The model of three-way decision on two universes generalizes various two-universe models of rough sets, and it is in fact defined on 0–1 tables, i.e. binary information tables. This paper generalizes ...the model of three-way decision from 0–1 tables to general information tables. The framework of three-way decision on general information tables is presented and the connection of existing related models is investigated. In our models, every element in the set of objects is assigned to a value and we can construct a tri-partition of the object set according to a pair of thresholds. We present a fundamental result of the models, which induces two concepts: the fundamental sequence and pair. On the one hand, the fundamental result shows that there exist finitely many pairs of thresholds. That is, we need only to consider the case of finitely many tri-partitions. On the other hand, it describes how the positive region varies based on thresholds and induces a concept of positive region tower. Finally, we evaluate these finite tri-partitions by the weighted entropy, which is a new measure defined as a variant of information entropy. An optimal tri-partition can be obtained according to weighted entropies of the finite tri-partitions.
Neighborhood rough sets based attribute reduction, as a common dimension reduction method, has been widely used in machine learning and data mining. Each attribute has the same weight (the degree of ...importance) in the existing neighborhood rough set models. In this work, we introduce different weights into neighborhood relations and propose a novel approach for attribute reduction. The main motivation is to fully mine the correlation between attributes and decisions before calculating neighborhood relations, and the attributes with high correlation are assigned higher weights. We first construct a Weighted Neighborhood Rough Set (WNRS) model based on weighted neighborhood relations and discuss its properties. Then WNRS based dependency is defined to evaluate the significance of attribute subsets. We design a greedy search algorithm based on WNRS to select an attribute subset which has both strong correlation and high dependency. Furthermore, we use isometric search to find the optimal neighborhood threshold. Finally, ten datasets from UCI machine learning repository and ELVIRA Biomedical data set repository are used to compare the performance of WNRS with those of other state-of-the-art reduction algorithms. The experimental results show that WNRS is feasible and effective, which has higher classification accuracy and compression ratio.
•The existing researches on neighborhood rough sets use the same attribute weights.•The attributes that are highly related to decisions should be highlighted.•We introduce partition coefficients of attributes to re-assign weights of attributes.•The results show WNRS can get higher classification accuracy and compression ratio.
Granular computing and acquisition of IF-THEN rules are two basic issues in knowledge representation and data mining. A rough set approach to knowledge discovery in incomplete multi-scale decision ...tables from the perspective of granular computing is proposed in this paper. The concept of incomplete multi-scale information tables in the context of rough sets is first introduced. Information granules at different levels of scales in incomplete multi-scale information tables are then described. Lower and upper approximations with reference to different levels of scales in incomplete multi-scale information tables are also defined and their properties are examined. Optimal scale selection with various requirements in incomplete multi-scale decision tables are further discussed. Relationships among different notions of optimal scales in incomplete multi-scale decision tables are presented. Finally, knowledge acquisition in the sense of rule induction in consistent and inconsistent incomplete multi-scale decision tables are explored.
The present paper introduces two models of three-way decision with ranking and reference tuple on hybrid information tables. One is the model with an importance ratio, and the other is the model with ...any importance ratio, where importance ratio describes the quantitative comparison of importance between two attribute subsets. A unique measure is proposed to assess the trisections generated by the two models and, correspondingly, the concepts of local optimal and global optimal trisections are proposed respectively. The two models have good properties which enable the algorithms provided in this paper to compute the optimal trisections in finite steps. Through comparison and experiments on real data, we show that the two models have strong expressive power and capture two different types of trisecting problems on hybrid information tables, and demonstrate the feasibility and practicality of our method in potential applications.
Granular computing and acquisition of if-then rules are two basic issues in knowledge representation and data mining. A formal approach to granular computing with multi-scale data measured at ...different levels of granulations is proposed in this paper. The concept of labelled blocks determined by a surjective function is first introduced. Lower and upper label-block approximations of sets are then defined. Multi-scale granular labelled partitions and multi-scale decision granular labelled partitions as well as their derived rough set approximations are further formulated to analyze hierarchically structured data. Finally, the concept of multi-scale information tables in the context of rough set is proposed and the unravelling of decision rules at different scales in multi-scale decision tables is discussed.
