adequately considers various modalities within the same category. To address this issue, this paper proposes a novel hyperbolic attention mechanism for few-shot learning, which adjusts weights based on the hyperbolic distance of samples to the average position. This approach balances the typicality and diversity of labeled samples, aiding the model in a deeper understanding of data structures. After hyperbolic embedding, weights were redistributed through this attention mechanism for few-shot learning. Experiments were conducted on the CUB and miniImageNet datasets. The experiments demonstrate the superiority of the proposed attention mechanism when using hyperbolic embedding for hierarchically category data.
In real-world scenarios, datasets characterized by nonlinear separability and fuzziness are quite common. Although fuzzy granular-balls generated by fuzzy c-means can capture the fuzziness of the datasets, it exhibits limitations in effectively handling nonlinearly separable datasets. Due to the advantage of spectral clustering in handling nonlinearly separable datasets, we fully leverage this capability to propose a novel clustering model, namely, fuzzy granular-balls based spectral clustering (FGBSC). It enhances spectral clustering by introducing fuzzy granular-balls as inputs, and effectively addresses the nonlinear separability of the datasets on the basis of capturing the fuzziness of the datasets. We perform experiments to evaluate the effectiveness of the proposed method in handling nonlinearly separable datasets.
Rough concepts have been introduced in [7] in the context of a mathematical framework unifying Rough Set Theory (RST) and Formal Concept Analysis (FCA). Algebraically, the lower and upper approximation operators on a concept lattice have similar order-theoretic properties to the and operators in modal logic. Thus, the logic of rough concepts has been defined as a (non-distributive) lattice-based modal logic whose relational semantics consists of formal contexts enriched with relations (interpreting the modal operators) satisfying the axioms classically corresponding to the reflexivity, symmetry, and transitivity of the accessibility relations of Kripke frames. Recently, the description logic LE- 𝒜ℒ𝒞 was introduced for reasoning in the semantic environment of these enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of knowledge bases with acyclic TBoxes [5]. In the present paper, we introduce the description logic of rough concepts LE- 𝒜ℒ𝒞ℛ , which extends LE- 𝒜ℒ𝒞 with the (modal) axioms classically corresponding to reflexivity, symmetry, and transitivity, and develop its corresponding tableaux algorithm. We then introduce two extensions of LE- 𝒜ℒ𝒞ℛ : the first one (LE- 𝒜ℒ𝒞ℛ𝒪 ) extending LE- 𝒜ℒ𝒞ℛ with generated concepts, and the second one (LE- 𝒜ℒ𝒞ℛ𝒩 ) extending LE- 𝒜ℒ𝒞ℛ with feature-pair inconsistencies. The resulting description logic is a framework for modeling reasoning problems related to rough concepts, which is demonstrated through the case-study of a knowledge base for Whittaker’s five kingdom classification of living things.
