In this paper, we introduce the concept of relative pre-reducts to derive the relative reducts from a large dataset. The relative reduct is considered a consistency-based attribute reduction method that is commonly utilized to extract concise subsets of condition attributes. Nonetheless, calculating all relative reducts necessitates substantial time and memory to build a discernibility matrix. In this research, we demonstrate that all relative pre-reducts can be computed using a simplified matrix referred to as the partial discernibility matrix, which can be readily converted into relative reducts. We also suggest employing a data partitioning approach to generate the discernibility matrix. This method alleviates the issue of an increased number of results for each partition. The outcomes from this technique yield the relative pre-reducts proposed in this study. Since our enhancements to the computation of relative reducts are independent of other advancements, they can be implemented in conjunction with existing methods. Experimental findings indicate that utilizing relative pre-reducts for computing relative reducts is efficient for large datasets.

Traditional rough set models represent concepts as sets. Vector-based concept representations have become mainstream in recent years, particularly in word embedding models, but existing rough set models are not designed to accommodate such representations. To address this, we propose a model that represents concepts as vectors. In rough set theory, concepts are approximated by defining granules, or basic concepts, as the basic units of knowledge. Approximations are then constructed as unions of these granules, such that each approximation is entirely dependent on the inclusion or exclusion of individual granules. When approximations are restricted to decision classes, the inclusion of a granule in a decision class approximation can be determined by associating a vector with each of the granule and the decision class and then evaluating their inner product. This methodology remains valid even within probabilistic rough set models. Building on this foundation, we propose vector-based rough set models, wherein granules and decision classes are represented as vectors from the outset. The proposed model preserves the properties of probabilistic rough sets in the approximation of the decision classes. Although our previous considerations required the vectors representing the decision classes to be linearly independent, we demonstrate that this restriction is unnecessary.

Point-of-interest (POI) recommendation has a wide range of application values in smart city services computing. However, extreme sparsity of user-POI matrix seriously affects the recommendation accuracy. Rich contextual information is often utilized to solve data sparsity, whereas how to efficiently integrate them becomes another challenge. To this end, we merge the contextual information into probabilistic diffusion process to propose a novel approach, namely context-enhanced probabilistic diffusion, to generate satisfying POI recommendations under sparse data environment. First, the check-in data is preprocessed to construct the relevant scores that can reflect the relevant degrees between users and POIs expressly. Then, we extract social explicit and implicit trusts from user relationships, and integrate them with time influence to present a time-enhanced social diffusion process to obtain time-social probabilistic score. Next, by merging time factor into geographical distance, a time-enhanced geographical diffusion process is executed to generate time-geographical probabilistic score. Furthermore, we present a context-aware probabilistic matrix factorization to predict the relevant score for a target user on each POI. Finally, unchecked-in POIs with highest predicted relevant scores are recommended for the target user. Experiments executed on real-world datasets suggest that, the proposed approach outperforms the state-of-the-art approaches in terms of the recommendation accuracy.

Abstract User-based collaborative filtering (UBCF) is widely used in recommender systems (RSs) as one of the most successful approaches, but traditional UBCF cannot provide recommendations with satisfactory accuracy and diversity simultaneously. Covering-based collaborative filtering (CBCF) is a useful approach that we have proposed in our previous work, which greatly improves the traditional UBCF and could provide satisfactory recommendations to an active user which often has sufficient rating information. However, different from an active user, a new user in RSs often has special characteristics (e.g., fewer ratings or ratings concentrating on popular items), and the previous CBCF approach cannot provide satisfactory recommendations for a new user. In this paper, aiming to provide personalized recommendations for a new user, through a detailed analysis of the characteristics of new users, we reconstruct a decision class to improve the previous CBCF and utilize the covering reduction algorithm in covering-based rough sets to remove redundant candidate neighbors for a new user. Furthermore, unlike the previous CBCF, our improved CBCF could provide personalized recommendations without needing special additional information. Experimental results suggest that for the sparse datasets that often occur in real RSs, the improved CBCF significantly outperforms those of existing work and can provide personalized recommendations for a new user with satisfactory accuracy and diversity simultaneously.

