361,428 research outputs found
Formal Development of Rough Inclusion Functions
Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, ÎșÂŁ, connected with Ćukasiewicz [14], and extend this research for two additional RIFs: Îș 1, and Îș 2, following a paper by GomoliĆska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].Institute of Informatics, University of BiaĆystok, PolandAnna Gomolinska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103â119, 2002.Anna Gomolinska. Rough approximation based on weak q-RIFs. In James F. Peters, Andrzej Skowron, Marcin Wolski, Mihir K. Chakraborty, and Wei-Zhi Wu, editors, Transactions on Rough Sets X, volume 5656 of Lecture Notes in Computer Science, pages 117â135, Berlin, Heidelberg, 2009. Springer. ISBN 978-3-642-03281-3. doi:10.1007/978-3-642-03281-3_4.Anna Gomolinska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybinski, and Andrzej Skowron, editors, Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Computer Science, pages 142â151, Berlin, Heidelberg, 2007. Springer. doi:10.1007/978-3-540-73451-2_16.Anna Gomolinska. On certain rough inclusion functions. In James F. Peters, Andrzej Skowron, and Henryk Rybinski, editors, Transactions on Rough Sets IX, volume 5390 of Lecture Notes in Computer Science, pages 35â55. Springer Berlin Heidelberg, 2008. doi:10.1007/978-3-540-89876-4_3.Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-KÄplicz, A. Jankowski, A. Skowron, and M. Szczuka, editors, International Workshop on Monitoring, Security, and Rescue Techniques in Multiagent Systems Location, volume 28 of Advances in Soft Computing, pages 215â226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371â385, 2014. doi:10.3233/FI-2014-1129.Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In TamĂĄs MihĂĄlydeĂĄk, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo DĂŒntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225â238, Cham, 2019. Springer International Publishing. ISBN 978-3-030-22815-6. doi:10.1007/978-3-030-22815-6_18.Adam Grabowski. Lattice theory for rough sets â a case study with Mizar. Fundamenta Informaticae, 147(2â3):223â240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55â64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets â an automated approach. Formalized Mathematics, 24(2):143â155, 2016. doi:10.1515/forma-2016-0011.Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5â10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300â314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and MichaĆ Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183â191, 2018. doi:10.2478/forma-2018-0016.Adam Grabowski, Artur KorniĆowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191â198, 2015. doi:10.1007/s10817-015-9345-1.Jan Ćukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Ćukasiewicz â Selected Works, pages 16â63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in KrakĂłw, 1913.ZdzisĆaw Pawlak. Rough sets. International Journal of Parallel Programming, 11:341â356, 1982. doi:10.1007/BF01001956.Lech Polkowski. Rough mereology. In Approximate Reasoning by Parts, volume 20 of Intelligent Systems Reference Library, pages 229â257, Berlin, Heidelberg, 2011. Springer. ISBN 978-3-642-22279-5. doi:10.1007/978-3-642-22279-5_6.Lech Polkowski and Andrzej Skowron. Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning, 15(4):333â365, 1996. doi:10.1016/S0888-613X(96)00072-2.Andrzej Skowron and JarosĆaw Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245â253, 1996. doi:10.3233/FI-1996-272311.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997â5011, 2007.27433734
Developing Complementary Rough Inclusion Functions
We continue the formal development of rough inclusion functions (RIFs), continuing the research on the formalization of rough sets [15] â a well-known tool of modelling of incomplete or partially unknown information. In this article we give the formal characterization of complementary RIFs, following a paper by Gomolinska [4].We expand this framework introducing Jaccard index, Steinhaus generate metric, and Marczewski-Steinhaus metric space [1]. This is the continuation of [9]; additionally we implement also parts of [2], [3], and the details of this work can be found in [7].Institute of Informatics, University of BiaĆystok, PolandMichel Marie Deza and Elena Deza. Encyclopedia of distances. Springer, 2009. doi:10.1007/978-3-642-30958-8.Anna Gomolinska. Rough approximation based on weak q-RIFs. In James F. Peters, Andrzej Skowron, Marcin Wolski, Mihir K. Chakraborty, and Wei-Zhi Wu, editors, Transactions on Rough Sets X, volume 5656 of Lecture Notes in Computer Science, pages 117â135, Berlin, Heidelberg, 2009. Springer. ISBN 978-3-642-03281-3. doi:10.1007/978-3-642-03281-3_4.Anna Gomolinska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybinski, and Andrzej Skowron, editors, Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Computer Science, pages 142â151, Berlin, Heidelberg, 2007. Springer. doi:10.1007/978-3-540-73451-2_16.Anna Gomolinska. On certain rough inclusion functions. In James F. Peters, Andrzej Skowron, and Henryk Rybinski, editors, Transactions on Rough Sets IX, volume 5390 of Lecture Notes in Computer Science, pages 35â55. Springer Berlin Heidelberg, 2008. doi:10.1007/978-3-540-89876-4_3.Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-KÄplicz, A. Jankowski, A. Skowron, and M. Szczuka, editors, International Workshop on Monitoring, Security, and Rescue Techniques in Multiagent Systems Location, volume 28 of Advances in Soft Computing, pages 215â226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371â385, 2014. doi:10.3233/FI-2014-1129.Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In TamĂĄs MihĂĄlydeĂĄk, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo DĂŒntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225â238, Cham, 2019. Springer International Publishing. ISBN 978-3-030-22815-6. doi:10.1007/978-3-030-22815-6_18.Adam Grabowski. Lattice theory for rough sets â a case study with Mizar. Fundamenta Informaticae, 147(2â3):223â240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Formal development of rough inclusion functions. Formalized Mathematics, 27(4):337â345, 2019. doi:10.2478/forma-2019-0028.