Algorithms for solving the reducts problem in rough sets

This work deals with finding minimal reducts of decision table based on the rough sets theory. Its goal is to develop algorithms capable of finding such reducts. Two algorithms are presented in this report: the first based on Boolean reasoning function, the second based on Genetic Algorithm. Test results on real data are given and conclusions are made

Two new feature selection algorithms with rough sets theory

Rough Sets Theory has opened new trends for the development of the Incomplete Information Theory. Inside this one, the notion of reduct is a very significant one, but to obtain a reduct in a decision system is an expensive computing process although very important in data analysis and knowledge discovery. Because of this, it has been necessary the development of different variants to calculate reducts. The present work look into the utility that offers Rough Sets Model and Information Theory in feature selection and a new method is presented with the purpose of calculate a good reduct. This new method consists of a greedy algorithm that uses heuristics to work out a good reduct in acceptable times. In this paper we propose other method to find good reducts, this method combines elements of Genetic Algorithm with Estimation of Distribution Algorithms. The new methods are compared with others which are implemented inside Pattern Recognition and Ant Colony Optimization Algorithms and the results of the statistical tests are shown.IFIP International Conference on Artificial Intelligence in Theory and Practice - Knowledge Acquisition and Data MiningRed de Universidades con Carreras en Informática (RedUNCI

Fuzzy-Rough Feature Significance for Fuzzy Decision Trees

Crisp decision trees are one of the most popular classification algorithms in current use within data mining and machine learning. However, although they possess many desirable features, they lack the ability to model vagueness. As a result of this, the induction of fuzzy decision trees (FDTs) has become an area of much interest. One important aspect of tree induction is the choice of feature at each stage of construction. If weak features are selected, the resulting decision tree will be meaningless and will exhibit poor performance. This paper introduces a new measure of feature significance based on fuzzy-rough sets for use within fuzzy ID3. The measure is experimentally compared with leading feature rankers, and is also compared with traditional fuzzy entropy for fuzzy tree induction.

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

NeutroAlgebra Theory, volume I

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more

Neutrosophic Algebraic Structures and Their Applications

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more

Knowledge reduction of dynamic covering decision information systems with varying attribute values

Knowledge reduction of dynamic covering information systems involves with the time in practical situations. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings because of varying attribute values. Then we present incremental algorithms of constructing the second and sixth approximations of sets by using characteristic matrices. We employ experimental results to illustrate that the incremental approaches are effective to calculate approximations of sets in dynamic covering information systems. Finally, we perform knowledge reduction of dynamic covering information systems with the incremental approaches