The recommender system (RS) can help us extract valuable data from a huge amount of raw information. User-based collaborative filtering (UBCF) is widely employed in practical RSs due to its outstanding performance. However, the traditional UBCF is subject to the new user cold-start issue because a new user is often extreme lack of available rating information. In this article, we develop a novel approach that incorporates a bipartite network into UBCF for enhancing the recommendation quality of new users. First, through the statistic and analysis of new users' rating characteristics, we collect niche items and map the corresponding rating matrix to a weighted bipartite network. Furthermore, a new weighted bipartite modularity index merging normalized rating information is present to conduct the community partition that realizes coclustering of users and items. Finally, for each individual clustering that is much smaller than the original rating matrix, a localized low-rank matrix factorization is executed to predict rating scores for unrated items. Items with the highest predicted rating scores are recommended to a new user. Experimental results from two real-world data sets suggest that without requiring additional complex information, the proposed approach is superior in terms of both recommendation accuracy and diversity and can alleviate the new user cold-start issue of UBCF effectively.

Mining from big data is one of the hottest topics in current trends of computer science. Attribute reduction to compute relative reducts from a given dataset is a key technique to use rough set theory as a tool in data mining, however, attribute reduction from a given dataset with numerous objects and attributes is very difficult. In this paper, to achieve attribute reduction from data with numerous objects and attributes, we try to combine generalized dynamic reducts and a heuristic attributed reduction using reduced decision tables.

Epistemic logic was proposed by Hintikka to model human knowledge and beliefs. Since then, a lot of work has been done to improve epistemic logic for applications to several problems. One of the interesting problems is to relate the concept of ignorance to that of knowledge. In this paper, we introduce an epistemic logic LNI founded on nonignorance by extending the classical propositional logic with the operator Ni. We describe its axiomatization and Kripke semantics. We show some technical results including a completeness and discuss some applications and extensions.

Recent behavioral medicine studies have revealed that some hormones secreted in human body sensitively changes according to his/her mental stress. Thus it is expected as an objective measurement of mental stress. However this newly developed interdisciplinary studies frequently showed inconsistent results. Some technical reasons were indicated for this discrepancy. Above all, we focused on the fact that in all these studies the only method introduced to estimate the relationship between the level of hormones and the subjective stress scale was the correlation analysis. In this study we employed Rough set analysis in place of conventional linear correlation analysis for mining the relationship between a subjective stress scale, “Profile of Mood Scale” (POMS), and a well known stress biomarker, salivary cortisol. As a developing result, numbers of items (inquiries in POMS) which relatively associated with cortisol level were found, whereas no significant linear correlation was obtained between them.

We propose a method of semantically nonmonotonic reasoning in prioritized knowledge bases based on incomplete information systems and granular reasoning. Our nonmonotonic reasoning is characterized as "reasoning with disregard of difference of detail." We provide granularized models and priority of each rule, and formulate the method of semantically non-monotonic reasoning based on the idea of ignored sets, rejected sets and possible tuples of atomic sentences that we propose.

In this paper, firstly, processes of classical inference are reviewed as granular reasoning from a point of view of reconstructing Kripke-style models with granularity. The essential point of the reconstruction is that some possible worlds are amalgamated to generate granules of worlds and vice versa. It is also called zoom reasoning systems. Then, the idea is applied for fuzzy reasoning processes by considering fuzzily granularized possible worlds. There linguistic truth values with linguistic hedges can be naturally introduced.

Proposes a faithful assignment function to construct W. Spohn's (1988) ordinal conditional functions (OCFs) that reflect ordinals in the current epistemic state represented by an OCF as long as possible. We also propose a composition schema for OCFs that construct a new OCF which satisfies postulates for updating and erasure in the AGM (Alchourron, Ga/spl uml/rdenfors & Makinson, 1985) paradigm. The faithful assignments for OCFs and the composition provide useful devices to represent iterated belief updates.

Belief change operations in logical settings and the possibilistic framework are reviewed. In logical settings, the Alchourron-Gardenfors-Makinson (AGM) paradigm (1985) and the Katsuno-Mendelzon framework (1992) are reviewed and interdefinability between update and erasure in the AGM paradigm is explained precisely. Moreover, a new identity that captures a relationship from contraction to erasure in the AGM paradigm is introduced and clear relationships among revision, contraction, update and erasure in the AGM paradigm are established. In the possibilistic framework, expansion and above four types of belief change are also formulated, and it is shown that two identities that capture the relationships between update and erasure in the AGM paradigm still remain valid between updating rule and the refined erasing rule.