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### Fuzzy Reasoning and Rough Sets [chapter]

T. Y. Lin
1994 Rough Sets, Fuzzy Sets and Knowledge Discovery
As in [2] , [3] , [4] , rough set theory, fuzzy logic control, and modern differential geometric view of non-linear dynamic systems are integrated into one mathematical formalism, called rough logic  ...  To avoid monotonous, we use space, collection, and family as synonym for set. Rough Sets Let U be an non-empty set, called the universe.  ...

### Axiomatic systems for rough sets and fuzzy rough sets

Guilong Liu
2008 International Journal of Approximate Reasoning
By this approach, we propose a unified lower approximation axiomatic system for Pawlak's rough sets and fuzzy rough sets.  ...  Rough set theory is an important tool for approximate reasoning about data. Axiomatic systems of rough sets are significant for using rough set theory in logical reasoning systems.  ...  This work is partially supported by the Key Project of Chinese Ministry of Education and the Project of Beijing Language and Culture University.  ...

### Rough Sets and Boolean Reasoning [chapter]

Andrzej Skowron
2001 Studies in Fuzziness and Soft Computing
In this article, we discuss methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis.  ...  Many thanks to Professors James Peters, Dominik Ś le ßzak, and Anna Gomoliń ska for their incisive comments and for suggesting many helpful ways to improve this article.  ...  Acknowledgement The research of Andrzej Skowron has been supported by the grant 3 T11C 002 26 from Ministry of Scientific Research and Information Technology of the Republic of Poland.  ...

### Advances in fuzzy sets and rough sets

Francesco Masulli, Alfredo Petrosino
2006 International Journal of Approximate Reasoning
In the second, Rough Fuzzy Set Based Scale Space Transforms and Their Use in Image Analysis by Petrosino et al., a scale-scale method based on the hybrid notion of rough fuzzy sets to extract relevant  ...  In the former, Fuzzy rough sets and multiple-premise gradual decision rules, Greco et al. present a new fuzzy rough set approach able to infer the most cautious conclusions from available imprecise information  ...

### Reasoning within expressive fuzzy rough description logics

Yuncheng Jiang, Ju Wang, Peimin Deng, Suqin Tang
2009 Fuzzy sets and systems (Print)
An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory.  ...  It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.  ...  Classical fuzzy rough sets It is well known that the main difference between classical fuzzy rough set theory [18] and generalized fuzzy rough set theory [52, 67] is as follows: in classical fuzzy  ...

### Approximate Reasoning Based on Rough Sets and Probability Theory

2001 Journal of Japan Society for Fuzzy Theory and Systems
「 Approximate Reasoning Based on Rough Sets and Probability Theory 」 111 内 ゆ か り ［ 博士 ( 理 学 ) 2001年 3 月 取 得 ( 明 治 大 学 ) ］ キ ー ワ ー ド ： ラ フ 集合， 確 率 推 論 ， Bayes の 定 理 〈要 約 〉 本 研 究 で は ，近 年 人 工 知 能 分 野 で 必  ...

### Fuzzy rough sets and multiple-premise gradual decision rules

Salvatore Greco, Masahiro Inuiguchi, Roman Slowinski
2006 International Journal of Approximate Reasoning
We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication).  ...  The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules.  ...  The third author wishes to acknowledge financial support from the Ministry of Scientific Research and Information Technology.  ...

### Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems

Min Liu, Degang Chen, Cheng Wu, Hongxing Li
2006 Computers and Mathematics with Applications
At last, we apply the fuzzy reasoning based on the new fuzzy rough set to the scheduling problems, and numerical computational results show that the fuzzy reasoning based on the new fuzzy rough set is  ...  In this paper, we study the fuzzy reasoning based on a new fuzzy rough set.  ...  FUZZY REASONING BASED ON A NEW FUZZY ROUGH SET B~ed on the lower and upper approximation operators in Section 3, we propose the fuzzy reasoning based on the new fuzzy rough set in this section.  ...

### Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection

Chris Cornelis, Jesús Medina, Nele Verbiest
2014 International Journal of Approximate Reasoning
This paper introduces a flexible extension of rough set theory: multi-adjoint fuzzy rough sets, in which a family of adjoint pairs are considered to compute the lower and upper approximations.  ...  This new setting increases the number of applications in which rough set theory can be used.  ...  In Section 2, we recall preliminaries from rough sets, fuzzy rough sets and multi-adjoint property-oriented concept lattices.  ...

### Weighted Generalized Fuzzy Petri Nets and Rough Sets for Knowledge Representation and Reasoning [chapter]

Zbigniew Suraj, Aboul Ella Hassanien, Sibasis Bandyopadhyay
2020 Lecture Notes in Computer Science
Our approach is based on rough set theory and weighted generalized fuzzy Petri nets.  ...  We construct an algorithm for executing a highly parallel program represented by a fuzzy Petri net from a given decision table.  ...  This work was partially supported by the Center for Innovation and Transfer of Natural Sciences and Engineering Knowledge at the University of Rzeszów.  ...

### A comparison of fuzzy set theory and rough set theory in the context of automatic object classification

1988 International Journal of Approximate Reasoning
This methodology is implemented using the fuzzy k-nearest neighbor and fuzzy perceptron classifiers and is tested on various synthetic and real data sets.  ...  This natural language confidence provides a symbolic interface to a human operator or to an artificial intelligence high level system incorporating the complexity and uncertainty inherent in the application  ...  The aim of this paper is to present a comparative analysis of fuzzy set theory and rough set theory.  ...

### Rough fuzzy set based scale space transforms and their use in image analysis

A. Petrosino, G. Salvi
2006 International Journal of Approximate Reasoning
In this paper we present a multi-scale method based on the hybrid notion of rough fuzzy sets, coming from the combination of two models of uncertainty like vagueness by handling rough sets and coarseness  ...  by handling fuzzy sets.  ...  Fuzzy sets, rough sets and C-sets Rough sets Let X = {x 1 , . . . , x n } be a set of U and R an equivalence relation on X.  ...

### Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

Tuan-Fang Fan, Churn-Jung Liau, Duen-Ren Liu
2011 International Journal of Approximate Reasoning
Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets.  ...  In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects  ...  We wish to thank the guest editor and the anonymous referees for their constructive suggestions.  ...

### Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications

Qinghua Hu, Lei Zhang, Degang Chen, Witold Pedrycz, Daren Yu
2010 International Journal of Approximate Reasoning
Based on this observation, we combine these methodologies by incorporating Gaussian kernel with fuzzy rough sets and propose a Gaussian kernel approximation based fuzzy rough set model.  ...  Kernel methods and rough sets are two general pursuits in the domain of machine learning and intelligent systems.  ...  Acknowledgement This work is supported by National Natural Science Foundation of China under Grants 60703013, 10978011 and 70871036. Prof.  ...

### Reducing the Memory Size of a Fuzzy Case-Based Reasoning System Applying Rough Set Techniques

F. Fernndez-Riverola, F. Daz, J. M. Corchado
2007 IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews)
and increasing the explanatory strength of the fuzzy rules.  ...  The rough feature weighting and selection method is applied as a pre-processing step prior to the generation of a fuzzy rule system which is employed in the revision phase of the proposed CBR system.  ...  for CBR systems while section III describes the Case-Based Reasoning platform used in this study; section IV introduces the Rough Set theory grounding and section V details the proposed Rough Set reduction  ...
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