New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (RST) and to represent rough semantics. The foundations of the theory also rely upon the axiomatic approach to granularity for all types of general RST recently developed by the...

KEY WORDS Contextual spaces, context relation, contextual rough sets, elements of a contextual rough set, the counterpart of the axiom of extensionality. ABSTRACT This paper originates from the conceptions of rough sets presented by Pawlak (1982, 1992). It also refers to Ziarko's conception (1993) and the conceptions of Blizard's multisets (1989a, 1989b), Zadeh's fuzzy sets (1965), and the auth...

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algor...

Theories of soft sets and rough sets are two different approaches to vagueness. A possible fusion of rough sets and soft sets is proposed by F.Feng et al. They introduce the concept of soft rough sets, where parametrized subsets of a universe set are basic building blocks for lower and upper approximations of a subset. In the present paper, a new approach is being introduced to study roughness ...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

Rough set theory is introduced into linear υ support vector machine (svm), and rough marginbased linear υ svm is proposed in this paper. By constructing rough lower margin, rough upper margin and rough boundary in linear υ svm, then we maximize the rough margin not margin in linear υ svm. Thus more points are considered in constructing the separating hyper-plane than those used in linear υ svm....

The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is...

In the present paper, we concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In...

As an alternative to the price-based traditional auction model, the multi-attribute auction model is an integrated model requiring the simultaneous trade of different types of attributes as the sellers and buyers deal. As a result, the design and modeling of the auction mechanism have become very difficult. This paper proposes a multiattribute auction model using the dominance-based rough sets ...