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

Partial Correctness of a Power Algorithm

This work continues a formal verification of algorithms written in terms of simple-named complex-valued nominative data [6],[8],[15],[11],[12],[13]. In this paper we present a formalization in the Mizar system [3],[1] of the partial correctness of the algorithm: i := val.1 j := val.2 b := val.3 n := val.4 s := val.5 while (i n) i := i + j s := s * b return s computing the natural n power of given complex number b, where variables i, b, n, s are located as values of a V-valued Function, loc, as: loc/.1 = i, loc/.3 = b, loc/.4 = n and loc/.5 = s, and the constant 1 is located in the location loc/.2 = j (set V represents simple names of considered nominative data [17]).The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2],[4] with partial pre- and post-conditions [14],[16],[7],[5].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.R.W. Floyd. Assigning meanings to programs. Mathematical aspects of computer science, 19(19–32), 1967.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.C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.Ievgen Ivanov and Mykola Nikitchenko. On the sequence rule for the Floyd-Hoare logic with partial pre- and post-conditions. In Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14–17, 2018, volume 2104 of CEUR Workshop Proceedings, pages 716–724, 2018.Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap, and Artur Korniłowicz. Simple-named complex-valued nominative data – definition and basic operations. Formalized Mathematics, 25(3):205–216, 2017. doi:10.1515/forma-2017-0020.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Implementation of the composition-nominative approach to program formalization in Mizar. The Computer Science Journal of Moldova, 26(1):59–76, 2018.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On an algorithmic algebra over simple-named complex-valued nominative data. Formalized Mathematics, 26(2):149–158, 2018. doi:10.2478/forma-2018-0012.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. An inference system of an extension of Floyd-Hoare logic for partial predicates. Formalized Mathematics, 26(2): 159–164, 2018. doi:10.2478/forma-2018-0013.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Partial correctness of GCD algorithm. Formalized Mathematics, 26(2):165–173, 2018. doi:10.2478/forma-2018-0014.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On algebras of algorithms and specifications over uninterpreted data. Formalized Mathematics, 26(2):141–147, 2018. doi:10.2478/forma-2018-0011.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Leszek Borzemski, Jerzy Świątek, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 – Part II, Szklarska Poręba, Poland, September 17–19, 2017, volume 656 of Advances in Intelligent Systems and Computing, pages 176–186. Springer, 2017. ISBN 978-3-319-67228-1. doi:10.1007/978-3-319-67229-8_16.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.Artur Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare logic for partial pre- and postconditions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications: 9th International Conference, ICTERI 2013, Kherson, Ukraine, June 19–22, 2013, Revised Selected Papers, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.27218919

A review of mobile robots: Concepts, methods, theoretical framework, and applications

