Knowledge Granulation, Rough Entropy and Uncertainty Measure in Incomplete Fuzzy Information System

Many real world problems deal with ordering of objects instead of classifying objects, although most of research in data analysis has been focused on the latter. One of the extensions of classical rough sets to take into account the ordering properties is dominance-based rough sets approach which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this paper, we address knowledge measures and reduction in incomplete fuzzy information system using the approach. Firstly, new definitions of knowledge granulation and rough entropy are given, and some important properties of them are investigated. Then, dominance matrix about the measures knowledge granulation and rough entropy is obtained, which could be used to eliminate the redundant attributes in incomplete fuzzy information system. Lastly, a matrix algorithm for knowledge reduction is proposed. An example illustrates the validity of this method and shows the method is applicable to complex fuzzy system. Experiments are also made to show the performance of the newly proposed algorithm

Dominance-based Rough Set Approach, basic ideas and main trends

Dominance-based Rough Approach (DRSA) has been proposed as a machine learning and knowledge discovery methodology to handle Multiple Criteria Decision Aiding (MCDA). Due to its capacity of asking the decision maker (DM) for simple preference information and supplying easily understandable and explainable recommendations, DRSA gained much interest during the years and it is now one of the most appreciated MCDA approaches. In fact, it has been applied also beyond MCDA domain, as a general knowledge discovery and data mining methodology for the analysis of monotonic (and also non-monotonic) data. In this contribution, we recall the basic principles and the main concepts of DRSA, with a general overview of its developments and software. We present also a historical reconstruction of the genesis of the methodology, with a specific focus on the contribution of Roman S{\l}owi\'nski.Comment: This research was partially supported by TAILOR, a project funded by European Union (EU) Horizon 2020 research and innovation programme under GA No 952215. This submission is a preprint of a book chapter accepted by Springer, with very few minor differences of just technical natur

Extension of the fuzzy dominance-based rough set approach using ordered weighted average operators

In the article we rst review some known results on fuzzy versions of the dominance-based rough set approach (DRSA) where we expand the theory considering additional properties. Also, we apply Ordinal Weighted Average (OWA) operators in fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables when it is combined with the indiscernibility-based rough set approach (IRSA).We examine theoretical properties of the proposed combination with fuzzy DRSA