# Rough sets

@article{Pawlak1995RoughS, title={Rough sets}, author={Zdzisa̵w Pawlak}, journal={International Journal of Computer \& Information Sciences}, year={1995}, volume={11}, pages={341-356} }

We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy sets theory and tolerance theory. Some applications are outlined.

## 1,361 Citations

### On the Measure of Many-Level Fuzzy Rough Approximation for L-Fuzzy Sets

- Computer Science, MathematicsComputational Intelligence and Mathematics for Tackling Complex Problems
- 2019

A many-level version of L-fuzzy rough approximation operators is introduced and measures of approximation obtained by such operators are defined, which characterize the quality of the resulting approximation.

### Fuzzy preorder based fuzzy rough sets using multiplication and division

- Computer ScienceJournal of Intelligent & Fuzzy Systems
- 2022

This paper constructs a kind of fuzzy rough set model based on the multiplication and division of real numbers and the definable sets and the related fuzzy topology are studied.

### Three-way decisions in fuzzy incomplete information systems

- Computer ScienceInt. J. Mach. Learn. Cybern.
- 2020

The intuitionistic fuzzy set is introduced to fuzzy incomplete information systems, the membership and non-membership degrees that an object belongs to a concept are constructed based on the…

### Rough approximation of a fuzzy set in semigroups based on soft relations

- Computer ScienceComput. Appl. Math.
- 2019

This paper focuses on a fuzzy set which is approximated in the sense of the aftersets and foresets, and a soft binary relation has been used to get two sets of fuzzy soft sets, called the lower approximation and upper approximation regarding the afterset and foreset.

### Overview of Rough Set Theory

- Computer Science, PhilosophyIntelligent Systems Reference Library
- 2019

This chapter overviews rough set theory and gives an exposition of algebras for rough set Theory, and considers logics for reasoning about knowledge and Logics for knowledge representation.

### Generalizations of rough sets via topology

- Computer Science
- 2020

This paper introduces several concepts and properties of $$\tau -R$$ τ - R -open sets and uses topology to generalize the basic rough set concepts and study their properties.

### On rough sets induced by fuzzy relations approach in semigroups

- Mathematics, Computer ScienceOpen Mathematics
- 2018

A rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation is introduced, and some interesting properties are investigated.

### Approximations of ∈ , ∈ ∨ q

- Mathematics
- 2021

This paper concerns the relationship between rough sets, - fuzzy sets, and the LA-semihypergroups. We proved that the lower approximation ( - approx) and the upper approximation ( - approx) of…

### A characterization of novel rough fuzzy sets of information systems and their application in decision making

- Computer ScienceExpert Syst. Appl.
- 2019

### Introduction to Fuzzy Sets and Logic

- PsychologyNeural Networks and Statistical Learning
- 2019

In many soft sciences (e.g., psychology, sociology, ethology), scientists provide verbal descriptions and explanations of various phenomena based on observations.

## References

SHOWING 1-10 OF 63 REFERENCES

### Rough sets. Algebraic and topological approach

- Computer Science
- 1982

This paper presents a meta-analysed version of the model derived from the model developed in the second edition of the ICS PAS Reports in 1982, showing the architecture of the Celada–Seiden cellular automaton and its role in the simulation of disease.

### Rough sets and information systems

- Computer Science
- 1988

This paper presents a meta-analysed version of the model derived from the simulation of the response of the immune system to the attacks of infectious disease.

### Rough membership functions

- Mathematics
- 1994

W: R. Yaeger, M. Fedrizzi, and J. Kacprzyk, editors, Advances in the Dempster-Shafer Theory of Evidence, pages 251-271. John Wiley and Sons, Inc., New York, NY, 1994

### Discriminant versus rough sets approach to vague data analysis

- Computer Science
- 1992

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data using the location model method from the field of discriminant analysis and a method based on rough sets theory.

### Knowledge acquisition under uncertainty — a rough set approach

- Computer ScienceJ. Intell. Robotic Syst.
- 1988

The paper describes knowledge acquisition under uncertainty using rough set theory, a concept introduced by Z. Pawlak in 1981, and shows that some classifications are theoretically (and, therefore, in practice) forbidden.

### The Discernibility Matrices and Functions in Information Systems

- Computer ScienceIntelligent Decision Support
- 1992

Two notions related to any information system, namely the discernibility matrix and discernibility function, are introduced and several algorithms for solving problems related among other things to the rough definability, reducts, core and dependencies generation are obtained.

### Rough Sets, Fuzzy Sets and Knowledge Discovery

- Computer ScienceWorkshops in Computing
- 1994

An Overview of Knowledge Discovery in Databases: Recent Progress and Challenges.- Rough Sets and Knowledge Discovery: An Overview.- Search for Concepts and Dependencies in Databases.- Rough Sets and…

### Intelligent Decision Support

- Computer ScienceTheory and Decision Library
- 1992

The paper presents the system LERS for rule induction, which computes lower and upper approximations of each concept and induces certain rules and possible rules that can be induced from the input data.

### INFORMATION SYSTEMS THEORETICAL FOUNDATIONS

- Computer Science

A certain mathematical model for attribute based information systems is proposed and investigated in this Group and a new formulation of the discussed model is used and some new problems are state.

### LERS-A System for Learning from Examples Based on Rough Sets

- Computer ScienceIntelligent Decision Support
- 1992

The paper presents the system LERS for rule induction, which handles inconsistencies in the input data due to its usage of rough set theory principle and induces all rules, each in the minimal form, that can be induced from the inputData.