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Generalizations of Rough Sets: From Crisp to Fuzzy Cases [chapter]

Masahiro Inuiguchi
2004 Lecture Notes in Computer Science  
Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency  ...  The Ordered Set of Rough Sets p. 49 A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysisp. 59 Structure of Rough Approximations Based on Molecular Lattices p. 69  ... 
doi:10.1007/978-3-540-25929-9_3 fatcat:saiacsrpovgphlh5zzhoq4tcrq

A Modal Characterization of Indiscernibility and Similarity Relations in Pawlak's Information Systems [chapter]

Dimiter Vakarelov
2005 Lecture Notes in Computer Science  
Xiaohua Hu 214 Reasoning in Information Systems On Consistent and Partially Consistent Extensions of Information Systems Zbigniew Suraj, Krzysztof Pancerz, Grzegorz Owsiany 224 Table of of  ...  , Approximations and Vagueness Patrick Doherty, Witold Lukaszewicz, Andrzej Szalas 541 Decision Theory = Performance Measure Theory + Uncertainty Theory Eugene Eberbach 551 Probabilistic Network  ... 
doi:10.1007/11548669_2 fatcat:izzj5s3t6nffzelnlkvdbn2qk4

Rudiments of rough sets

Zdzisław Pawlak, Andrzej Skowron
2007 Information Sciences  
In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs.  ...  In the article, we present the basic concepts of rough set theory and point out some rough setbased research directions and applications.  ...  Acknowledgements 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.  ... 
doi:10.1016/j.ins.2006.06.003 fatcat:ejtuxp4zubfadpnldddilhwqgi

A granularity-based framework of deduction, induction, and abduction

Yasuo Kudo, Tetsuya Murai, Seiki Akama
2009 International Journal of Approximate Reasoning  
The proposed framework is based on a-level fuzzy measure models on the basis of background knowledge, as described in the paper.  ...  In the proposed framework, deduction, induction, and abduction are characterized as reasoning processes based on typical situations about the facts and rules used in these processes.  ...  This work was partially supported by Grant-in-Aid for Young Scientists (B) (20700192,(2008)(2009)) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.  ... 
doi:10.1016/j.ijar.2009.06.002 fatcat:vnazgd5o6rdsdjicimocgci4kq

An Overview of Rough Set Semantics for Modal and Quantifier Logics

C Liau
2000 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
On the other hand, philosophers and logicians have spent centuries of time in developing formal tools for the representation and reasoning of knowledge.  ...  Since set theory and logic systems are strongly coupled in the development of modern logic, it is expected that the rough set-based knowledge representation framework and the logic-based one have close  ...  Introduction The rough set theory is invented by Pawlak 3, 4, 5 to account for the definability of a concept in terms of some elementary ones in an approximation space.  ... 
doi:10.1016/s0218-4885(00)00007-1 fatcat:qfbkcvoytrcebd5vwohwqumbpe

AN OVERVIEW OF ROUGH SET SEMANTICS FOR MODAL AND QUANTIFIER LOGICS

CHURN-JUNG LIAU
2000 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
On the other hand, philosophers and logicians have spent centuries of time in developing formal tools for the representation and reasoning of knowledge.  ...  Since set theory and logic systems are strongly coupled in the development of modern logic, it is expected that the rough set-based knowledge representation framework and the logic-based one have close  ...  Introduction The rough set theory is invented by Pawlak 3, 4, 5 to account for the definability of a concept in terms of some elementary ones in an approximation space.  ... 
doi:10.1142/s0218488500000071 fatcat:4ephf4rgvrfpxlk7qtmsexm6iy

Modal reasoning and rough set theory [chapter]

Churn-Jung Liau
1998 Lecture Notes in Computer Science  
In this paper, we would like to present some modal logics with semantics based on rough set theory and related notions.  ...  In addition to surveying some well-known results about the links between modal logics and rough set theory, we also develop some new applied logics inspired I)y generalized rough set theory.  ...  Introduction Tile rough set theory is invented by Pawlak [15, 16] to account for the definability of a concept in terms of some elementary ones in an approximation space.  ... 
doi:10.1007/bfb0057455 fatcat:4tjb2af3d5f5zkgmk7xj2azkqa

Page 7911 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
These transformations are based on a well-justified measure of uncertainty in the Dempster-Shafer theory.  ...  From the text: “This collection of articles reflects a variety of research themes pursued in rough set theory and its applications. The collection consists of 25 chapters.  ... 

