Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets,...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

Decision table reduction in KDD refers to the problem of selecting those input feature values that are most predictive of a given outcome by reducing a decision table like database from both vertical and horizontal directions. Fuzzy rough sets has been proven to be a useful tool of attribute reduction (i.e. reduce decision table from vertical direction). However, relatively less researches on d...

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classic...

This paper examines two interval based uncertain reasoning methods, one is based on interval fuzzy sets, and the other is based on rough sets. The notion of interval triangular norms is introduced. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are addressed. Inference rules are given for using both numeric intervals and lattice based intervals. The theory...

Structure of Rough Approximations Based on Molecular Lattices p. 69 Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Base...

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...

In this paper we define rough intuitionistic fuzzy sets (analogous to the definition of rough fuzzy sets introduced by Dubois and Prade [8] ) and study their properties. Some propositions in this notion are proved.

Intuitionistic fuzzy rough sets are investigated in a general framework which includes generalizations of many related results in early literatures. A new definition of intuitionistic fuzzy rough sets is given with the analysis of its basic properties based on the notion of two universes, general binary relations, and a pair ðT , IÞ of intuitionistic fuzzy t-norm T and intuitionistic fuzzy impl...

Algebraic structures and lattice structures of rough sets are basic and important topics in rough sets theory. In this paper we pointed out that a basic problem had been overlooked, that is the closeness of union and intersection operations of rough approximation pairs, i.e. (lower approximation, upper approximation). We present that the union and intersection operations of rough approximation ...