In this paper we focus upon a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to any binary reflexive relation. We aim at finding the best of several candidates for generalized rough approximation mappings, where both definability of sets by elementary granules of information as well as the issue of distinction among posi...

Induction of decision rules within the dominance-based rough set approach to the multiple-criteria sorting decision problem is discussed in this paper. We introduce an algorithm called DOMLEM that induces a minimal set of generalized decision rules consistent with the dominance principle. An extension of this algorithm for a variable consistency model of dominance based rough set approach is al...

The graded rough set and multi-granulation rough set are two significant generalized rough set models which be constructed on the indiscernibility relation. They solve the issues that the degree of overlap between the equivalence class and basic set in different view points of quantitative information. The purpose of this study is that research the good points of graded rough set in the multi-g...

The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

A calculus of typed relations subsuming the classical relational database theory is presented. An associated sound and complete deduction mechanism is developed. The formulation is generalized to deal with nondeterministic databases and information relations in the rough set-style. keywords: relational logic, typed relations, relational database, nondeterministic databases, information relation...

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft coveri...

Dominance-based Rough Set Approach (DRSA) has been proposed to deal with multi-criteria classification problems, where data may be inconsistent with respect to the dominance principle. However, in real-life datasets, in the presence of noise, the notions of lower and upper approximations handling inconsistencies were found to be excessively restrictive which led to the proposal of the variable ...

This paper proposes a generalized definition of rough set approximations, based on a subsystem of subsets of a universe. The subsystem is not assumed to be closed under set complement, union and intersection. The lower or upper approximation is no longer one set but composed of several sets. As special cases, approximations in formal concept analysis and knowledge spaces are examined. The resul...