NMGRS: Neighborhood-based multigranulation rough sets

AbstractRecently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is based on multiple binary relations on the universe. However, it is worth noticing that the original MGRS can not be used to discover knowledge from information systems with various domains of attributes. In order to extend the theory of MGRS, the objective of this study is to develop a so-called neighborhood-based multigranulation rough set (NMGRS) in the framework of multigranulation rough sets. Furthermore, by using two different approximating strategies, i.e., seeking common reserving difference and seeking common rejecting difference, we first present optimistic and pessimistic 1-type neighborhood-based multigranulation rough sets and optimistic and pessimistic 2-type neighborhood-based multigranulation rough sets, respectively. Through analyzing several important properties of neighborhood-based multigranulation rough sets, we find that the new rough sets degenerate to the original MGRS when the size of neighborhood equals zero. To obtain covering reducts under neighborhood-based multigranulation rough sets, we then propose a new definition of covering reduct to describe the smallest attribute subset that preserves the consistency of the neighborhood decision system, which can be calculated by Chen’s discernibility matrix approach. These results show that the proposed NMGRS largely extends the theory and application of classical MGRS in the context of multiple granulations

A Novel Approach of Rough Conditional Entropy-Based Attribute Selection for Incomplete Decision System

Pawlak's classical rough set theory has been applied in analyzing ordinary information systems and decision systems. However, few studies have been carried out on the attribute selection problem in incomplete decision systems because of its complexity. It is therefore necessary to investigate effective algorithms to deal with this issue. In this paper, a new rough conditional entropy-based uncertainty measure is introduced to evaluate the significance of subsets of attributes in incomplete decision systems. Furthermore, some important properties of rough conditional entropy are derived and three attribute selection approaches are constructed, including an exhaustive search strategy approach, a heuristic search strategy approach, and a probabilistic search strategy approach for incomplete decision systems. Moreover, several experiments on real-life incomplete data sets are conducted to assess the efficiency of the proposed approaches. The final experimental results indicate that two of these approaches can give satisfying performances in the process of attribute selection in incomplete decision systems

Rough sets theory and uncertainty into information system

This article is focused on rough sets approach to expression of uncertainty into information system. We assume that the data are presented in the decision table and that some attribute values are lost. At first the theoretical background is described and after that, computations on real-life data are presented. In computation we wok with uncertainty coming from missing attribute values

Class Association Rules Mining based Rough Set Method

This paper investigates the mining of class association rules with rough set approach. In data mining, an association occurs between two set of elements when one element set happen together with another. A class association rule set (CARs) is a subset of association rules with classes specified as their consequences. We present an efficient algorithm for mining the finest class rule set inspired form Apriori algorithm, where the support and confidence are computed based on the elementary set of lower approximation included in the property of rough set theory. Our proposed approach has been shown very effective, where the rough set approach for class association discovery is much simpler than the classic association method.Comment: 10 pages, 2 figure

Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples

This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology

Autonomous clustering using rough set theory

This paper proposes a clustering technique that minimises the need for subjective human intervention and is based on elements of rough set theory. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency

Dealing with uncertain entities in ontology alignment using rough sets

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Ontology alignment facilitates exchange of knowledge among heterogeneous data sources. Many approaches to ontology alignment use multiple similarity measures to map entities between ontologies. However, it remains a key challenge in dealing with uncertain entities for which the employed ontology alignment measures produce conflicting results on similarity of the mapped entities. This paper presents OARS, a rough-set based approach to ontology alignment which achieves a high degree of accuracy in situations where uncertainty arises because of the conflicting results generated by different similarity measures. OARS employs a combinational approach and considers both lexical and structural similarity measures. OARS is extensively evaluated with the benchmark ontologies of the ontology alignment evaluation initiative (OAEI) 2010, and performs best in the aspect of recall in comparison with a number of alignment systems while generating a comparable performance in precision