[EN] Humanoid robots, unmanned rovers, entertainment pets, drones, and so on are great examples of mobile robots. They can be distinguished from other robots by their ability to move autonomously, with enough intelligence to react and make decisions based on the perception they receive from the environment. Mobile robots must have some source of input data, some way of decoding that input, and a way of taking actions (including its own motion) to respond to a changing world. The need to sense and adapt to an unknown environment requires a powerful cognition system. Nowadays, there are mobile robots that can walk, run, jump, and so on like their biological counterparts. Several fields of robotics have arisen, such as wheeled mobile robots, legged robots, flying robots, robot vision, artificial intelligence, and so on, which involve different technological areas such as mechanics, electronics, and computer science. In this article, the world of mobile robots is explored including the new trends. These new trends are led by artificial intelligence, autonomous driving, network communication, cooperative work, nanorobotics, friendly human-robot interfaces, safe human-robot interaction, and emotion expression and perception. Furthermore, these news trends are applied to different fields such as medicine, health care, sports, ergonomics, industry, distribution of goods, and service robotics. These tendencies will keep going their evolution in the coming years.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Spanish Ministry of Economy and Competitiveness, which has funded the DPI2013-44227-R project.Rubio Montoya, FJ.; Valero Chuliá, FJ.; Llopis Albert, C. (2019). A review of mobile robots: Concepts, methods, theoretical framework, and applications. International Journal of Advanced Robotic Systems. 16(2):1-22. https://doi.org/10.1177/1729881419839596S122162Brunete, A., Ranganath, A., Segovia, S., de Frutos, J. P., Hernando, M., & Gambao, E. (2017). Current trends in reconfigurable modular robots design. International Journal of Advanced Robotic Systems, 14(3), 172988141771045. doi:10.1177/1729881417710457Bajracharya, M., Maimone, M. W., & Helmick, D. (2008). Autonomy for Mars Rovers: Past, Present, and Future. Computer, 41(12), 44-50. doi:10.1109/mc.2008.479Carsten, J., Rankin, A., Ferguson, D., & Stentz, A. (2007). Global Path Planning on Board the Mars Exploration Rovers. 2007 IEEE Aerospace Conference. doi:10.1109/aero.2007.352683Grotzinger, J. P., Crisp, J., Vasavada, A. R., Anderson, R. C., Baker, C. J., Barry, R., … Wiens, R. C. (2012). Mars Science Laboratory Mission and Science Investigation. Space Science Reviews, 170(1-4), 5-56. doi:10.1007/s11214-012-9892-2Khatib, O., Yeh, X., Brantner, G., Soe, B., Kim, B., Ganguly, S., … Creuze, V. (2016). Ocean One: A Robotic Avatar for Oceanic Discovery. IEEE Robotics & Automation Magazine, 23(4), 20-29. doi:10.1109/mra.2016.2613281Ceccarelli, M. (2012). Notes for a History of Grasping Devices. Mechanisms and Machine Science, 3-16. doi:10.1007/978-1-4471-4664-3_1Campion, G., & Chung, W. (2008). Wheeled Robots. Springer Handbook of Robotics, 391-410. doi:10.1007/978-3-540-30301-5_18Ferriere, L., Raucent, B., & Campion, G. (s. f.). Design of omnimobile robot wheels. Proceedings of IEEE International Conference on Robotics and Automation. doi:10.1109/robot.1996.509271Campion, G., Bastin, G., & Dandrea-Novel, B. (1996). Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Transactions on Robotics and Automation, 12(1), 47-62. doi:10.1109/70.481750Bałchanowski, J. (2012). Mobile Wheel-Legged Robot: Researching of Suspension Leveling System. Mechanisms and Machine Science, 3-12. doi:10.1007/978-94-007-5125-5_1Williams, R. L., Carter, B. E., Gallina, P., & Rosati, G. (2002). Dynamic model with slip for wheeled omnidirectional robots. IEEE Transactions on Robotics and Automation, 18(3), 285-293. doi:10.1109/tra.2002.1019459Chan, R. P. M., Stol, K. A., & Halkyard, C. R. (2013). Review of modelling and control of two-wheeled robots. Annual Reviews in Control, 37(1), 89-103. doi:10.1016/j.arcontrol.2013.03.004Kim, H., & Kim, B. K. (2014). Online Minimum-Energy Trajectory Planning and Control on a Straight-Line Path for Three-Wheeled Omnidirectional Mobile Robots. IEEE Transactions on Industrial Electronics, 61(9), 4771-4779. doi:10.1109/tie.2013.2293706Carbone, G., & Ceccarelli, M. (2005). Legged Robotic Systems. Cutting Edge Robotics. doi:10.5772/4669Chestnutt, J., Lau, M., Cheung, G., Kuffner, J., Hodgins, J., & Kanade, T. (s. f.). Footstep Planning for the Honda ASIMO Humanoid. Proceedings of the 2005 IEEE International Conference on Robotics and Automation. doi:10.1109/robot.2005.1570188Arikawa, K., & Hirose, S. (s. f.). Development of quadruped walking robot TITAN-VIII. