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Vaguely Quantified Rough Sets [chapter]

Chris Cornelis, Martine De Cock, Anna Maria Radzikowska
2007 Lecture Notes in Computer Science  
The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way.  ...  In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a single element may drastically alter the outcome of the approximations.  ...  To demonstrate that the VQRS construct offers a worthwhile alternative to the traditional "logic"-based operations of fuzzy rough set theory in the context of rough data analysis, we ran an experiment  ... 
doi:10.1007/978-3-540-72530-5_10 fatcat:mrf4nszr7ndjbjrtvk4ohdszpu

Some Relationships Between Fuzzy Sets, Mathematical Morphology, Rough Sets, F-Transforms, and Formal Concept Analysis

Jamal Atif, Isabelle Bloch, Céline Hudelot
2016 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
Links with other lattice-based formalisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.  ...  We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it.  ...  Rough sets with two universes can be interpreted as follows: a set or fuzzy set of objects X is defined in an approximate way by some sets of properties verified by the elements (objects) of X.  ... 
doi:10.1142/s0218488516400080 fatcat:gr7xoaxojza2vpfyamzhfjvq6a

Algebraic Structures for Rough Sets [chapter]

Gianpiero Cattaneo, Davide Ciucci
2004 Lecture Notes in Computer Science  
This structure enables us to define two rough approximations based on a similarity and on a preclusive relation, with the second one always better that the former.  ...  Particular attention is given to HW algebra which is a strong and rich structure able to characterize both rough sets and fuzzy sets. X q q q q q q q q q q q J J J J J J J J J J {1, 2, 9, 11}  ...  The major drawback of this approximation is that the rough approximation based on modal operators is worst than the corresponding one based on the interior -closure operators, in the sense that it captures  ... 
doi:10.1007/978-3-540-27778-1_12 fatcat:lo3xbn3l65favgmbfjdflmapqe

On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets

Jiří Močkoř, David Hýnar
2021 Mathematics  
It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only  ...  The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based  ...  We also prove that both an analogy of Zadeh's extension principle and approximation operators defined for intuitionistic L-fuzzy sets are defined by this monad.  ... 
doi:10.3390/math9040447 fatcat:fe5cq66grrg3pp6ghl65witcdi

Multi-label Attribute Reduction Based on Variable Precision Fuzzy Neighborhood Rough Set

Panpan Chen, Menglei Lin, Jinghua Liu
2020 IEEE Access  
rough set model, and we define its approximation space as follows.  ...  In order to exactly calculate the lower and upper approximation operators of multilabel variable precision neighborhood rough set, we first take a large function and small function to define the fuzzy  ... 
doi:10.1109/access.2020.3010314 fatcat:yh3tpxiqlnfonmufu3574okmva

Rough sets, their extensions and applications

Qiang Shen, Richard Jensen
2007 International Journal of Automation and Computing  
This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets.  ...  Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge.  ...  An arbitrary residuated lattice L is used as a basic algebraic structure, and several classes of L-fuzzy-rough sets, defined using the product operator and its residuum provided by the residuated lattice  ... 
doi:10.1007/s11633-007-0217-y fatcat:lbbdbi5afvdtzadiouwuubillu

On Robust Fuzzy Rough Set Models

Qinghua Hu, Lei Zhang, Shuang An, David Zhang, Daren Yu
2012 IEEE transactions on fuzzy systems  
This theory granulates the universe of discourse into a set of fuzzy concepts based on fuzzy relations, and then approximates arbitrary fuzzy sets with these fuzzy concepts.  ...  Index Terms-rough sets; fuzzy rough sets; model; robustness. I.  ...  Rough sets are introduced to characterize the boundary in approximation. In fuzzy rough sets, operators of fuzzy lower and upper approximations were defined.  ... 
doi:10.1109/tfuzz.2011.2181180 fatcat:ekvcvkvztjffxmdsdge6vwbu64

fuzzy-rough-learn 0.1: A Python Library for Machine Learning with Fuzzy Rough Sets [chapter]

Oliver Urs Lenz, Daniel Peralta, Chris Cornelis
2020 Lecture Notes in Computer Science  
We present fuzzy-rough-learn, the first Python library of fuzzy rough set machine learning algorithms.  ...  We briefly discuss the use cases of fuzzy-rough-learn and the design philosophy guiding its development, before providing an overview of the included algorithms and their parameters.  ...  OWA operators and nearest neighbour searches Each of the algorithms in fuzzy-rough-learn uses OWA operators [20] to calculate upper and lower approximations.  ... 
doi:10.1007/978-3-030-52705-1_36 fatcat:ruhnfbri55fdlgyf2e2molttfa

