# Rough fuzzy sets and fuzzy rough sets pdf

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- Fuzzy rough sets with a fuzzy ideal
- Rough Atanassov's Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications
- Putting Rough Sets and Fuzzy Sets Together

*Li, F. L-valued Fuzzy Rough Sets.*

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Thiele Published By replacing this equivalence relation by an arbitrary binary relation satisfying certain properties, for instance, reflexivity and transitivity we shall obtain generalized crisp!! Our ideas in the paper are: 1.

## Fuzzy rough sets with a fuzzy ideal

Recently, much attention has been given to the rough set models based on two universes. And many rough set models based on two universes have been developed from different points of view. In this paper, a novel model, that is, rough Atanassov's intuitionistic fuzzy sets model over two different universes, is firstly proposed from Atanassov's intuitionistic point of view. We study some important properties of approximation operators and investigate the rough degree in the novel model. Furthermore, an illustrated example is employed to demonstrate the conceptual arguments of the model. Finally, rough Atanassov's intuitionistic fuzzy sets approach to decision is presented in the generalized approximation space over two universes by considering the problem about how to arrange patients to see the doctor reasonably, from which it can be found that the method is valuable and useful in real life.

## Rough Atanassov's Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications

Metrics details. Fuzzy ideal approximation connectedness and the fuzzy ideal approximation continuity between fuzzy ideal approximation spaces are introduced. The notion of rough sets was given by Pawlak [ 1 ] referring to uncertainty of intelligent systems characterized by insufficient and incomplete information. Basically, rough sets are defined depending on some equivalence relation R on a universal finite set X. The pair X , R was called an approximation space based on an equivalence relation imposed on X. In any approximation space, the notions of lower approximation, upper approximation, and boundary region operators of some subset could be induced. On the other hand, the relationships between rough sets and topological spaces were studied in [ 2 ].

## Putting Rough Sets and Fuzzy Sets Together

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Fuzzy Rough Sets: The Forgotten Step Abstract: Traditional rough set theory uses equivalence relations to compute lower and upper approximations of sets. The corresponding equivalence classes either coincide or are disjoint.

Intelligent Decision Support pp Cite as. In this paper we argue that fuzzy sets and rough sets aim to different purposes and that it is more natural to try to combine the two models of uncertainty vagueness for fuzzy sets and coarseness for rough sets in order to get a more accurate account of imperfect information. First, the upper and lower approximations of a fuzzy set are defined, when the universe of discourse of a fuzzy sets is coarsened by means of an equivalence relation. Another idea is to turn the equivalence relation relation into a fuzzy similarity relation, for a more expressive modeling of coarseness.

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