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Four-Valued Extension of Rough Sets [chapter]

Aida Vitória, Andrzej Szałas, Jan Małuszyński
Rough Sets and Knowledge Technology  
Several properties of lower and upper approximations of four-valued sets are also presented.  ...  A set is four-valued in the sense that its membership function can have one of the four logical values: unknown (u), false (f), inconsistent (i), or true (t).  ...  Four-valued Set Approximations In the usual rough-set framework, given a set and a similarity relation, lower and upper approximations of the set can be obtained.  ... 
doi:10.1007/978-3-540-79721-0_19 dblp:conf/rskt/VitoriaSM08 fatcat:vm6n7iwscfe7feosez7zyhudfq

A New Challenge: Path Planning for Autonomous Truck of Open-Pit Mines in The Last Transport Section

Ziyu Zhao, Lin Bi
2020 Applied Sciences  
the roughness.  ...  Finally, we incorporate the contact cost between tire and ground to improve the node extension and path smoothing part of the Hybrid A* algorithm and further enhance the algorithm's capability of avoiding  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/app10186622 fatcat:y5mbpjr5vbhjzeithyilfrkhma

A Novel Extension Data Mining Approach based on Rough Sets Pair Analysis

Zhi-hang Tang
2010 Journal of Software  
In this paper, reducing the condition attributes based on the matter-element theory and rough set method, calculating the importance to the decision attribute for each condition attribute after reduction  ...  , and data mining the relevant rules based on the reduced attributes, extension relevant function is used to depict quality of data gather in data mining.  ...  EXTENSION DATA MINING BASE ON ROUGH SET A.  ... 
doi:10.4304/jsw.5.4.447-454 fatcat:n7x3m2x5kbcbplgmopmwcngcsq

Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China

Luliang Liu, Yuanming Dou, Jiangang Qiao
2022 Mathematics  
The rough set theory approach and the analytic hierarchy process were used to solve the weights of the slope evaluation indexes.  ...  Based on a rough set and an analytic hierarchy process, an evaluation model is proposed.  ...  In the discretization of the rough set, a limitation of this study is that there were four discrete values. These discrete values have certain limitations.  ... 
doi:10.3390/math10081264 fatcat:buk2p5gnabd5voocjrqogzet4e

History of Set Theory and Its Extensions in the Context of Soft Computing [chapter]

Sarjerao Nimse, Pawan Lingras
2011 Lecture Notes in Computer Science  
The arithmetization programs of mathematicians in later half of nineteenth century showed that it is necessary to rebuild analysis. Riemanns attempt to find necessary and sufficient conditions for  ...  During last four decades researchers realized the tremendous scope of fuzzy sets and fuzzy logic in Soft Computing.  ...  In this paper, we propose comparative advantages of fuzzy sets and rough sets in the context of Soft Computing. J.T. Yao et al.  ... 
doi:10.1007/978-3-642-24425-4_5 fatcat:tqfbkv6s3fdhtpyhe7ycr552bu

Rough Clustering Using an Evolutionary Algorithm

Kevin E. Voges, Nigel K. Ll. Pope
2012 2012 45th Hawaii International Conference on System Sciences  
Rough clusters are defined in a similar manner to Pawlak's rough set concept, with a lower and upper approximation, allowing multiple cluster membership for objects in the data set.  ...  It also provides an overview of the evolutionary algorithm used to develop viable cluster solutions, consisting of an optimal number of templates providing descriptions of the clusters.  ...  For example, a cluster solution could be developed using one attribute with four values by simply having four templates -value 1, value 2, value 3 and value 4.  ... 
doi:10.1109/hicss.2012.510 dblp:conf/hicss/VogesP12 fatcat:syehfp3izzgtzeqwr3zesqk52i

A Novel Feature Weighted Clustering Algorithm Based on Rough Sets for Shot Boundary Detection [chapter]

Bing Han, Xinbo Gao, Hongbing Ji
2006 Lecture Notes in Computer Science  
Each paper was reviewed by two to four referees. Since the introduction of rough sets in 1981 by Zdzis law Pawlak, many great advances in both the theory and applications have been introduced.  ...  It is our great pleasure to dedicate this volume to the father of rough sets theory, Zdzis law Pawlak, who passed away just 3 months before the conference.  ...  Systems Hongru Li, Wenxiu Zhang, Ping Xu, Hong Wang . . . . . . . . . . . . . . . . . . 135 A New Extension Model of Rough Sets Under Incomplete Information Xuri Yin, Xiuyi Jia, Lin Shang . . . . . .  ... 
doi:10.1007/11881599_55 fatcat:bomxoqyvjjfr5o6mqsw4eup3qu

