Implicator-Conjunctor Based Models of Fuzzy Rough Sets: Definitions and Properties

D'eer, Lynn; Verbiest, Nele; Cornelis, Chris; Godo, Lluı́s

doi:10.1007/978-3-642-41218-9_18

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…In [107,108], general conjunctors were considered instead of t-norms. All these different approaches using fuzzy logical connectives are encapsulated in a general implicator-conjunctor fuzzy rough set model [33,34]: let R be a fuzzy relation, I an implicator and C a conjunctor, then the lower and upper approximation of a fuzzy set A are defined by…”

Section: Fuzzy Rough Set Modelsmentioning

confidence: 99%

Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey

Vluymans

D'eer

Saeys

et al. 2015

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Data used in machine learning applications is prone to contain both vague and incomplete information. Many authors have proposed to use fuzzy rough set theory in the development of new techniques tackling these characteristics. Fuzzy sets deal with vague data, while rough sets allow to model incomplete information. As such, the hybrid setting of the two paradigms is an ideal candidate tool to confront the separate challenges. In this paper, we present a thorough review on the use of fuzzy rough sets in machine learning applications. We recall their integration in preprocessing methods and consider learning algorithms in the supervised, unsupervised and semi-supervised domains and outline future challenges. Throughout the paper, we highlight the interaction between theoretical advances on fuzzy rough sets and practical machine learning tools that take advantage of them.

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Section: Fuzzy Rough Set Modelsmentioning

confidence: 99%

Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey

Vluymans

D'eer

Saeys

et al. 2015

Self Cite

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show abstract

“…[4] Let (U, R) be a fuzzy approximation space, A a fuzzy set in U , I an implicator and C a conjunctor. The (I, C)-fuzzy rough approximation of A by R is the pair of fuzzy sets (R↓ I A, R↑ C A) defined by, for x ∈ U , In Table 1, the extensions of the classical rough set properties to a fuzzy approximation space are shown; (U, R), (U, R 1 ) and (U, R 2 ) are fuzzy approximation spaces, A, B andα 3 are fuzzy sets in U , I is an implicator, C a conjunctor, N an involutive negator 4 and R the inverse relation of R, defined by, for x, y ∈ U , R (y, x) = R(x, y).…”

Section: The Ic-modelmentioning

confidence: 99%

“…In addition, approximations by general fuzzy relations are studied, instead of considering fuzzy equivalence relations. All these studies can be covered by a general implicator-conjunctor-based fuzzy rough set model (IC-model), discussed in [4].…”

Section: Introductionmentioning

confidence: 99%

Improving the β-Precision and OWA Based Fuzzy Rough Set Models: Definitions, Properties and Robustness Analysis

D'eer

Verbiest

2014

Lecture Notes in Computer Science

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Abstract. Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and compare them to a general implicator-conjunctor-based fuzzy rough set model.

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“…(The term "implicator" has been extensively used in Fuzzy logic and Fuzzy set theory; see for example [9].) Throughout this paper I denotes the variety of implicator groupoids.…”

Section: Introductionmentioning

confidence: 99%

“…(The term "implicator" has been extensively used in Fuzzy logic and Fuzzy set theory; see for example [9]. )…”

Section: Introductionmentioning

confidence: 99%

On implicator groupoids

Cornejo

Sankappanavar

2017

Algebra Univers.

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In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras-this result led him to introduce, and investigate (in the same paper), the variety I of algebras, there called implication zroupoids (I-zroupoids) and here called implicator gruopids (Igroupoids), that generalize De Morgan algebras.The present paper is a continuation of the paper mentioned above and is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implicator groupoids. Several new subvarieties of I are introduced and their relationship with each other, and with the subvarieties of I which were already investigated in the paper mentioned above, are explored.

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Implicator-Conjunctor Based Models of Fuzzy Rough Sets: Definitions and Properties

Cited by 6 publications

References 28 publications

Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey

Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey

Improving the β-Precision and OWA Based Fuzzy Rough Set Models: Definitions, Properties and Robustness Analysis

On implicator groupoids

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