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Book ChapterDOI

Fuzzy-Rough Hybridization

TL;DR: This chapter describes the state-of-the-art in the combinations of fuzzy and rough sets dividing into three parts.
Abstract: Fuzzy sets and rough sets are known as uncertainty models. They are proposed to treat different aspects of uncertainty. Therefore, it is natural to combine them to build more powerful mathematical tools for treating problems under uncertainty. In this chapter, we describe the state-of-the-art in the combinations of fuzzy and rough sets dividing into three parts.

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Citations
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01 Jun 2005

3,154 citations

Book
23 Mar 2003
TL;DR: Qualitative Decision Rules under Uncertainty Applications of Latent Class Analysis in Social Science Research and Foundations of Unc uncertainty Concepts.
Abstract: Invited Papers.- Qualitative Decision Rules under Uncertainty.- Applications of Latent Class Analysis in Social Science Research.- Foundations of Uncertainty Concepts.- Transformations from Imprecise to Precise Probabilities.- A Representation Theorem and Applications.- On Modal Probability and Belief.- Bayesian Networks.- A Multi-layered Bayesian Network Model for Structured Document Retrieval.- Using Kappas as Indicators of Strength in Qualitative Probabilistic Networks.- Qualitative Bayesian Networks with Logical Constraints.- Introducing Situational Influences in QPNs.- Classification of Aerial Missions Using Hidden Markov Models.- Algorithms for Uncertainty Inference.- Dynamic Importance Sampling Computation in Bayesian Networks.- Morphing the Hugin and Shenoy-Shafer Architectures.- Learning.- Characterization of Inclusion Neighbourhood in Terms of the Essential Graph: Upper Neighbours.- Approximating Conditional MTE Distributions by Means of Mixed Trees.- Effective Dimensions of Partially Observed Polytrees.- Decision Graphs.- Applying Numerical Trees to Evaluate Asymmetric Decision Problems.- Mixed Influence Diagrams.- Decision Making Based on Sampled Disease Occurrence in Animal Herds.- Decision Network Semantics of Branching Constraint Satisfaction Problems.- Belief Functions.- Web of Trust: Applying Probabilistic Argumentation to Public-Key Cryptography.- A Comparison of Methods for Transforming Belief Function Models to Probability Models.- Fuzzy Matching and Evidential Reasoning.- Modeling Positive and Negative Pieces of Evidence in Uncertainty.- Directed Evidential Networks with Conditional Belief Functions.- Computational-Workload Based Binarization and Partition of Qualitative Markov Trees for Belief Combination.- Risk Assessment in Drinking Water Production Using Belief Functions.- Algebraic Structures Related to the Consensus Operator for Combining of Beliefs.- Fuzzy Sets.- Inclusion Measures in Intuitionistic Fuzzy Set Theory.- A Random Set Model for Fuzzy Labels.- On the Induction of Different Kinds of First-Order Fuzzy Rules.- Reasoning under Vagueness Expressed by Nuanced Statements.- Possibility Theory.- Partial Lattice-Valued Possibilistic Measures and Some Relations Induced by Them.- Coherent Conditional Probability as a Measure of Uncertainty of the Relevant Conditioning Events.- Decision Trees and Qualitative Possibilistic Inference: Application to the Intrusion Detection Problem.- Default Reasoning.- Multi-valued Conditional Events Avoid Lewis' Triviality Result.- Solving Semantic Problems with Odd-Length Cycles in Argumentation.- On the Relation between Reiter's Default Logic and Its (Major) Variants.- Belief Revision and Inconsistency Handling.- Probable Consistency Checking for Sets of Propositional Clauses.- On Iterated Revision in the AGM Framework.- Epistemic Logics for Information Fusion.- Logics.- Propositional Fusion Rules.- Preferential Logics for Reasoning with Graded Uncertainty.- Paraconsistent Reasoning via Quantified Boolean Formulas, II: Circumscribing Inconsistent Theories.- Modal (Logic) Paraconsistency.- A Formal Framework for Handling Conflicting Desires.- A Sequent Calculus for Skeptical Reasoning in Predicate Default Logic (Extended Abstract).- Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding.- Demo Papers.- ABEL: An Interactive Tool for Probabilistic Argumentative Reasoning.- The Hugin Tool for Learning Bayesian Networks.

73 citations

Proceedings ArticleDOI
01 Jan 1970
TL;DR: The operation of the National Crime Information Center (NCIC) was presented and its effectiveness was clearly demonstrated by some case histories.
Abstract: Mr. Roderick presented the operation of the National Crime Information Center (NCIC). Its effectiveness is clearly demonstrated by some case histories.

