International Journal of Approximate Reasoning最新文献

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.

Differential privacy (DP) is a class of mathematical standards for assessing the privacy provided by a data-release mechanism. This work concerns two important flavors of DP that are related yet conceptually distinct: pure ε-differential privacy (ε-DP) and Pufferfish privacy. We restate ε-DP and Pufferfish privacy as Lipschitz continuity conditions and provide their formulations in terms of an object from the imprecise probability literature: the interval of measures. We use these formulations to derive limits on key quantities in frequentist hypothesis testing and in Bayesian inference using data that are sanitised according to either of these two privacy standards. Under very mild conditions, the results in this work are valid for arbitrary parameters, priors and data generating models. These bounds are weaker than those attainable when analysing specific data generating models or data-release mechanisms. However, they provide generally applicable limits on the ability to learn from differentially private data – even when the analyst's knowledge of the model or mechanism is limited. They also shed light on the semantic interpretations of the two DP flavors under examination, a subject of contention in the current literature.¹

Formal concept analysis is a powerful mathematical framework based on mathematical logic and lattice theory for analyzing object-attribute relational systems. Over the decades, Formal concept analysis has evolved from its theoretical foundations into a versatile methodology applied across various disciplines. A heterogeneous formal context provides a feasible generalization of a formal context, enabling diverse truth-degrees of objects, attributes, and fuzzy relations. In our paper, we present extended theoretical results on heterogeneous formal contexts, including bimorphisms, Galois connections, and heterogeneous attribute implications. We recall the basic notions and properties of the heterogeneous formal context and its concept lattice. Moreover, we present extended results on bimorphisms and Galois connections in a heterogeneous formal context, including a self-contained proof of the main result. We include examples of introduced notions in heterogeneous formal contexts and two-valued logic. We propose the extension of attribute implications for heterogeneous formal contexts and explore their validity. By embracing heterogeneity in Formal concept analysis, we enrich its extended theoretical foundations and pave the way for innovative applications across diverse domains, including personal data protection and cybersecurity.

We identify the (filter representation of the) logic behind the recent theory of coherent sets of desirable (sets of) things, which generalise coherent sets of desirable (sets of) gambles as well as coherent choice functions, and show that this identification allows us to establish various representation results for such coherent models in terms of simpler ones.

We give a complete characterisation of the single and double arrow relations of the standard context $K\left(L_n\right)$ of the lattice $L_n$ of partitions of any positive integer n under the dominance order, thereby addressing an open question of Ganter, 2020/2022.

Our study is centered on the aggregation of fuzzy graphs, looking for conditions under which the aggregation process yields another fuzzy graph. We conduct an in-depth analysis of the preservation of several important properties and structures inherent to fuzzy graphs, like paths, cycles, or bridges. In addition we obtain appropriate criteria for when the aggregation of complete fuzzy graphs is again a complete fuzzy graph.