Feature Selection in Decision Systems: A Mean-Variance Approach

Chengdong Yang, Wenyin Zhang, Jilin Zou, Shunbo Hu, Jianlong Qiu
2013 Mathematical Problems in Engineering  
Uncertainty measure is an important implement for characterizing the degree of uncertainty. It has been extensively applied in pattern recognition and data clustering.  ...  Experiment analysis shows the validity and effectiveness of MVM.  ...  Along with the development of rough sets, attribute reduction has been studied extensively in the past decade, such as fuzzy rough sets based attribute reduction [19] [20] [21] [22] [23] , neighborhood  ... 
doi:10.1155/2013/268063 fatcat:ofbt7fff55dcxlv47u2o6jwqn4

A New Data Mining Approach Combined with Extension Set and Rough Set

Zhi-hang Tang, Wen-bin Tian
2014 Journal of Software  
Extension data mining can play a role in classification transformation, finding the root causes of the problem, identifying potential transformation knowledge.  ...  Finally, how to tap new customers and how to recommend an appropriate brand to new customers, Research results indicate that extension data mining can provide effective support for decision-making of enterprise  ...  EXTENSION DATA MINING BASE ON ROUGH SET 1) Attribute Reduction based on Rough Set We often encounter problems whether we can remove some data from a data table preserving its basic properties, i.e. whether  ... 
doi:10.4304/jsw.9.2.451-457 fatcat:bigsfan2p5hjpfjkee7pevfx3u


2003 TASK Quarterly  
Each relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic.  ...  Two orderings on relative sets are considered; one is an extension of the classical set inclusion ordering while the other is a new ordering of knowledge or information.  ...  The direction of the line is from a lower value to a higher value Using Belnap's four-valued logic in [3] [4] [5] [6] , an extension of classical sets were introduced.  ... 
doaj:0679a2d3255949c8adc36e639651e85f fatcat:gkwpqgbrrvckdbah4xsuu67jmq

On rough sets, their recent extensions and applications

N. Mac Parthaláin, Q. Shen
2010 Knowledge engineering review (Print)  
Rough set theory (RST) has enjoyed an enormous amount of attention in recent years and has been applied to many real-world problems including data mining, pattern recognition, and intelligent control.  ...  This paper attempts to summarize the advances in RST, its extensions, and their applications. It also identifies important areas which require further investigation.  ...  Rough set extensions The simplicity of the rough set approach is undoubtedly one of the main reasons for its success.  ... 
doi:10.1017/s0269888910000263 fatcat:ta7bxxa34jc5pmsdxwx4nudnwa

Page 6348 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
Summary: “In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a coun- terpart of Belnap’s four-valued logic is achieved.  ...  Every relative set partitions all objects into four distinct regions corresponding to the four truth-values of Belnap’s logic.  ... 

Paraconsistent Logic Programs with Four-Valued Rough Sets [chapter]

Jan Małuszyński, Andrzej Szałas, Aida Vitória
2008 Lecture Notes in Computer Science  
This paper presents a language for defining four-valued rough sets and to reason about them. Our framework brings together two major fields: rough sets and paraconsistent logic programming.  ...  On the one hand it provides a paraconsistent approach, based on four-valued rough sets, for integrating knowledge from different sources and reasoning in the presence of inconsistencies.  ...  A four-valued extension of rough sets is then defined by four-valued set approximations as follows (cf. [9] ). Note that (four-valued) relations are (four-valued) sets of tuples. Definition 1.  ... 
doi:10.1007/978-3-540-88425-5_5 fatcat:g4mkxinvmfdqdgxyk2tqopzsgm

An Intelligent Traffic Control System Using Neutrosophic Sets, Rough sets, Graph Theory, Fuzzy sets and its Extended Approach: A Literature Review

Broumi Said, Malayalan Lathamaheswari, Prem Kumar Singh, A. Ait Ouallane
2022 Zenodo  
To deal with this issue some available mathematical technique for traffic flow using rough set, fuzzy rough set, and its extension with the neutrosophic set is discussed in this paper.  ...  The rough set theory can be useful for dealing the uncertain, incomplete, and indeterminate data set.  ...  The fuzzy-rough set theory (FRST) is a continuous numerical attribute extension of the rough set theory.  ... 
doi:10.5281/zenodo.6774620 fatcat:c3ufhug2hzch5frihb4pnnbufu

Page 5154 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
Summary: “Two fundamental questions on the extensions of many-valued equivalence relations, whose solutions are of cru- cial concern for the applications of many-valued equivalence re- lations, are explicitly  ...  Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.” 2004g:03085 03472 Demirci, Mustafa Representations of the extensions of many-valued  ... 
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