This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed. 1 Formulations of Standard Rough Sets The theory of rough sets can be developed in at least two different manners, the constructive and ...

Credit scoring analysis is an important activity, especially nowadays after a huge number of defaults has been one of the main causes of the financial crisis. Among the many different tools used to model credit risk, the recent development of rough set models has proved effective. The original development of rough set theory has been widely generalized and combined with other approaches to unce...

A fuzzy set can be represented by a family of crisp sets using its α-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets....

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

Rough set theory uses the concept of upper and lower approximations to encapsulate inherent inconsistency in real-world objects. Information multisystems are represented using multisets instead of crisp sets. This paper begins with an overview of recent works on multisets and rough sets. Rough multiset is introduced in terms of lower and upper approximations and explores related properties. The...

In the paper, we present a integrated approach combined Rough Set theory and SVM algorithm. The approach udl be divided into two steps. The fust step is classified roughlv with Rough Set, rule should be induced in this step by infonilation system. The second step should ht: classified precisely based on SVM Algorithn~, in this step we present two new fiuidrunental principles to help us select b...

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we llve in consists of problems which fail to fall into this category, i.e. uncertainty is all too common. In this work, we look at a problem which involves uncertainty. To be specific we deal with attributes which are fuzzy sets. Und...

This paper proposes new deenitions of lower and upper approximations which are basic concepts of rough set theory. These deenitions follow naturally from the concepts of ambiguity and deenability introduced in this paper. The new deenitions are compared to the classical deenitions and are shown to be more general in the sense that they are the only ones which can be used for any type of indisce...

The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough...