# Generalizations of Rough Sets: From Crisp to Fuzzy Cases

@inproceedings{Inuiguchi2004GeneralizationsOR, title={Generalizations of Rough Sets: From Crisp to Fuzzy Cases}, author={Masahiro Inuiguchi}, booktitle={Rough Sets and Current Trends in Computing}, year={2004} }

Rough sets can be interpreted in two ways: classification of objects and approximation of a set. In this paper, we discuss the differences and similarities of generalized rough sets based on those two different interpretations. We describe the relations between generalized rough sets and types of extracted decision rules. Moreover, we extend the discussion to fuzzy rough sets. Through this paper, the relations among generalized crisp rough sets and fuzzy rough sets are clarified and two…

## 19 Citations

Determining Significance of Attributes in the Unified Rough Set Approach

- Computer ScienceRSFDGrC
- 2007

The problems arising in applications of the unified rough and fuzzy rough set approach to analysis of inconsistent information systems are discussed and a generalized definition of the fuzzy extension i¾?is proposed.

Fuzzy-Rough Hybridization

- Computer ScienceHandbook of Computational Intelligence
- 2015

This chapter describes the state-of-the-art in the combinations of fuzzy and rough sets dividing into three parts.

An Approach to Parameterized Approximation of Crisp and Fuzzy Sets

- Computer ScienceRSCTC
- 2006

The presented parameterized approach to approximation constitutes an easy to implement, straightforward generalization of the variable precision crisp and fuzzy rough set model.

Variable Precision Fuzzy Rough Set Model with Linguistic Labels

- Computer Science2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
- 2020

This paper presents an approach which combines unified variable precision fuzzy rough set model together with the concept of fuzzy linguistic labels, which can be used to determine the quality of the considered information system by evaluating its consistency, and to obtain a system of fuzzy decision rules.

Approximation-oriented Fuzzy Rough Set Approaches

- Computer ScienceFundam. Informaticae
- 2015

This paper defines fuzzy rough set models in the approximation aspect, investigates their fundamental properties and demonstrates the advantages of fuzzy set approximation, and considers attribute r eduction based on the proposed fuzzy roughSet models.

Upper and Lower Probabilities of Fuzzy Events Induced by a Fuzzy Set-Valued Mapping

- Computer ScienceRSFDGrC
- 2005

A fuzzy set-valued mapping defines a pair of upper and lower fuzzy rough approximations that carry a probability measure defined over subsets of U into a system of higher and lower probabilities over subset of W.

Variable precision rough set model over two universes and its properties

- Computer ScienceSoft Comput.
- 2011

This paper firstly proposes the variable precision rough set model (VPRS-model) over two universes using the inclsion degree, and the concepts of the reverse lower and upper approximation operators are presented.

On Representation and Analysis of Crisp and Fuzzy Information Systems

- Computer ScienceTrans. Rough Sets
- 2007

This paper proposes an approach to representation and analysis of information systems with fuzzy attributes, which combines the variable precision fuzzy rough set (VPFRS) model with the fuzzy flow…

On Rough Fuzzy Set Algebras

- Computer ScienceFSKD
- 2006

It is proved that if a system $({\cal F}(U), \cap, \cup, \sim, L, H)$ is a (a serial, a reflexive, a symmetric, a transitive, an Euclidean, a Pawlak, respectively) rough fuzzy set algebra then the derived system is a rough fuzzySet algebras.

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