The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to amulti-granulation rough set model (MGRS), where the set approximations a...

In this paper, lower/upper, boundary, and negative regions of set approximations, the fundamental concepts of classical rough set theory, have been considered as primitive ones. Assuming that they are independent of each other, a generalized framework for their investigations is outlined. Its main building blocks are base sets and definable sets. Lower/upper approximations, boundaries and negat...

Rough sets theory is a method to represent, analyze, and manipulate knowledge in an information table. To remove superfluous attributes without changing the original knowledge, reduction is a must in rough sets. The process of finding all reducts has been proven to be NP-hard. In order to find an efficient method to generate all reducts, this paper develops the pseudo consistency method. Simula...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

The decision theory is defined typically as the combination of utility theory and probability theory. In this paper we generalize the decision theory as the performance measure theory and uncertainty theory. Intelligent agents look for approximate optimal decisions under bounded resources and uncertainty. The $-calculus process algebra for problem solving applies the cost performance measures t...

Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T -rough semiprime ideal, T -rough fuzzy semiprime ideal and T -rough quotient ideal in a commutative rin...

There exists a direct relation between fuzzy rough sets and fuzzy preorders. On the other hand, it is well known the existing parallelism between Formal Concept Analysis and Rough Set Theory. In both cases, Galois connections play a central role. In this work, we focus on adjunctions (also named isotone Galois connections) between fuzzy preordered sets; specifically, we study necessary conditio...

Constructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In order to understand intuitively the relationships between these two theories, we study this probl...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...