A Treatise on Rough Sets [chapter]

Zdzisław Pawlak
2005 Lecture Notes in Computer Science  
This article presents some general remarks on rough sets and their place in general picture of research on vagueness and uncertainty -concepts of utmost interest, for many years, for philosophers, mathematicians  ...  Therefore we also refrain from presentation of many interesting applications and some generalizations of the theory.  ...  Acknowledgments Thanks are due to Professor Andrzej Skowron and Professor Jim Peters for critical remarks.  ... 
doi:10.1007/11574798_1 fatcat:a556pxalg5g7rk6vdf4qsw25l4

Rough Sets and Rough Logic: A KDD Perspective [chapter]

Zdzisław Pawlak, Lech Polkowski, Andrzej Skowron
2000 Studies in Fuzziness and Soft Computing  
We point out the role of Boolean reasoning in solving discussed problems. Rough sets induce via its methods a specific logic, which we call rough logic.  ...  Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980's.  ...  Approximation spaces (cf. Chapter by STEPANIUK) consist of two main constructs: sets of objects called neighborhoods and a measure of inclusion on sets.  ... 
doi:10.1007/978-3-7908-1840-6_13 fatcat:vy35ujzaszcwvevywvjcms4wzy

Page 4686 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
Summary: “This paper presents the idea of establishing the theory of fuzzy logic in a broader sense (approximate reasoning) to integrate the results of fuzzy logic in the narrow sense, parts of the theory  ...  Thus, the generalization of the rough set approach consists in handling the case of multiple descriptors for both condition and decision attributes.  ... 

Reasoning about Data — A Rough Set Perspective [chapter]

Zdzisław Pawlak
1998 Lecture Notes in Computer Science  
The paper contains some considerations concerning the relationship between decision rules and inference rules from the rough set theory perspective.  ...  Decision rules in the rough set approach are used to describe dependencies in data, whereas modus ponens is used in general to derive conclusions from premises. L. Polkowski and A.  ...  Conclusions Using rough sets to reason about data hinges on three basic concepts of rough set theory: approximations, decision rules and dependencies.  ... 
doi:10.1007/3-540-69115-4_4 fatcat:teie3a762rfuzhlivpn26pdroy

A NUMERICAL APPROACH TO UNCERTAINTY IN ROUGH LOGIC

YAN-HONG SHE, XIAO-LI HE
2013 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
Lastly, by employing the proposed notions, we develop two types of approximate reasoning patterns in the framework of rough logic.  ...  However, very few of them are explored from the viewpoint of rough logic, which, however, helps to establish a kind of approximate reasoning mechanism.  ...  This work was supported by the NSF of China under Grant 61103133, Scientific Research Program Funded by Shaanxi Provincial  ... 
doi:10.1142/s0218488513500207 fatcat:k5sqrjmx6zaopaxd5ip5t3bbxm

A first-order logic for reasoning under uncertainty using rough sets

Simon Parsons, Miroslav Kubat
1994 Journal of Intelligent Manufacturing  
The theory of rough sets allows us to handle uncertainty without the need for precise numbers, and so has some advantages in such situations.  ...  logic formulae are used in automated reasoning.  ...  In Pawlak's original work on rough sets the envelope and core were named 'upper approximation' and 'lower approximation' respectively. 4 Note that ~R c is ~(R c ), the complement of the core of R and  ... 
doi:10.1007/bf00123694 fatcat:s6zcaxxwbbdjbbva7cuczlonqa

Approximate Reasoning in MAS: Rough Set Approach

Andrzej Skowron
2006 2006 IEEE/WIC/ACM International Conference on Intelligent Agent Technology  
Andrzej Jankowski for cooperation on wistech. The research has been supported by the grant 3 T11C 002 26 from Ministry of Scientific Research and Information Technology of the Republic of Poland.  ...  A successful methodology based on the discernibility of objects and Boolean reasoning has been developed in rough set theory for computing of many key constructs like reducts and their approximations,  ...  The foundations of such an approach, creating a core of perception logic, are based on rough set theory [43, 46, 45, 44, 17] and its extension rough mereology [48, 55, 42] .  ... 
doi:10.1109/iat.2006.38 dblp:conf/iat/Skowron06 fatcat:hceu4eympjem7cltvv4ipc73oa
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