56 citations

Journal ArticleDOI
01 Jan 2018
TL;DR: This work proposes automatic support vector data description (ASVDD) based on both validation degree, which is originated from fuzzy rough set to discover data characteristic, and assigning effective values for tuning parameters by chaotic bat algorithm, and demonstrates superiority of the proposed method over state-of-the-art ones in terms of classification accuracy and AUC.
Abstract: Event handlers have wide range of applications such as medical assistant systems and fire suppression systems. These systems try to provide accurate responses based on the least information. Support vector data description (SVDD) is one of the appropriate tools for such detections, which should handle lack of information. Therefore, many efforts have been done to improve SVDD. Unfortunately, the existing descriptors suffer from weak data characteristic in sparse data sets and their tuning parameters are organized improperly. These issues cause reduction of accuracy in event handlers when they are faced with data shortage. Therefore, we propose automatic support vector data description (ASVDD) based on both validation degree, which is originated from fuzzy rough set to discover data characteristic, and assigning effective values for tuning parameters by chaotic bat algorithm. To evaluate the performance of ASVDD, several experiments have been conducted on various data sets of UCI repository. The experimental results demonstrate superiority of the proposed method over state-of-the-art ones in terms of classification accuracy and AUC. In order to prove meaningful distinction between the accuracy results of the proposed method and the leading-edge ones, the Wilcoxon statistical test has been conducted.

44 citations

Journal ArticleDOI
01 Apr 2018
TL;DR: Internal evaluations show that in contrast to state-of-the-art algorithms, FRS-WRD achieves better results in terms of G-mean 95%, Jaccard 88%, entropy 0.36, and finally, purity 96%.
Abstract: Despite emerging of Web 2.0 applications and increasing requirements to well-behaved Web robots, malicious ones can reveal irreparable risks for Web sites. Regardless of behavior of Web robots, they may occupy bandwidth and reduce performance of Web servers. In spite of many prestigious researches trying to characterize Web visitors and classify them, there is a lack of concentration on feature selection to dynamically choose attributes used to describe Web sessions. On the other hand, depending on an accurate clustering technique, which can deal with huge number of samples in a reasonable amount of time, is practically important. Therefore, in this paper, a new algorithm, fuzzy rough set–Web robot detection (FRS-WRD), is proposed based on fuzzy rough set theory to better characterize and cluster Web visitors of three real Web sites. External evaluations show that in contrast to state-of-the-art algorithms, FRS-WRD achieves better results in terms of G-mean 95%, Jaccard 88%, entropy 0.36, and finally, purity 96%. Moreover, according to confusion matrixes, it can better detect malicious Web visitors.

37 citations

References
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Book
01 Jan 1976
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Abstract: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.

14,565 citations


"Fuzzy-Rough Hybridization" refers background or methods in this paper

  • ...Another important method used to deal with uncertainty in intelligent systems is the Dempster-Shafer theory of evidence [27]....

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  • ...When U is finite, a CC-belief function can be equivalently defined as a monotone Choquet capacity [60] on U which satisfies the following properties [27]: (MC1) Bel(∅) = 0, (MC2) Bel(U) = 1, (MC3) for all Xi ∈ P(U), i = 1, 2, ....

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Book
31 Oct 1991
TL;DR: Theoretical Foundations.
Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.

7,826 citations

Journal ArticleDOI
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of a fichier do not necessarily imply a mention of copyright.
Abstract: © Annales de l’institut Fourier, 1954, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

4,135 citations


"Fuzzy-Rough Hybridization" refers background in this paper

  • ...When U is finite, a CC-belief function can be equivalently defined as a monotone Choquet capacity [60] on U which satisfies the following properties [27]: (MC1) Bel(∅) = 0, (MC2) Bel(U) = 1, (MC3) for all Xi ∈ P(U), i = 1, 2, ....

    [...]

01 Jun 2005

3,154 citations


"Fuzzy-Rough Hybridization" refers methods in this paper

  • ...More recently, fuzzy rough sets have been applied to identify imprecision in temporal database models [137, 138]....

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Journal ArticleDOI
TL;DR: 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.
Abstract: The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, 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. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribut...

2,452 citations


"Fuzzy-Rough Hybridization" refers background or methods in this paper

  • ...Those definitions of lower and upper approximations have been proposed by Dubois and Prade [4, 5] and Radzikowska and Kerre [9]....

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  • ...(8) Those definitions of lower and upper approximations have been proposed by Dubois and Prade [4, 5] and Radzikowska and Kerre [9]....

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  • ...The fundamental properties of fuzzy rough sets have been investigated by Dubois and Prade [4, 5] and Radzikowska and Kerre [9]....

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  • ...Fuzzy rough sets were originally proposed by Nakamura [3] and by Dubois and Prade [4, 5]....

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  • ...The other many researchers [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23] generalized an equivalence relation to a fuzzy binary relation or a family of fuzzy sets....

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What is rough fuzzy hybridization?

The paper does not provide a direct explanation of rough fuzzy hybridization.