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS ’96. doi:10.1109/iros.1996.570670Kurazume, R., Byong-won, A., Ohta, K., & Hasegawa, T. (s. f.). Experimental study on energy efficiency for quadruped walking vehicles. Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453). doi:10.1109/iros.2003.1250697Hirose, S., Fukuda, Y., Yoneda, K., Nagakubo, A., Tsukagoshi, H., Arikawa, K., … Hodoshima, R. (2009). Quadruped walking robots at Tokyo Institute of Technology. IEEE Robotics & Automation Magazine, 16(2), 104-114. doi:10.1109/mra.2009.932524Stoica, A., Carbone, G., Ceccarelli, M., & Pisla, D. (2010). Cassino Hexapod : Experiences and new leg design. 2010 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR). doi:10.1109/aqtr.2010.5520756Bares, J. E., & Wettergreen, D. S. (1999). Dante II: Technical Description, Results, and Lessons Learned. The International Journal of Robotics Research, 18(7), 621-649. doi:10.1177/02783649922066475Schiele, A., Romstedt, J., Lee, C., Henkel, H., Klinkner, S., Bertrand, R., … Michaelis, H. (2008). NanoKhod Exploration Rover - A Rugged Rover Suited for Small, Low-Cost, Planetary Lander Mission. IEEE Robotics & Automation Magazine, 15(2), 96-107. doi:10.1109/mra.2008.917888Takayama, T., & Hirose, S. (2003). Development of Souryu I & II -Connected Crawler Vehicle for Inspection of Narrow and Winding Space. Journal of Robotics and Mechatronics, 15(1), 61-69. doi:10.20965/jrm.2003.p0061Cuesta, F., & Ollero, A. (2005). Intelligent Mobile Robot Navigation. Springer Tracts in Advanced Robotics. doi:10.1007/b14079Ohya, I., Kosaka, A., & Kak, A. (1998). Vision-based navigation by a mobile robot with obstacle avoidance using single-camera vision and ultrasonic sensing. IEEE Transactions on Robotics and Automation, 14(6), 969-978. doi:10.1109/70.736780Desouza, G. N., & Kak, A. C. (2002). Vision for mobile robot navigation: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(2), 237-267. doi:10.1109/34.982903Borenstein, J., Everett, H. R., Feng, L., & Wehe, D. (1997). Mobile robot positioning: Sensors and techniques. Journal of Robotic Systems, 14(4), 231-249. doi:10.1002/(sici)1097-4563(199704)14:43.0.co;2-rBetke, M., & Gurvits, L. (1997). Mobile robot localization using landmarks. IEEE Transactions on Robotics and Automation, 13(2), 251-263. doi:10.1109/70.563647Kuffner, J., Nishiwaki, K., Kagami, S., Inaba, M., & Inoue, H. (2005). Motion Planning for Humanoid Robots. Robotics Research. The Eleventh International Symposium, 365-374. doi:10.1007/11008941_39Lee, Y.-J., & Bien, Z. (2002). Path planning for a quadruped robot: an artificial field approach. Advanced Robotics, 16(7), 609-627. doi:10.1163/15685530260390746Petres, C., Pailhas, Y., Patron, P., Petillot, Y., Evans, J., & Lane, D. (2007). Path Planning for Autonomous Underwater Vehicles. IEEE Transactions on Robotics, 23(2), 331-341. doi:10.1109/tro.2007.895057P. Raja. (2012). Optimal path planning of mobile robots: A review. International Journal of the Physical Sciences, 7(9). doi:10.5897/ijps11.1745Hart, P., Nilsson, N., & Raphael, B. (1968). A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics, 4(2), 100-107. doi:10.1109/tssc.1968.300136Lozano-Pérez, T., & Wesley, M. A. (1979). An algorithm for planning collision-free paths among polyhedral obstacles. Communications of the ACM, 22(10), 