Soft Sets - Motivation and Overview

B.V.S.T. Sai, P.D.N. Srinivasu, N.V.E.S. Murthy
2019 Global Journal of Pure and Applied Mathematics  
In this paper we present some of the main developments in the soft set theory as well as in the theory of algebraic structures and soft topology as a review of literature motivated by Molodsov.  ...  Aktas-Cagman [5] compared Soft sets to the related concepts of Fuzzy sets and Rough sets. And also defined the notion of soft groups and derived some properties.  ...  In 2001 Maji-Biswas-Roy [50] introduced the notion of fuzzy soft set by fuzzyfying the soft set and defined some basic operations on these sets.  ... 
doi:10.37622/gjpam/15.6.2019.1055-1067 fatcat:q5nvpshfbbdzpgli35cyob3m7u

On rough sets, their recent extensions and applications

N. Mac Parthaláin, Q. Shen
2010 Knowledge engineering review (Print)  
Rough set theory (RST) has enjoyed an enormous amount of attention in recent years and has been applied to many real-world problems including data mining, pattern recognition, and intelligent control.  ...  Typical example application domains are examined which demonstrate the success of the application of RST to a wide variety of areas and disciplines, and which also exhibit the strengths and limitations  ...  The properties of generalized fuzzy-rough sets are investigated in (Wu et al., 2003) , and a pair of dual generalized fuzzy approximation operators are defined based on arbitrary fuzzy relations.  ... 
doi:10.1017/s0269888910000263 fatcat:ta7bxxa34jc5pmsdxwx4nudnwa

Rough approximations of vague sets in fuzzy approximation space

Yonghong Shen, Faxing Wang
2011 International Journal of Approximate Reasoning  
Firstly, the b-operator and its complement operator are introduced, and some new properties are examined. Secondly, the approximation operators are constructed based on b-(complement) operator.  ...  The results show that the proposed rough approximations and roughness measure of a vague set in fuzzy environment are reasonable. Crown  ...  Acknowledgements The authors would like to express their sincere thanks to the editor and two anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the  ... 
doi:10.1016/j.ijar.2010.08.013 fatcat:k3k3b3cjnrbjro4xwv36n5ynyy

Fuzzy Sets: History and Basic Notions [chapter]

Didier Dubois, Walenty Ostasiewicz, Henri Prade
2000 Fundamentals of Fuzzy Sets  
Lastly, a survey of variants of fuzzy sets and related matters is provided.  ...  This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective.  ...  The idea of upper and lower approximations of sets (in terms of approximate covering by equivalence classes), underlying rough sets, can be extended to fuzzy sets.  ... 
doi:10.1007/978-1-4615-4429-6_2 fatcat:sboduqw2l5a4beutph36bfynku

Implementing algorithms of rough set theory and fuzzy rough set theory in the R package "RoughSets"

Lala Septem Riza, Andrzej Janusz, Christoph Bergmeir, Chris Cornelis, Francisco Herrera, Dominik Śle¸zak, José Manuel Benítez
2014 Information Sciences  
Rough set and fuzzy rough set preliminaries In this section, we review some basic notions related to RST and FRST.  ...  The package RoughSets, written mainly in the R language, provides implementations of methods from the rough set theory (RST) and fuzzy rough set theory (FRST) for data modeling and analysis.  ...  ) [118] , soft fuzzy rough sets (SFRS) [35] , robust fuzzy rough sets (RFRS) [37] , and b-precision fuzzy rough sets (b-PFRS) [86] .  ... 
doi:10.1016/j.ins.2014.07.029 fatcat:5l4ivczoavbmnhcgv7dwdsmk6e

A Unified Granular-ball Learning Model of Pawlak Rough Set and Neighborhood Rough Set [article]

Shuyin Xia, Cheng Wang, Guoyin Wang, Weiping Ding, Xinbo Gao, Jianhang Yu, Yujia Zhai, Zizhong Chen
2022 arXiv   pre-print
Pawlak rough set and neighborhood rough set are the two most common rough set theoretical models.  ...  To this end, this paper presents a granular-ball rough set based on the granular-ball computing.  ...  and by NICE: NRT for Integrated Computational Entomology, US NSF award 1631776.  ... 
arXiv:2201.03349v3 fatcat:nbdq2do3pnfivazhmlfbta2wka

Nature-inspired framework for measuring visual image resemblance: A near rough set approach

Sheela Ramanna, Amir H. Meghdadi, James F. Peters
2011 Theoretical Computer Science  
This is accomplished via a near rough set framework in the approximation of a pair of disjoint sets and measurement of distances between sets using various fuzzy pseudometrics.  ...  of fuzzy metrics in content-based image retrieval experiments.  ...  This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) research grants 185986 and 194376, Manitoba Centre of Excellence Fund (MCEF) grant, Canadian  ... 
doi:10.1016/j.tcs.2011.05.044 fatcat:6cbcodbulbcxfdhps7yo5gnxe4
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