International Journal of Approximate Reasoning最新文献

Dempster-Shafer theory of evidence is a framework that is expressive enough to represent both ignorance and probabilistic information. However, decision models based on belief functions proposed in the literature face limitations in a sequential context: they either abandon the principle of dynamic consistency, restrict the combination of lotteries, or relax the requirement for transitive and complete comparisons. This work formally establishes that these requirements are indeed incompatible when any form of compensation is considered. It then demonstrates that these requirements can be satisfied in non-compensatory frameworks by introducting and characterizing a dynamically consistent rule based on first-order dominance.

The neighborhood threshold in the neighborhood rough set has a significant impact on the neighborhood relation. When the neighborhood threshold of an object exceeds the critical value, the labels of objects in the neighborhood are not completely consistent, and the critical value of each object often differs. Most existing neighborhood rough set models cannot adaptively regulate the neighborhood threshold. In this paper, we introduce a novel neighborhood rough set model that incorporates a self-tuning mechanism for the neighborhood threshold, taking into account the distribution of objects across different areas. The neighborhood margin is a measure proposed to assess the condition of neighborhoods, and it is calculated by subtracting the neighborhood threshold from the closest distance between heterogeneous elements. The neighborhood margin accurately represents the local state of the neighborhood, taking into account decision information. The margin neighborhood is proposed with a self-tuning the neighborhood threshold. Finally, we introduce the margin neighborhood rough set model and margin neighborhood-based attribute reduction algorithm, and explore the relationship between the proposed model and the neighborhood rough set model. The experiment examines the performance of reducts under various measures, and demonstrates that the neighborhood margin rough set reduces the uncertainty of neighborhood granules effectively, leading to excellent classification performance compared to other neighborhood-based SOTA models.

Three-way concept lattices (TCLs) have been widely explored due to their clear hierarchical structures, concise visual description and good interpretability. In contrast to classic formal contexts, lattice-valued fuzzy contexts exhibit great capability in describing and representing concepts with uncertainty. Different from conventional approaches to research of TCLs, this paper focuses on investigating the algebraic structure and properties of three-way concept lattice (TCL) stemmed from the positive concept lattice and negative concept lattice in a lattice-valued formal context. Several associated concept lattices such as the Cartesian product of positive concept lattice and negative lattice (i.e., pos-neg lattice), lattices induced from the partition of the pos-neg lattice, and their relationship are explored. Specifically, the isomorphism, embedding and order-preserving mappings between them are built. The quotient set of pos-neg lattice when being defined a specific equivalence relation on it is a complete lattice and each equivalence class is a lower semi-lattice. It is further declared that the structure of TCL is intrinsically and determined wholly by the pos-neg lattice. A practical application of the built theory of TCL is provided to sort alternatives in multi-criteria decision making.

In this article, we present a new approach to tackle lattice generation for complex and heterogeneous data using the concept of convexity. This is a work that we have already carried out, albeit intuitively [11] where we proposed the NextPriorityConcept algorithm for generating a meet-semilattice of concepts based on suitable descriptions and strategies. Now, we revisit the essential properties of our description spaces using a stronger formalism based on the properties of closure operators.

A theory of three-way decision is about thinking, problem-solving, and computing in threes or through triads. In this paper, we review fifteen years of research on three-way decision by using the philosophy-theory-application triad and the who-what-when triad. First, we discuss the philosophy, theory, and application of three-way decision. At the philosophy level, we delve into the philosophical roots and fundamental nature of three-way decision to reveal the underlying philosophical thinking. At the theory level, we provide an insightful analysis of the theory and methodology of three-way decision. At the application level, we examine the integration of three-way decision with other theories and their applications and effectiveness in real-world scenarios. Second, we focus on bibliometrics analytics by using the who-what-when triad, which attempts to answer a fundamental question of “who did what when”. We propose a $3\times 3$ model by applying the $3\times 3$ method of three-way decision. The first 3 is the author-topic-time triad. The second 3 represents a three-level analysis for each of the first three: (1) categorizing authors into the three levels of prolific authors, frequent authors, and occasional authors, (2) classifying topics into the three levels of the core topics, emerging topics, and to-be-explored topics, and (3) dividing articles into the three levels of initial investigations, further developments, and most recent studies. Finally, we perform a bibliometrics analysis of three-way decision articles by using the $3\times 3$ model of three-way decision. The results not only reveal the current status and trend of three-way decision research but also provide a road map for future research.

The automatic identification of argument units within a text is a crucial task, as it is the first step that should be performed by an end-to-end argument mining system. In this work, we propose an approach for categorizing errors in predicted argument units, which allows the evaluation of segmentation models from an argumentative perspective. We assess the ability of several models to generalize knowledge across different text domains and, through the proposed categorization, we show differences in their behavior that may not be noticeable using standard classification metrics. Furthermore, we assess how the errors in predicted argument units impact on a task that rely on accurate unit identification, an aspect that has not been studied in previous research, and that helps to evaluate the usability of an imperfect segmentation model beyond the segmentation task itself.

Many works within robust combinatorial optimisation consider interval-valued costs or constraints. While most of these works focus on finding a unique solution following a robust criteria such as minimax, a few consider the problem of characterising a set of possibly optimal solutions. This paper is situated within this line of work, and considers the problem of exactly enumerating the set of possibly optimal matroids under interval-valued costs. We show in particular that each solution in this set can be obtained through a polynomial procedure, and provide an efficient algorithm to achieve the enumeration.

Our primary interest is understanding reciprocal matrices all of whose efficient vectors are ordinally the same, i.e., there is only one efficient order (we call these matrices uniformly ordered, UO). These are reciprocal matrices for which no efficient vector produces strict order reversals. A reciprocal matrix is called column ordered (CO) if each column is ordinally the same. Efficient vectors for a CO matrix with the same order of the columns always exist. For example, the entry-wise geometric mean of some or all columns of a reciprocal matrix is efficient and, if the matrix is CO, has the same order of the columns. A necessary, but not sufficient, condition for UO is that the matrix be CO and then the only efficient order should be satisfied by the columns (possibly weakly). In the case $n=3$, CO is necessary and sufficient for UO, but not for $n>3$. We characterize the 4-by-4 UO matrices and identify the three possible alternate orders when the matrix is CO (and give entry-wise conditions for their occurrence). We also describe the simple perturbed consistent matrices that are UO. Some of the technology developed for this purpose is of independent interest.

The common cause principle for two random variables A and B is examined in the case of causal insufficiency, when their common cause C is known to exist, but only the joint probability of A and B is observed. As a result, C cannot be uniquely identified (the latent confounder problem). We show that the generalized maximum likelihood method can be applied to this situation and allows identification of C that is consistent with the common cause principle. It closely relates to the maximum entropy principle. Investigation of the two binary symmetric variables reveals a non-analytic behavior of conditional probabilities reminiscent of a second-order phase transition. This occurs during the transition from correlation to anti-correlation in the observed probability distribution. The relation between the generalized likelihood approach and alternative methods, such as predictive likelihood and minimum common entropy, is discussed. The consideration of the common cause for three observed variables (and one hidden cause) uncovers causal structures that defy representation through directed acyclic graphs with the Markov condition.