International Journal of Approximate Reasoning最新文献

Neighborhood rough sets are well-known as an interesting approach for attribute reduction in numerical/continuous data tables. Nevertheless, in most existing neighborhood rough set models, all attributes are assigned the same weights. This may undermine the capacity to select important attributes, especially for high-dimensional datasets. To establish attribute weights, in this study, we will utilize fuzzy divergence to evaluate the distinction between each attribute with the whole attributes in classifying the objects to the decision classes. Then, we construct a new model of fuzzy divergence-based weighted neighborhood rough sets, as well as propose an efficient attribute reduction algorithm. In our method, reducts are considered under the scenario of the α-certainty region, which is introduced as an extension of the positive region. Several related properties will show that attribute reduction based on the α-certainty region can significantly enhance the ability to identify optimal attributes due to reducing the influence of noisy information. To validate the effectiveness of the proposed algorithm, we conduct experiments on 12 benchmark datasets. The results demonstrate that our algorithm not only significantly reduces the number of attributes compared to the original data but also enhances classification accuracy. In comparison to some other state-of-the-art algorithms, the proposed algorithm also outperforms in terms of classification accuracy for almost all of datasets, while also maintaining a highly competitive reduct size and computation time.

We present a principle-based analysis of contribution functions for quantitative bipolar argumentation graphs that quantify the contribution of one argument to another. The introduced principles formalise the intuitions underlying different contribution functions as well as expectations one would have regarding the behaviour of contribution functions in general. As none of the covered contribution functions satisfies all principles, our analysis can serve as a tool that enables the selection of the most suitable function based on the requirements of a given use case.

Chain event graphs are a family of probabilistic graphical models that generalise Bayesian networks and have been successfully applied to a wide range of domains. Unlike Bayesian networks, these models can encode context-specific conditional independencies as well as asymmetric developments within the evolution of a process. More recently, new model classes belonging to the chain event graph family have been developed for modelling time-to-event data to study the temporal dynamics of a process. However, existing Bayesian model selection algorithms for chain event graphs and its variants rely on all parameters having conjugate priors. This is unrealistic for many real-world applications. In this paper, we propose a mixture modelling approach to model selection in chain event graphs that does not rely on conjugacy. Moreover, we show that this methodology is more amenable to being robustly scaled than the existing model selection algorithms used for this family. We demonstrate our techniques on simulated datasets.

Based on the properties of the difference operator on crisp sets, a fuzzy difference operator in fuzzy logic is defined as a continuous binary operator on the closed unit interval with some boundary conditions. In this paper, the structures and properties of fuzzy difference operators are studied. The main results are: (1) Using the axiomatic approach, some generalizations of classical tautologies for fuzzy difference operators are obtained. (2) Based on the model theoretic approach, the fuzzy difference operator constructed by a nilpotent t-norm and a strong negation is characterized. (3) the paper discusses the relationship between the fuzzy difference operator and symmetric difference operator which was raised in [3].

Feature selection has shown noticeable benefits to the tasks of machine learning and data mining, and an extensive variety of feature selection methods has been proposed to remove redundant and irrelevant features. However, most of the existing methods aim to find a feature subset to perfectly fit data with the minimum empirical risk, thus causing the problems of overfitting and noise sensitivity. In this study, a robust weighted fuzzy margin-based feature selection is proposed for uncertain data with noise. Concretely, a robust weighted fuzzy margin based on fuzzy rough sets is first introduced to evaluate the significance of different features. Then, a gradient ascent algorithm based on the noise filtering strategy and three-way decision is developed to optimize the sample and feature weights to further enlarge the fuzzy margin. Finally, an adaptive feature selection algorithm based on the robust weighted fuzzy margin is presented to generate an optimal feature subset with a large margin. Extensive experiments on the UCI benchmark datasets show that the proposed method could obtain high-quality feature subsets and outperform other representative methods under different noise rates.

