This paper introduces a neural network architecture based on rough sets and rough membership functions. The neurons of such networks instantiate approximate reasoning in assessing knowledge gleaned from input data. Each neuron constructs upper and lower approximations as an aid to classifying inputs. Rough neuron output has various forms. In this paper, rough neuron output results from the appl...

This paper introduces the intuitionistic rough set and intuitionistic rough relational and rough object oriented database models. Rough set, fuzzy set, and intuitionistic set uncertainty management are discussed and compared, and the model based on intuitionistic and rough sets developed here is applied to databases. The intuitionistic rough set database models draw benefits from both the rough...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

Many researchers have combined rough set theory and fuzzy set theory in order to easily approach problems of imprecision and uncertainty. Covering-based rough sets are one of the important generalizations of classical rough sets. Naturally, covering-based fuzzy rough sets can be studied as a combination of covering-based rough set theory and fuzzy set theory. It is clear that Pawlak’s rough set...

The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterize...

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...

In generalized rough set covering reduction theory, it is necessary to find a new measure to knowledge and rough set because the upper and lower approximations of rough sets are determined by their covering reduction. In this paper, information entropy is introduced to discuss the rough entropy of knowledge and the roughness of rough set, based on generalized rough set covering reduction. A new...

Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering-based rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as subbase, neighborhood and separation axioms have bee...

The concept, rough truth, is first presented in rough logic. It is a logical value, and lies between truth and falsity. By combining rough logic with modal logic, rough validity of the rough axioms is studied in this paper, which has close links with the logical value: rough truth. Because an axiom of modal logic corresponds to a rough axiom, the study of this paper actually focuses on the anal...

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...