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A comparative study of fuzzy sets and rough sets

Y YAO
1998 Information Sciences  
Two approaches for the formulation of fuzzy sets are reviewed, one is based on many-valued logic and the other is based on modal logic.  ...  Rough sets under set-oriented view are closely related to fuzzy sets, which leads to non-truth-functional fuzzy set operators. Both of them may be considered as deviations of classical set algebra.  ...  Properties (m1)-(m4) are similar to properties (f1)-(f4) of fuzzy sets formulated based on modal logic.  ... 
doi:10.1016/s0020-0255(98)10023-3 fatcat:cjwsznhjdjdolbo262ek5uuv4i

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

Dimiter Vakarelov
2005 Lecture Notes in Computer Science  
Approximation Spaces Piotr Wasilewski 114 Rough Sets over the Boolean Algebras Gui-Long Liu 124 Algebraic Approach to Generalized Rough Sets Michiro Kondo 132 Logic for Rough Sets with Rough  ...  and Kansei Representations Yuji Muto, Mineichi Kudo 692 Rough Set Approximation Based on Dynamic Granulation Jiye Liang, Yuhua Qian, Chengyuan Chu, Deyu Li, Junhong Wang 701 Granulär Logic with Closeness  ... 
doi:10.1007/11548669_2 fatcat:izzj5s3t6nffzelnlkvdbn2qk4

Page 19 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
The idea of rough logic based on Pawlak’s rough set concept uses the Kripke models for the modal system S5.  ...  On the semantic side, a special class of Lewis’ systems of comparative similarity relations is de- fined, SM, which includes a material, algorithmic definition of the similarity relation.”  ... 

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

Masahiro Inuiguchi
2004 Lecture Notes in Computer Science  
Fuzzy Relations On the Correspondence between Approximations and Similarity p. 143 Toward Rough Knowledge Bases with Quantitative Measures p. 153 Considering Semantic Ambiguity and Indistinguishability  ...  and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Based on Propositional Modal Logic p. 109 Granular Computing  ... 
doi:10.1007/978-3-540-25929-9_3 fatcat:saiacsrpovgphlh5zzhoq4tcrq

Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations [chapter]

Claudia d'Amato, Nicola Fanizzi, Floriana Esposito, Thomas Lukasiewicz
2013 Lecture Notes in Computer Science  
Introduction & Motivation Rough Description Logics: Basics Conceptual Indescernibility Relations Conclusions & Future Works The concept approximations are based on capturing uncertainty as an indiscernibility  ...  Works Context based Indescernibility Relation Similarity based Indescernibility Relation Defining Conceptual Indescernibility Relations Problem: RDLs do not specify any indiscernibility relation  ... 
doi:10.1007/978-3-642-35975-0_16 fatcat:k6acwalglfcfnetgxxv4kx5etq

Survey of Rough and Fuzzy Hybridization

Pawan Lingras, Richard Jensen
2007 IEEE International Fuzzy Systems conference proceedings  
This paper provides a broad overview of logical and black box approaches to fuzzy and rough hybridization.  ...  The logical approaches include theoretical, supervised learning, feature selection, and unsupervised learning. The black box approaches consist of neural and evolutionary computing.  ...  It is demonstrated that the existing fuzzy-rough sets are special cases of the approximations on a CCD lattice for T-similarity relations.  ... 
doi:10.1109/fuzzy.2007.4295352 dblp:conf/fuzzIEEE/LingrasJ07 fatcat:vygojaq46zb6zej6q3jtlna5au

Theory and Application on Rough Set, Fuzzy Logic, and Granular Computing

Xibei Yang, Weihua Xu, Yanhong She
2015 The Scientific World Journal  
Based on a kernelized information entropy model, an application on the fault detection and diagnosis for gas turbines is presented.  ...  This issue on the theory and application about rough set, fuzzy logic and granular computing, most of which are very meticulously performed reviews of the available current literature.  ...  This issue on the theory and application about rough set, fuzzy logic and granular computing, most of which are very meticulously performed reviews of the available current literature.  ... 
doi:10.1155/2015/967350 pmid:26258170 pmcid:PMC4519527 fatcat:76duqu4majb47al2xvadchk4cy

AN ENHANCED FUZZY ROUGH SET-BASED CLUSTERING ALGORITHM FOR CATEGORICAL DATA

Raval Dhwani Jayant .
2014 International Journal of Research in Engineering and Technology  
In this paper we have shown what is the problem with clustering categorical data with rough set and who we can overcome with improvement. ---  ...  Clustering is such a technique where we put closely related data together. Furthermore we have types of data sequential, interval, categorical etc.  ...  Cluster Data based on roughness As X(A1=Medium)and X(A1=Big) have similar lower Roughness we will split into two Cluster  ... 
doi:10.15623/ijret.2014.0311030 fatcat:ur54nhrzqrh4vjunst6doa7j6m

