Rough Set Approximations in Incomplete Multi-scale Information Systems

The key to granular computing is to make use of granules in problem solving. However, there are different granules at different levels of scale in data sets having hierarchical scale structures. Therefore, the concept of multi-scale decision systems is introduced in this paper, and a formal approach to knowledge acquisition measured at different levels of granulations is also proposed, and some algorithms for knowledge acquisition in consistent and inconsistent multi-scale decision systems are proposed with illustrative examples.

The traditional rough set (RS) theory is a powerful tool to deal with complete information system, and its performance to process incomplete information system is weak, especially, its effect of combining the incomplete information system with fuzzy objective information system is weaker. The paper improves the tolerance relation proposed by M.Kryszkiewcz to obtain the γ− tolerance relation and γ− tolerance classes, presents the concept of the incomplete and fuzzy objective information system (IFOIS in short), and gives its rough set model based on the γ− tolerance relation, i.e., the rough set model in incomplete and fuzzy objective information system. Finally, the concept of precision reduction is defined, and the corresponding algorithm is provided.

Updating three-way decisions in incomplete multi-scale information systems

A three-way decision approach with a probability dominance relation based on prospect theory for incomplete information systems

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.

Science is made feasible by the adoption of common systems of units. As research has become more data intensive, especially in the biomedical domain, it requires the adoption of a common system of information models, to make explicit the relationship between one set of data and another, regardless of format. This is being realised through the OBO Foundry to develop a suite of reference ontologies, and NCBO Bioportal to provide services to integrate biomedical resources and functionality to visualise and create mappings between ontology terms. Biomedical experts tend to be focused at one level of spatial scale, be it biochemistry, cell biology, or anatomy. Likewise, the ontologies they use tend to be focused at a particular level of scale. There is increasing interest in a multiscale systems approach, which attempts to integrate between different levels of scale to gain understanding of emergent effects. This is a return to physiological medicine with a computational emphasis, exemplified by the worldwide Physiome initiative, and the European Union funded Network of Excellence in the Virtual Physiological Human. However, little work has been done on how information modelling itself may be tailored to a multiscale systems approach. We demonstrate how this can be done for the complex process of heart morphogenesis, which requires multiscale understanding in both time and spatial domains. Such an effort enables the integration of multiscale metrology.

The three-way decision theory provides a three-way philosophical thinking to solve problems, and the regret theory quantifies the risk preferences of decision makers under different psychological behaviors. On the one hand, the combination of these two theories makes models more practical by considering the psychological behaviors of decision makers. On the other hand, we can effectively combine the advantages of the three-way decision theory with the regret theory to highlight the interpretability of decision-making processes. In this article, we propose a novel approximate estimation method for incomplete utility values via the regret theory and establish a wide sense of a three-way decision model on incomplete multiscale decision information systems. First, the degree of consistency for each scale is measured via using the dependence degree, then the optimal subsystem is selected by evaluating the scale selection cost. Furthermore, the incomplete multiscale evaluation information is transformed into triangular fuzzy numbers via linguistic term sets. Second, in light of fuzzy evaluation values and tradeoff factors, an estimation method for incomplete fuzzy subsystems is constructed, which can be used to calculate the utility difference and regret-rejoicing values for pairwise comparisons. Finally, from the perspective of human cognition, the tripartition and the corresponding decision rules are built by the tolerance degree, and the ranking of objects is calculated by the relative closeness degree. Additionally, multiaspect comparative and experimental analyses are performed by extensive experiments, and the feasibility, validity, and stability of the constructed model are shown by parametric analyses.

Based on responses to a survey of international migrants and Norway-born residents in three rural municipalities, this article analyses place attachment at various levels of scale. It compares international migrants to Norwegian-born internal migrants and local natives. Three questions are addressed: 1) Are there differences in the three resident categories’ levels of place attachment at different levels of scale?; 2) What are the predictors of place attachment, and is being a migrant a predictor in its own right? and 3) Are the predictors of place attachment the same for international migrants, internal migrants and local natives, and for different levels of scale? After controlling for other factors, the study found that all three categories have similar place attachment levels to the local scales. However, place attachment predictors differ, and predictors of place attachment have different relevance on different scales for the three categories. Institutional trust, usually not addressed in the research tradition, predicts place attachment for all categories.

A regret theory-based multi-granularity three-way decision model with incomplete T-spherical fuzzy information and its application in forest fire management

Due to rampant existence of missing values in E-commerce information systems, the research on knowledge acquisition in incomplete E-commerce information systems becomes necessary. In this paper, a novel method of rough reduction is proposed to obtain the latent knowledge in incomplete E-commerce information systems. By constructing the discernibility matrix, the useful knowledge can finally be extracted from incomplete E-commerce information systems.

Chapter 4 - Geographic Space as a Living Structure for Predicting Human Activities Using Big Data

Further Investigation of Characteristic Relation in Incomplete Information System

In incomplete information system, new information entropy and conditional entropy based on general relation are proposed. The results that the information entropy is extended from the general relation to equivalent relation and tolerance relation are found. Then the conclusion that the conditional entropy based on general relation decreases monotonously as the neighbor operators become finer is obtained. This paper presents some useful exploration about the incomplete information system from information views.

Pawlak’s classical model of rough set approximations provides an efficient tool for extracting information exactly by employing available knowledge (i.e., known knowledge) in an information system, since many problems in rough set theory are NP-hard and their solution process is therefore greedy and approximate. Many extensions of Pawlak’s classical model have been proposed in recent years. Most of them are considered over one or two sets, that is, one- or two-dimensional space or one- or two-dimensional data. Aided by relation-based rough set models, a few of these extensions are considered over three sets. However, the real world is in three-dimensional space. Therefore, it is necessary to solve these problems with other models, such as covering rough set models. For this purpose, we propose the TP-matroid—a matroidal structure over three sets. Employing the family of feasible sets of a TP-matroid as the available knowledge, a pair of rough set approximations—lower and upper approximations—is provided. In addition, for an information system defined over three sets, assisted by formal concept analysis, we establish a pair of rough set approximations. Furthermore, two TP-matroids are established based on the above pair of rough set approximations. The integration between the two pairs of rough set approximations presented here is discussed. The results show that for an information system in three-dimensional space, the rough set approximations provided here can effectively explore unknown knowledge by using available knowledge based on the family of feasible sets of a TP-matroid.

In this paper three types of information granular structures, called similarity classes, maximal consistent blocks, and labeled blocks, in incomplete information systems are introduced. Their properties are examined. Based on the three structures of granules, three types of rough set approximation models are derived for mining of certain and possible rules in incomplete decision tables. The relationships among the three rough set models are established.