Variable Precision Rough Set Model for Incomplete Information Systems and Its Beta-Reducts

As the original rough set model is quite sensitive to noisy data, Ziarko proposed the variable precision rough set (VPRS) model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. In this paper, the variable precision rough set model for an incomplete information system is proposed by combining the VPRS model and incomplete information system, and the beta-lower and beta-upper approximations are defined. Considering that classical VPRS model lacks a feasible method to determine the precision parameter beta when calculating the beta-reducts, we present an approach to determine the parameter beta. Then, by calculating discernibility matrix and discernibility functions based on beta-lower approximation, the beta-reducts and the generalized decision rules are obtained. Finally, a concrete example is given to explain the validity and practicability of beta-reducts which is proposed in this paper

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

A relative tolerance relation of rough set with reduct and core approach, and application to incomplete information systems

Data mining concepts and methods can be applied in various fields. Many methods have been proposed and one of those methods is the classical 'rough set theory' which is used to analyze the complete data. However, the Rough Set classical theory cannot overcome the incomplete data. The simplest method for operating an incomplete data is removing unknown objects. Besides, the continuation of Rough Set theory is called tolerance relation which is less convincing decision in terms of approximation. As a result, a similarity relation is proposed to improve the results obtained through a tolerance relation technique. However, when applying the similarity relation, little information will be lost. Therefore, a limited tolerance relation has been introduced. However, little information will also be lost as limited tolerance relation does not take into account the accuracy of the similarity between the two objects. Hence, this study proposed a new method called Relative Tolerance Relation of Rough Set with Reduct and Core (RTRS) which is based on limited tolerance relation that takes into account relative similarity precision between two objects. Several incomplete datasets have been used for data classification and comparison of our approach with existing baseline approaches, such as the Tolerance Relation, Limited Tolerance Relation, and NonSymmetric Similarity Relations approaches are made based on two different scenarios. In the first scenario, the datasets are given the same weighting for all attributes. In the second scenario, each attribute is given a different weighting. Once the classification process is complete, the proposed approach will eliminate redundant attributes to develop an efficient reduce set and formulate the basic attribute specified in the incomplete information system. Several datasets have been tested and the rules generated from the proposes approach give better accuracy. Generally, the findings show that the RTRS method is better compared to the other methods as discussed in this study

Going Deeper than Supervised Discretisation in Processing of Stylometric Features

Rough set theory is employed in cases where data are incomplete and inconsistent and an ap- proximation of concepts is needed. The classical approach works for discrete data and allows only nominal classification. To induce the best rules, access to all available information is ad- vantageous, which can be endangered if discretisation is a necessary step in the data preparation stage. Discretisation, even executed with taking into account class labels of instances, brings some information loss. The research methodology illustrated in this paper is dedicated to ex- tended transformations of continuous input features into categorical, with the goal of enhancing the performance of rule-based classifiers, constructed with rough set data mining. The experi- ments were carried out in the stylometry domain, with its key task of authorship attribution. The obtained results indicate that supporting supervised discretisation with elements of unsuper- vised transformations can lead to enhanced predictions, which shows the merits of the proposed research framework

A Relative Tolerance Relation of Rough Set (RTRS) for potential fish yields in Indonesia

The sea is essential to life on earth, including regulating the climate, producing oxygen, providing medicines, providing habitats for marine animals, and feeding millions of people. It must be ensured that the sea continues to meet the needs of life without sacrificing the people of future generations. The sea regulates the planet’s climate and is a significant source of nutrients. The sea becomes an essential part of global commerce, while the contents of the ocean become the solution of human energy needs today and the future. The wealth and potential of the sea as a source of energy for humans today and the future needs to be mapped and described to provide a picture of marine potential to all concerned. As part of the government, the Ministry of Marine Affairs and Fisheries is responsible for the process of formulating, determining, and implementing policies in the field of marine and fisheries based on the results of mapping and extracting information from existing conditions. The results of this information can be used to predict the marine potential in a marine area. This prediction process can be developed using data-mining techniques such as applying the association rule by looking at the relationship between the quantity of fish based on the plankton abundance index. However, this association rules data-mining techniques that require complete data, which are data sets with no missing values to generate interesting rules for detection systems. The problem is often that required marine data are not available or that marine data are available, but they contain incomplete data. To address this problem, this paper introduces a Relative Tolerance Relation of Rough Set (RTRS). Novelty RTRS differs from previous rough approaches that use tolerance relationships, nonsymmetric equation relationships, and limited tolerance relationships. The RTRS approach is based on a limited tolerance relationship considering the relative precision between two objects; therefore, this is the first job to use relative precision. In addition, this paper presents the mathematical approach of the RTRS and compares it with other existing approaches using the marine real dataset to classify the marine potential level of the region. The results show that the proposed approach is better than the existing approach in terms of accuracy