Graded Many-Valued Modal Logic and Its Graded Rough Truth

Jiansheng Li, Zengtai Gong
2022 Axioms  
Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning.  ...  Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established  ...  Later, based on rough set theory, various study of logic system were proposed continuously.  ... 
doi:10.3390/axioms11070341 fatcat:owvwd7f2bfbshkcifi24ixb35q

Rough Description Logics for Modeling Uncertainty in Instance Unification

Michel C. A. Klein, Peter Mika, Stefan Schlobach
2007 International Semantic Web Conference  
Our tentative solution is Rough DL, a simple extension of classical Description Logics, which allows for approximations of vague concept.  ...  In this paper, we present openacademia, a semantics-based system for the management of distributed bibliographic information collected from the Web, in which the Instance Unification problem is ubiquitous  ...  One could even add similarity relations based on the textual overlap of the abstract.  ... 
dblp:conf/semweb/KleinMS07 fatcat:ux3jbkbb3fh3zpw5ykw7hafnry

Research on the Rough Extension of Ontology Description Language of SWRL

Xian-kun Zhang, Xin-ya Gao, Qian Zhang, Jia Jia
2016 Journal of Electrical and Computer Engineering  
According to the rough ontology and the rules of SWRL, it updates the knowledge base.  ...  Firstly, the concept of rough ontology and the extension of rough relationship of ontology are put forward; secondly, it gives the extension method for concepts, relationships, axioms, examples, and rules  ...  ̸ = Φ is a nonempty finite set; which is one of the relations of is called the equivalent relation on , only when it is a partition { 1 , 2 , . . . , } of based on , ⊆ , ̸ = Φ, and ∩ = Φ, ̸ = , , = 1,  ... 
doi:10.1155/2016/5636254 fatcat:j46w7snohbhgjkqsmy3fjzknku

Incomplete Information: Structure, Inference, Complexity

Jouni Järvinen
2006 Studia Logica: An International Journal for Symbolic Logic  
While Codd's model is widely used in contemporary database design, information systems in the sense of Pawlak have became popular in rough-set-based data analysis and data mining.  ...  Formally, a set C ⊆ A is said to be dependent on a set B ⊆ A, denoted B → C, if ind(B) ⊆ ind(C).  ...  Also a large amount of so-called information logics based on information relations with Kripke-style semantics can be found in the literature.  ... 
doi:10.1007/s11225-006-9018-5 fatcat:et7azj3uhrfhjm6vacixqamfne

A rough set approach to reasoning under uncertainty

SIMON PARSONS, MIROSLAV KUBAT, MIRKO DOHNAL
1995 Journal of experimental and theoretical artificial intelligence (Print)  
This paper presents an introduction to various forms of reasoning under uncertainty that are based on rough sets.  ...  In particular, a number of sets of numerical and symbolic truth values which may be used to augment propositional logic are developed, and a semantics for these values is provided based upon the notion  ...  Alternatively it is possible to write down the logical relations between the E j and T k , based on an unknown set A , from expert knowledge, quantifying the relations in much the same way as other certainty  ... 
doi:10.1080/09528139508953805 fatcat:3stdindoyrab5htq26qrmxzciy

A Semantic Information Retrieval Approach Based on Rough Ontology

Jun Hu, Xinzhou Lu, Chun Guan
2014 Open Cybernetics and Systemics Journal  
relations to construct an approximation space of rough ontology.  ...  To tackle this problem, a semantic information retrieval approach based on a rough ontology is proposed. Rough ontology in this paper is in the form of an ontology information system.  ...  Rough set classifies objects using upper-approximation and lower-approximation defined on an indiscernibility relation which is a kind of equivalent relation.  ... 
doi:10.2174/1874110x01408010399 fatcat:ssnnjjkcynaylb6o7mjlh5ustu

Searching contexts in paraconsistent rough description logic

Henrique Viana, João Alcântara, Ana Teresa Martins
2015 Journal of the Brazilian Computer Society  
This method is based on the notion of the discernibility matrix commonly used in the process of attribute reduction in the rough set theory.  ...  is grounded on Belnap's Logic.  ...  In this paper, we propose a new method settled on the rough set theory and description logics (DLs) for automatically generating refinements or related terms to queries.  ... 
doi:10.1186/s13173-015-0031-2 fatcat:bfn63byts5f6fjtk5amb3zq66i
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