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55â64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets â an automated approach. Formalized Mathematics, 24(2):143â155, 2016. doi:10.1515/forma-2016-0011.Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5â10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300â314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and MichaĆ Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183â191, 2018. doi:10.2478/forma-2018-0016.Jan Ćukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Ćukasiewicz â Selected Works, pages 16â63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in KrakĂłw, 1913.ZdzisĆaw Pawlak. Rough sets. International Journal of Parallel Programming, 11:341â356, 1982. doi:10.1007/BF01001956.Andrzej Skowron and JarosĆaw Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245â253, 1996. doi:10.3233/FI-1996-272311.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997â5011, 2007.10511
Interoperability, Trust Based Information Sharing Protocol and Security: Digital Government Key Issues
Improved interoperability between public and private organizations is of key
significance to make digital government newest triumphant. Digital Government
interoperability, information sharing protocol and security are measured the
key issue for achieving a refined stage of digital government. Flawless
interoperability is essential to share the information between diverse and
merely dispersed organisations in several network environments by using
computer based tools. Digital government must ensure security for its
information systems, including computers and networks for providing better
service to the citizens. Governments around the world are increasingly
revolving to information sharing and integration for solving problems in
programs and policy areas. Evils of global worry such as syndrome discovery and
manage, terror campaign, immigration and border control, prohibited drug
trafficking, and more demand information sharing, harmonization and cooperation
amid government agencies within a country and across national borders. A number
of daunting challenges survive to the progress of an efficient information
sharing protocol. A secure and trusted information-sharing protocol is required
to enable users to interact and share information easily and perfectly across
many diverse networks and databases globally.Comment: 20 page
Operations of Points on Elliptic Curve in Affine Coordinates
In this article, we formalize in Mizar [1], [2] a binary operation of points on an elliptic curve over GF(p) in affine coordinates. We show that the operation is unital, complementable and commutative. Elliptic curve cryptography [3], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.This work was supported by JSPS KAKENHI Grant Numbers JP15K00183 and JP17K00182.Yuichi Futa - Tokyo University of Technology, Tokyo, JapanHiroyuki Okazaki - Shinshu University, Nagano, JapanYasunari Shidama - Shinshu University, Nagano, JapanGrzegorz Bancerek, CzesĆaw Bylinski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.Grzegorz Bancerek, CzesĆaw Bylinski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9â32, 2018. doi:10.1007/s10817-017-9440-6.I. Blake, G. Seroussi, and N. Smart. Elliptic Curves in Cryptography. Number 265 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1999.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Set of points on elliptic curve in projective coordinates. Formalized Mathematics, 19(3):131â138, 2011. doi:10.2478/v10037-011-0021-6.Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, and Yasunari Shidama. Operations of points on elliptic curve in projective coordinates. Formalized Mathematics, 20(1): 87â95, 2012. doi:10.2478/v10037-012-0012-2.Artur KorniĆowicz. Recursive definitions. Part II. Formalized Mathematics, 12(2):167â172, 2004.27331532
Lightweight Mutual Authentication Protocol for Low Cost RFID Tags
Radio Frequency Identification (RFID) technology one of the most promising
technologies in the field of ubiquitous computing. Indeed, RFID technology may
well replace barcode technology. Although it offers many advantages over other
identification systems, there are also associated security risks that are not
easy to be addressed. When designing a real lightweight authentication protocol
for low cost RFID tags, a number of challenges arise due to the extremely
limited computational, storage and communication abilities of Low-cost RFID
tags. This paper proposes a real mutual authentication protocol for low cost
RFID tags. The proposed protocol prevents passive attacks as active attacks are
discounted when designing a protocol to meet the requirements of low cost RFID
tags. However the implementation of the protocol meets the limited abilities of
low cost RFID tags.Comment: 11 Pages, IJNS
The effect of cyber-attacks on stock returns
A widely debated issue in recent years is cybercrime. Breaches in the security of accessibility, integrity and confidentiality of information involve potentially high explicit and implicit costs for firms. This paper investigates the impact of information security breaches on stock returns. Using event-study methodology, the study provides empirical evidence on the effect of announcements of cyber-attacks on the market value of firms from 1995 to 2015. Results show that substantial negative market returns occur following announcements of cyber-attacks. Financial entities often suffer greater negative effects than other companies and non-confidential cyber-attacks are the most dangerous, especially for the financial sector. Overall findings seem to show a link between cybercrime and insider trading
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