Non-symmetric Similarity Relation Research Articles

A Relative Tolerance Relation of Rough Set in Incomplete Information

University is an educational institution that has objectives to increase student retention and also to make sure students graduate on time. Student learning performance can be predicted using data mining techniques e.g. the application of finding essential association rules on student learning base on demographic data by the university in order to achieve these objectives. However, the complete data i.e. the dataset without missing values to generate interesting rules for the detection system, is the key requirement for any mining technique. Furthermore, it is problematic to capture complete information from the nature of student data, due to high computational time to scan the datasets. To overcome these problems, this paper introduces a relative tolerance relation of rough set (RTRS). The novelty of RTRS is that, unlike previous rough set approaches that use tolerance relation, non-symmetric similarity relation, and limited tolerance relation, it is based on limited tolerance relation by taking account into consideration the relatively precision between two objects and therefore this is the first work that uses relatively precision. Moreover, this paper presents the mathematical properties of the RTRS approach and compares the performance and the existing approaches by using real-world student dataset for classifying university’s student performance. The results show that the proposed approach outperformed the existing approaches in terms of computational time and accuracy.

Rough Set Extension under Incomplete Information System with “?” Values

Classical rough set theory (RST) can't process incomplete information system (IIS) because it is based on an indiscernibility relation which is a kind of equivalent relation. In the literature a non-symmetric similarity relation based rough set model (NS-RSM) has been introduced as an extended model under IIS with ``?" values directly. Unfortunately, in this model objects in the same similarity class are not necessarily similar to each other and may belong to different target classes. In this paper, a new inequivalent relation called Maximal Limited Consistent block relation (MLC) is proposed. The proposed MLC relation improves the lower approximation accuracy by finding the maximal limited blocks of indiscernible objects in IIS with ``?" values. Maximal Limited Similarity rough set model (MLS) is introduced as an integration between our proposed relation (MLC) and NS-RSM. The resulted MLS model works efficiently under IIS with ``?" values. Finally, an illustrative example is given to validate MLS model. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS. The results of this work demonstrate that the MLS model outperform NS-RSM.

A Comparative Analysis of Rough Sets for Incomplete Information System in Student Dataset

Rough set theory is a mathematical model for dealing with the vague, imprecise, and uncertain knowledge that has been successfully used to handle incomplete information system. Since we know that in fact, in the real-world problems, it is regular to find conditions where the user is not able to provide all the necessary preference values. In this paper, we compare the performance accuracy of the extension of rough set theory, i.e. Tolerance Relation, Limited Tolerance Relation, Non-Symmetric Similarity Relation and New Limited Tolerance Relation of Rough Sets for handling incomplete information system in real-world student dataset. Based on the results, it is shown that New Limited Tolerance Relation of Rough Sets has outperformed the previous techniques.

Maximal limited similarity-based rough set model

Non-symmetric similarity relation-based rough set model (NS-RSM) is viewed as mathematical tool to deal with the analysis of imprecise and uncertain information in incomplete information systems with "?" values. NS-RSM relies on the concept of non-symmetric similarity relation to group equivalent objects and generate knowledge granules that are then used to approximate the target set. However, NS-RSM results in unpromising approximation space when addressing inconsistent data sets that have lots of boundary objects. This is because objects in the same similarity classes are not necessarily similar to each other and may belong to different target classes. To enhance NS-RSM capability, we introduce the maximal limited similarity-based rough set model (MLS-RSM) which describes the maximal collection of indistinguishable objects that are limited tolerance to each other in similarity classes. This allows accurate computation to be done for the approximation space. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS-RSM. The results demonstrate that MLS-RSM model outperforms NS-RSM and can approximate the target set more efficiently.

The Application of Incomplete Information System of Rough Set Theory in Spam Filtering

The spread of spam brings a great deal of disturbance to e-mail users. In order to improve the efficiency of spam filtering and solve the problem that some attributes extracted from the e-mail header are null, we first applied the knowledge reduction algorithm and the sample recognition algorithm based on incomplete information system of Rough Set theory to spam filtering on e-mail header. In this paper, we proposed an improved non-symmetric similarity relation and defined the attribute complete importance for attribute reduction. Experimental results showed that the algorithm got higher recall and precision, lower fake recognition than other algorithms.