Concept cognition and knowledge discovery under network data combine formal concept analysis with complex network analysis. However, in real life, network data is uncertain due to some limitations. Fuzzy sets are a powerful tool to deal with uncertainty and imprecision. Therefore, this paper focuses on concept-cognitive learning in fuzzy network formal contexts. Fuzzy object-induced network three-way concept (network OEF-concept) lattices and their properties are mainly investigated. In addition, three fuzzy network weaken-concepts are proposed. As the real data is too large, attribute reduction can simplify concept-cognitive learning by removing redundant attributes. Thus, the paper proposes attribute reduction methods that can keep the concept lattice structure isomorphic and the set of extents of granular concepts unchanged. Finally, an example is given to show the attribute reduction process of a fuzzy network three-way concept lattice. Attribute reduction experiments are conducted on nine datasets, and the results prove the feasibility of attribute reduction.

In recent years, there has been significant research in the field of possibilistic temporal logic. However, existing works have not yet addressed the issue of frequency, which is a common form of uncertainty in the real world. This article aims to fill this gap by incorporating frequency information into possibilistic temporal logic and focusing on the model-checking problem of generalized possibility computation tree logic (GPoCTL) with frequency information. Specifically, we introduce generalized possibility computation tree logic with frequency (GPoCTL_F). Although its syntax can be considered as an extension of frequency constraints of the always operator (□) in GPoCTL, they are fundamentally different in semantics and model-checking methods. To facilitate this extension, useful frequency words such as “always”, “usually”, “often”, “sometimes”, “occasionally”, “rarely”, “hardly ever” and “never” are defined as fuzzy frequency operators in this article. Therefore, this article focuses on investigating the model-checking problem of the frequency-constrained always operator. In addition, we analyze the relationship between some GPoCTL_F path formulas and GPoCTL path formulas. Then, we provide a model-checking algorithm for GPoCTL_F and analyze its time complexity. Finally, an example of a social network is used to illustrate the calculation process of the proposed method and its potential applications.

Configurable software systems and families of similar software systems are increasingly being considered by industry to provide software tailored to each customer's needs. Their development requires managing software variability, i.e. commonalities, differences and constraints. A primary step is properly analyzing the variability of software, which can be done at various levels, from specification to deployment. In this paper, we focus on the software variability expressed through user-stories, viz. short formatted sentences indicating which user role can perform which action at the specification level. At this level, variability is usually analyzed in a two dimension view, i.e. software described by features, and considering the roles apart. The novelty of this work is to model the three dimensions of the variability (i.e. software, roles, features) and explore it using Triadic Concept Analysis (TCA), an extension of Formal Concept Analysis. The variability exploration is based on the extraction of 3-dimensional implication rules. The adopted methodology is applied to a case study made of 65 commercial web sites in four domains, i.e. manga, martial arts sports equipment, board games including trading cards, and video-games. This work highlights the diversity of information provided by such methodology to draw directions for the development of a new product or for building software variability models.

Formal Concept Analysis (FCA) is a method rooted in order theory, with the aim of analyzing and visually representing concepts. Decision implication serves as a fundamental means of knowledge representation in FCA in the case of decision-making. This paper extends the scope of knowledge discovery within FCA in single domains to the realm of multi-domains, with introducing a framework for knowledge representation and reasoning within correlative data from the perspectives of cross-domain and multi-granularity. Firstly, we delve into the acquisition and modeling of decision knowledge within correlative data, and introduce the concept of multi-granularity decision implication. We then establish multi-granularity decision implication logic to study the completeness, non-redundancy and optimality of multi-granularity decision implications and introduce inference rules with semantical compatibility. Furthermore, we define lattice fusion decision context to seamlessly integrate information within correlative data and construct a multi-granularity decision implication basis (MGDIB) based on lattice fusion decision context. Finally, we conduct an experiment of generating MGDIB based on GroupLens_MovieLens dataset.

We use now available psychological data involving human concepts, objects covered by these concepts, and binary attributes describing the objects to explore selected semantic aspects of Boolean matrix factorization. Our basic perspective derives from the intuitive requirement that the factors computed from data should represent natural categories latently present in the data. This idea is examined for factorization algorithms that utilize formal concepts to build factors. We provide several experimental observations which imply that the inspected factorization methods deliver semantically sound factors that resemble significant human concepts of the examined domains.