Kaba küme tabanlı çok kriterli karar verme yöntemi ve uygulaması

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Çok kriterli karar verme problemi, çağımız yöneticilerinin sıklıkla başvurmuş olduğu yöntemlerden birisidir. Verilerin belirsiz ya da eksik olması durumunda, mevcut olan çok kriterli karar verme yöntemleri yetersiz kalırken, önermiş olduğumuz kaba küme tabanlı çok kriterli karar verme algoritması, bu eksikliği gidermede en büyük yardımcı olarak karşımıza çıkmaktadır. Bununla birlikte, hızla artan veri trafiğinde, mevcut verilerin verimli bir şekilde kullanılması da beraberinde önemli bir durumu ortaya çıkartmaktadır. 1982 yılında ilk olarak Pawlak[1] tarafından önerilen kaba küme kavramı, büyük veri tabanlarını kullanarak gerekli olan bilginin keşfini sağlayan önemli bir araç olarak kullanılmaktadır. Kaba küme kavramı, çok kriterli karar verme problemlerinde kullanılmak üzere, kesin olmayan yapıların analizi için bulanık mantık yaklaşımından türetilmiştir. Kaba küme teorisi, kural indirgeme ve sınıflandırma yaklaşım özellikleri ile büyük verilerin analiz işleminin yanı sıra çok kriterli karar verme problemlerinde de kullanılabilmektedir. Kaba küme teorisi bulanık küme teorisinin bir alt kolu olarak geliştirilmiştir. Eksik, belirsiz verilerin değerlendirilmesi sürecinde, alt ve üst yaklaşımlar kullanılarak, veriler analiz edilmektedir. Bulanık kümeler gibi kesin sınırlamaları içermeyen bir yapıya sahiptir. Eksik bilgi analizi, bilgi tabanı indirgemesi yöntemleri kullanılarak, verilerdeki belirsizlik en aza indirgenmeye çalışılmaktadır. Tutarsız, eksik bilgi içeren veri yapılarından kural çıkarımı ve sınıflandırma konusunda kaba küme teorisi ilerleyen zamanlarda daha fazla tercih edilecek bir yöntem olarak çıkabilecektir. Bu çalışmada kaba kümeleme teorisine ait temel kavramlar kaba küme tabanlı bilgi keşfi ve kaba küme kavramı dikkate alınarak geliştirilen algoritma ile birlikte, çok kriterli karar verme probleminin çözümüne yönelik algoritma geliştirilmiştir ve diğer ÇKKV algoritmaları ile karşılaştırılmıştır. Anahtar kelimeler:Kaba Küme Teorisi, Çok Kriterli Karar Verme EntropiThe multi-criteria decision-making problem is one of the methods that preffered and applied by the managers. Multi criteria decision making data set may include the uncertain or incomplete data, in this situation, decision is getting difficult and impossible, the suggested rough set based multi criteria decision making algorithm can able to solve this manner problem. However, in the rapidly increasing data traffic, the efficient use of existing data also brings about an important situation. The rough set concept firstly proposed by Pawlak in 1982[1] that is used as an important tool for the discovery of the necessary information by using large databases. In the case of multi-criteria decision-making problems, the concept of rough set theory is derived from the fuzzy logic approach to perform the analysis of uncertain structures. The rough set theory also has the property of being able to be used in multi-criteria decision-making problems with the rules of rule reduction and classification during the analysis of large data. Rough set theory has a structure that does not contain definite limitations, such as fuzzy sets. Therefore, the rough set approach can able to analysis of the incomplete, inadequate and ambiguous information suitable for data analysis, uses incomplete information analysis, knowledge base reduction methods during this process. Rough set theory can be used as a natural method that deals with inconsistent and incomplete information, which is the basic problem of rule extraction and classification. In this study, the basic concepts of rough set theory is given. The algorithm for solving multi-criteria decision making has been developed by considering the rough set based knowledge discovery and rough set concept. Keywords: Rough Set Theory, Multi Criteria Decision Making Entrop

Experiments on Incomplete Data Sets Using Modifications to Characteristic Relation

Rough set theory is a useful approach for decision rule induction which is applied to large life data sets. Lower and upper approximations of concept values are used to induce rules for incomplete data sets. In our research we will study validity of modifications suggested to characteristic relation. We discuss the implementation of modifications to characteristic relation, and the local definability of each modified set.We show that all suggested modification sets are not locally definable except for maximal consistent blocks that are restricted to data set with "do not care" conditions. A comparative analysis was conducted for characteristic sets and modifications in terms of cardinality of lower and upper approximations of each concept and decision rules induced by each modification. In this research, experiments were conducted on four incomplete data sets with lost and do not care conditions. LEM2 algorithm was implemented to induce certain and possible rules from the incomplete data set. To measure the classification average error rate for induced rules, ten-fold cross validation was implemented. Our results show that there is no significant difference between the qualities of rule induced from each modification

A weighted rough set based fuzzy axiomatic design approach for the selection of AM processes

Additive manufacturing (AM) or 3D printing, as an enabling technology for mass customization or personalization, has been developed rapidly in recent years. Various design tools, materials, machines and service bureaus can be found in the market. Clearly, the choices are abundant, but users can be easily confused as to which AM process they should use. This paper first reviews the existing multi-attribute decision-making methods for AM process selection and assesses their suitability with regard to two aspects, preference rating flexibility and performance evaluation objectivity. We propose that an approach that is capable of handling incomplete attribute information and objective assessment within inherent data has advantages over other approaches. Based on this proposition, this paper proposes a weighted preference graph method for personalized preference evaluation and a rough set based fuzzy axiomatic design approach for performance evaluation and the selection of appropriate AM processes. An example based on the previous research work of AM machine selection is given to validate its robustness for the priori articulation of AM process selection decision support