Probabilistic approaches have been applied to the theory of rough set in several forms, including decision-theoretic analysis, variable precision analysis, and information-theoretic analysis. Based on rough membership functions and rough inclusion functions, we revisit probabilistic rough set approximation operators and present a critical review of existing studies. Intuitively, they are define...

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we defne concepts of Rough Neutrosophic algebra and investigate some of their properties.

This paper presents a method for updating approximations of a concept incrementally. The results can be used to implement a quasi-incremental algorithm for learning classification rules from very large data bases generalized by dynamic conceptual hierarchies provided by users. In general, the process of attribute generalization may introduce inconsistency into a generalized relation. This issue...

“Our claim is that knowledge is deep–seated in the classificatory abilities of human beings and other species. For example, knowledge about the environment is primarily manifested as an ability to classify a variety of situations from the point of view of survival in the real world : : : Classification on more abstract levels, seems to be a key issue in reasoning, learning and decision making, ...

Bipolar neutrosophic set theory and rough neutrosophic set theory are emerging as powerful tool for dealing with uncertainty, and indeterminate, incomlete, and inprecise information. In the present study we develop a hybrid structure called “rough bipoar neutrsophic set”. In the study, we define rough bipoar neutrsophic set and define union, complement, intersection and containment of rough bip...

In this paper, we propose a new rough set classifier induced from partially uncertain decision system. The proposed classifier aims at simplifying the uncertain decision system and generating more significant belief decision rules for classification process. The uncertainty is reperesented by the belief functions and exists only in the decision attribute and not in condition attribute values.

In rough set theory, the multiplicity of methods calculating neighborhood systems is very useful to calculate measures accuracy and roughness. line with this research direction, in article we present novel kinds inspired by system maximal systems. We benefit from symmetry between approximations (lower upper) topological operators (interior closure) structure current generalized approximation sp...

This paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized approximation operators is defined. The connections between fuzzy relations and fuzzy rough approximation operators are examined. In axiomatic approach, various classes of fuzzy rough approximation...