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}
}
  • M. Inuiguchi
  • Published in
    Rough Sets and Current Trends…
     1 June 2004
  • Computer Science
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… 
View via Publisher
gbv.de
19 Citations
Background Citations
5

19 Citations

Citation Type

Citation Type

Determining Significance of Attributes in the Unified Rough Set Approach
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
Fuzzy rough approximations of process data
Upper and Lower Probabilities of Fuzzy Events Induced by a Fuzzy Set-Valued Mapping
TLDR
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
TLDR
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
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
TLDR
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.
...
1
2
...

References

SHOWING 1-10 OF 20 REFERENCES
Two Directions toward Generalization of Rough Sets
TLDR
Two interpretations of rough sets are introduced: rough sets as distinction among positive, negative and boundary regions and rough set as approximations by means of elementary sets and the differences of the extracted if-then rules by the rough set interpretations.
Rough Sets and Gradual Decision Rules
We propose a new fuzzy rough set approach which, differently from all known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication).…
Putting Rough Sets and Fuzzy Sets Together
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…
New Fuzzy Rough Sets Based on Certainty Qualification
TLDR
Rough sets were originally defined in the presence of an equivalence relation and defined under an ordering relation and showed the importance of their approach in multicriteria decision making problems.
A Generalized Definition of Rough Approximations Based on Similarity
TLDR
New definitions of lower and upper approximations are proposed, which are basic concepts of the rough set theory and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.
The Use of Rough Sets and Fuzzy Sets in MCDM
TLDR
The main change is the substitution of the indiscernibility relation by a dominance relation (crisp or fuzzy), which permits approximation of ordered sets in multicriteria sorting and exploitation procedures of the set of decision rules.
ROUGH FUZZY SETS AND FUZZY ROUGH SETS
TLDR
It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
Function Approximation by Fuzzy Rough Sets
Two views of the theory of rough sets in finite universes
  • Yiyu Yao
  • Computer Science
    Int. J. Approx. Reason.
  • 1996
Generalization of Rough Sets using Modal Logics
TLDR
A number of extended rough set models are proposed and examined based on the properties satisfied by a binary relation, such as serial, reflexive, symmetric, transitive, and Euclidean, which correspond to different modal logic systems.
...
1
2
...