Fuzzy sets and rough sets are known as uncertainty models. They are proposed to treat different aspects of uncertainty. Therefore, it is natural to combine them to build more powerful mathematical tools for treating problems under uncertainty. In this chapter, we describe the state of the art in the combinations of fuzzy and rough sets dividing into three parts. In the first part, we first desc...

To keep the key idea of rough set and the representation of information in rough set theory, empty representation is processed properly and three new forms of rough approximation sets are defined as a generation of general binary relation based rough set model. Moreover, the properties of approximation operators in these new rough sets are discussed. The relations among them are studied in this...

We discuss work of Zdzisław Pawlak in the area of databases and the extension of that work to the theory of rough sets. In particular we look at his motivations for introducing information storage and retrieval systems and how this, eventually, led to rough sets theory.

Rough set theory is a framework of dealing with uncertainty based on computation of equivalence relations/clases. Since a proability is defined as a measure of sample space, defined by equivalence classes, rough sets are closely related with probabilities in the deep level of mathematics. Furthermore, since rough sets are closely related with Demster-Shafer theory or fuzzy sets, this theory can...

Based on rough sets, fuzzy set theory gives a model of information retrieval. "Contains" relationship reflects a match between the set of documents and user queries using fuzzy set theory, and its inclusion degree to achieve the sort of document sets of search results. The use of rough set equivalence relation reflects the correlation between keywords, achieve synonyms retrieve. Compared with t...

Rough sets have been applied in spatial information theory to construct theories of granularity – presenting information at different levels of detail. Mathematical morphology can also be seen as a framework for granularity, and the question of how rough sets relate to mathematical morphology has been raised by Bloch. This paper shows how by developing mathematical morphology in terms of relati...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

Research techniques are often divided into quantitative approaches, concerned with measurement, and qualitative approaches, concerned with meaning. Methodologists have often found it difficult to reconcile this division. However, computational intelligence is directly concerned with capturing meaning in a rigorous form. One commonly used technique is rough sets theory, which analyses an informa...

The conventional rough set theory based on complete information systems stems from the observation that objects with the same characteristics are indiscernible according to available information. Although rough sets theory has been applied in many fields, the use of the indiscernibility relation may be too rigid in some real situations. Therefore, several generalizations of the rough set theory...