Formal Introduction to Fuzzy Implications

SummaryIn the article we present in the Mizar system the catalogue of nine basic fuzzy implications, used especially in the theory of fuzzy sets. This work is a continuation of the development of fuzzy sets in Mizar; it could be used to give a variety of more general operations, and also it could be a good starting point towards the formalization of fuzzy logic (together with t-norms and t-conorms, formalized previously).Institute of Informatics, University of Białystok, PolandMichał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:10.1007/978-3-540-69082-5.Adam Grabowski. Basic formal properties of triangular norms and conorms. Formalized Mathematics, 25(2):93–100, 2017. doi:10.1515/forma-2017-0009.Adam Grabowski. The formal construction of fuzzy numbers. Formalized Mathematics, 22(4):321–327, 2014. doi:10.2478/forma-2014-0032.Adam Grabowski. On the computer certification of fuzzy numbers. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, 2013 Federated Conference on Computer Science and Information Systems (FedCSIS), Federated Conference on Computer Science and Information Systems, pages 51–54, 2013.Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski and Magdalena Jastrzębska. Rough set theory from a math-assistant perspective. In Rough Sets and Intelligent Systems Paradigms, International Conference, RSEISP 2007, Warsaw, Poland, June 28–30, 2007, Proceedings, pages 152–161, 2007. doi:10.1007/978-3-540-73451-2_17.Adam Grabowski and Takashi Mitsuishi. Extending Formal Fuzzy Sets with Triangular Norms and Conorms, volume 642: Advances in Intelligent Systems and Computing, pages 176–187. Springer International Publishing, Cham, 2018. doi:10.1007/978-3-319-66824-6_16.Adam Grabowski and Takashi Mitsuishi. Initial comparison of formal approaches to fuzzy and rough sets. In Leszek Rutkowski, Marcin Korytkowski, Rafal Scherer, Ryszard Tadeusiewicz, Lotfi A. Zadeh, and Jacek M. Zurada, editors, Artificial Intelligence and Soft Computing - 14th International Conference, ICAISC 2015, Zakopane, Poland, June 14-18, 2015, Proceedings, Part I, volume 9119 of Lecture Notes in Computer Science, pages 160–171. Springer, 2015. doi:10.1007/978-3-319-19324-3_15.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.Takashi Mitsuishi, Noboru Endou, and Yasunari Shidama. The concept of fuzzy set and membership function and basic properties of fuzzy set operation. Formalized Mathematics, 9(2):351–356, 2001.Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.Lotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.25324124

Intelligent Integrated Management for Telecommunication Networks

As the size of communication networks keeps on growing, faster connections, cooperating technologies and the divergence of equipment and data communications, the management of the resulting networks gets additional important and time-critical. More advanced tools are needed to support this activity. In this article we describe the design and implementation of a management platform using Artificial Intelligent reasoning technique. For this goal we make use of an expert system. This study focuses on an intelligent framework and a language for formalizing knowledge management descriptions and combining them with existing OSI management model. We propose a new paradigm where the intelligent network management is integrated into the conceptual repository of management information called Managed Information Base (MIB). This paper outlines the development of an expert system prototype based in our propose GDMO+ standard and describes the most important facets, advantages and drawbacks that were found after prototyping our proposal

Formalizing Two Generalized Approximation Operators

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article we give the formal characterization of two closely related rough approximations, along the lines proposed in a paper by Gomolińska [2]. We continue the formalization of rough sets in Mizar [1] started in [6].Adam Grabowski - Institute of Informatics, University of Białystok, PolandMichał Sielwiesiuk - Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, 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 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Anna Gomolińska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 2002.Adam Grabowski. Automated discovery of properties of rough sets. Fundamenta Informaticae, 128:65–79, 2013. doi:10.3233/FI-2013-933.Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Formalization of generalized almost distributive lattices. Formalized Mathematics, 22(3):257–267, 2014. doi:10.2478/forma-2014-0026.Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21–28, 2004.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.Adam Grabowski and Magdalena Jastrzębska. A note on a formal approach to rough operators. In Marcin S. Szczuka and Marzena Kryszkiewicz et al., editors, Rough Sets and Current Trends in Computing – 7th International Conference, RSCTC 2010, Warsaw, Poland, June 28-30, 2010. Proceedings, volume 6086 of Lecture Notes in Computer Science, pages 307–316. Springer, 2010. doi:10.1007/978-3-642-13529-3_33.Adam Grabowski and Magdalena Jastrzębska. Rough set theory from a math-assistant perspective. In Rough Sets and Intelligent Systems Paradigms, International Conference, RSEISP 2007, Warsaw, Poland, June 28–30, 2007, Proceedings, pages 152–161, 2007. doi:10.1007/978-3-540-73451-2_17.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 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and Christoph Schwarzweller. Rough Concept Analysis - theory development in the Mizar system. In Asperti, Andrea and Bancerek, Grzegorz and Trybulec, Andrzej, editor, Mathematical Knowledge Management, Third International Conference, MKM 2004, Bialowieza, Poland, September 19–21, 2004, Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 130–144, 2004. doi:10.1007/978-3-540-27818-4_10. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19-21, 2004.Jouni Järvinen. Lattice theory for rough sets. Transactions of Rough Sets, VI, Lecture Notes in Computer Science, 4374:400–498, 2007.Eliza Niewiadomska and Adam Grabowski. Introduction to formal preference spaces. Formalized Mathematics, 21(3):223–233, 2013. doi:10.2478/forma-2013-0024.Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.Y.Y. Yao. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning, 15(4):291–317, 1996. doi:10.1016/S0888-613X(96)00071-0.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.26218319

Intelligent Packaging Systems: Sensors and Nanosensors to Monitor Food Quality and Safety

Indexación: Web of Science y Scopus.The application of nanotechnology in different areas of food packaging is an emerging field that will grow rapidly in the coming years. Advances in food safety have yielded promising results leading to the development of intelligent packaging (IP). By these containers, it is possible to monitor and provide information of the condition of food, packaging, or the environment. This article describes the role of the different concepts of intelligent packaging. It is possible that this new technology could reach enhancing food safety, improving pathogen detection time, and controlling the quality of food and packaging throughout the supply chain.https://www.hindawi.com/journals/js/2016/4046061/cta

An Advanced Conceptual Diagnostic Healthcare Framework for Diabetes and Cardiovascular Disorders

The data mining along with emerging computing techniques have astonishingly influenced the healthcare industry. Researchers have used different Data Mining and Internet of Things (IoT) for enrooting a programmed solution for diabetes and heart patients. However, still, more advanced and united solution is needed that can offer a therapeutic opinion to individual diabetic and cardio patients. Therefore, here, a smart data mining and IoT (SMDIoT) based advanced healthcare system for proficient diabetes and cardiovascular diseases have been proposed. The hybridization of data mining and IoT with other emerging computing techniques is supposed to give an effective and economical solution to diabetes and cardio patients. SMDIoT hybridized the ideas of data mining, Internet of Things, chatbots, contextual entity search (CES), bio-sensors, semantic analysis and granular computing (GC). The bio-sensors of the proposed system assist in getting the current and precise status of the concerned patients so that in case of an emergency, the needful medical assistance can be provided. The novelty lies in the hybrid framework and the adequate support of chatbots, granular computing, context entity search and semantic analysis. The practical implementation of this system is very challenging and costly. However, it appears to be more operative and economical solution for diabetes and cardio patients.Comment: 11 PAGE