In many real-life applications, data are often hierarchically structured at different levels of granulations. A multi-scale information table is a special hierarchical data set in which each object ...can take on as many values as there are scales under the same attribute. An important issue in such a data set is to select optimal scale combination in order to keep certain condition for final decision. In this paper, by employing Shannon’s entropy, we study the selection of optimal scale combination to maintain uncertain measure of a knowledge from a generalized multi-scale information table. We first review the concept of entropy and its basic properties in information tables. We then introduce the notion of scale combinations in a generalized multi-scale information table. We further define entropy optimal scale combination in generalized multi-scale information tables and generalized multi-scale decision tables. Finally, we examine relationship between the entropy optimal scale combination and the classical optimal scale combination. We show that, in either a generalized multi-scale information table or a consistent generalized multi-scale decision table, the entropy optimal scale combination and the classical optimal scale combination are equivalent. And in an inconsistent generalized multi-scale decision table, a scale combination is generalized decision optimal if and only if it is a generalized decision entropy optimal.
In this work we use the granular computing paradigm to study specific types of families of subsets, operators and families of ordered pairs of sets of attributes which are naturally induced by ...information tables. In an unifying perspective, by means of some representation results, we connect the study of finite closure systems, matroids and finite lattice theory in the scope of the more general notion of attribute dependency based on information tables. For a fixed finite set Ω and for a corresponding information table J having attribute set Ω, the fundamental tool we use to proceed in our investigation is the equivalence relation ≈J on the power set P(Ω) which identifies two any sets of attributes inducing the same indiscernibility relation on the object set of J. We interpret the attribute dependency as a preorder ≥J on P(Ω) whose induced equivalence relation coincides with ≈J. Then we investigate in detail the links between the preorder ≥J, a closure system and an abstract simplicial complex on Ω naturally induced by ≈J and specific families of ordered pairs of sets of attributes on Ω.
Simple graphs in granular computing Chiaselotti, Giampiero; Ciucci, Davide; Gentile, Tommaso
Information sciences,
05/2016, Letnik:
340-341
Journal Article
Recenzirano
Odprti dostop
Given a graph, we interpret its adjacency matrix as an information table. We study this correspondence in two directions. Firstly, on the side of graphs by applying to it standard techniques from ...granular computing. In this way, we are able to connect automorphisms on graphs to the so-called indiscernibility relation and a particular hypergraph built from the starting graph to core and reducts. On the other hand, new concepts are introduced on graphs that have an interesting correspondence on information tables. In particular, some new topological interpretations of the graph and the concept of extended core are given.
Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. In this paper, we study optimal scale selection in multi-scale decision tables from ...the perspective of granular computation. A multi-scale information table is an attribute-value system in which each object under each attribute is represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser labelled value. The concept of multi-scale information tables in the context of rough sets is introduced. Lower and upper approximations with reference to different levels of granulations in multi-scale information tables are defined and their properties are examined. Optimal scale selection with various requirements in multi-scale decision tables with the standard rough set model and a dual probabilistic rough set model are discussed respectively. Relationships among different notions of optimal scales in multi-scale decision tables are further analyzed.
Traditional rough set approach is mainly used to unravel rules from a decision table in which objects can possess a unique attribute-value. In a real world data set, for the same attribute objects ...are usually measured at different scales. The main objective of this paper is to study optimal scale combinations in generalized multi-scale decision tables. A generalized multi-scale information table is an attribute-value system in which different attributes are measured at different levels of scales. With the aim of investigating knowledge representation and knowledge acquisition in inconsistent generalized multi-scale decision tables, we first introduce the notion of scale combinations in a generalized multi-scale information table. We then formulate information granules with different scale combinations in multi-scale information systems and discuss their relationships. Furthermore, we define lower and upper approximations of sets with different scale combinations and examine their properties. Finally, we examine optimal scale combinations in inconsistent generalized multi-scale decision tables. We clarify relationships among different concepts of optimal scale combinations in inconsistent generalized multi-scale decision tables.
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