560-570. doi:10.1145/359156.359164Lozano-Perez. (1983). Spatial Planning: A Configuration Space Approach. IEEE Transactions on Computers, C-32(2), 108-120. doi:10.1109/tc.1983.1676196Brooks, R. A. (1983). Solving the find-path problem by good representation of free space. IEEE Transactions on Systems, Man, and Cybernetics, SMC-13(2), 190-197. doi:10.1109/tsmc.1983.6313112Schwartz, J. T., & Sharir, M. (1983). On the «piano movers» problem. II. General techniques for computing topological properties of real algebraic manifolds. Advances in Applied Mathematics, 4(3), 298-351. doi:10.1016/0196-8858(83)90014-3Kavraki LE. Random networks in configurations space for fast path planning. Doctoral dissertation, Department of Computer Science, Stanford University, Stanford, CA, 1994.Kavraki, L. E., Latombe, J.-C., Motwani, R., & Raghavan, P. (1998). Randomized Query Processing in Robot Path Planning. Journal of Computer and System Sciences, 57(1), 50-60. doi:10.1006/jcss.1998.1578Hsu, D., Kindel, R., Latombe, J.-C., & Rock, S. (2002). Randomized Kinodynamic Motion Planning with Moving Obstacles. The International Journal of Robotics Research, 21(3), 233-255. doi:10.1177/027836402320556421Kavraki, L. E., Svestka, P., Latombe, J.-C., & Overmars, M. H. (1996). Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, 12(4), 566-580. doi:10.1109/70.508439Rubio, F., Valero, F., Sunyer, J., & Mata, V. (2009). Direct step‐by‐step method for industrial robot path planning. Industrial Robot: An International Journal, 36(6), 594-607. doi:10.1108/01439910910994669Howard, T. M., & Kelly, A. (2007). Optimal Rough Terrain Trajectory Generation for Wheeled Mobile Robots. The International Journal of Robotics Research, 26(2), 141-166. doi:10.1177/0278364906075328Valero FJ. Planificación de trayectorias libres de obstáculos para un manipulador plano. Doctoral Thesis, UPV, Spain, 1990.Valero, F., Mata, V., Cuadrado, J. I., & Ceccarelli, M. (1996). A formulation for path planning of manipulators in complex environments by using adjacent configurations. Advanced Robotics, 11(1), 33-56. doi:10.1163/156855397x00038Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Garcia, M. A. P., Montiel, O., Castillo, O., Sepúlveda, R., & Melin, P. (2009). Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation. Applied Soft Computing, 9(3), 1102-1110. doi:10.1016/j.asoc.2009.02.014Miao, H., & Tian, Y.-C. (2013). Dynamic robot path planning using an enhanced simulated annealing approach. Applied Mathematics and Computation, 222, 420-437. doi:10.1016/j.amc.2013.07.022Bobrow, J. E., Dubowsky, S., & Gibson, J. S. (1985). Time-Optimal Control of Robotic Manipulators Along Specified Paths. 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Tracking Control of Mobile Robots: A Case Study in Backstepping**This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Alberto Isidori under the direction of Editor Tamer Başar. Automatica, 33(7), 1393-1399. doi:10.1016/s0005-1098(97)00055-1Klosowski, J. T., Held, M., Mitchell, J. S. B., Sowizral, H., & Zikan, K. (1998). Efficient collision detection using bounding volume hierarchies of k-DOPs. IEEE Transactions on Visualization and Computer Graphics, 4(1), 21-36. doi:10.1109/2945.675649Mirtich B. V-Clip: fast and robust polyhedral collision detection. Technical Report TR97-05, Mitsubishi Electric Research Laboratory, 1997.Mohamed, E. F., El-Metwally, K., & Hanafy, A. R. (2011). An improved Tangent Bug method integrated with artificial potential field for multi-robot path planning. 2011 International Symposium on Innovations in Intelligent Systems and Applications. doi:10.1109/inista.2011.5946136Seder, M., & Petrovic, I. (2007). Dynamic window based approach to mobile robot motion control in the presence of moving obstacles. Proceedings 2007 IEEE International Conference on Robotics and Automation. doi:10.1109/robot.2007.363613Simmons, R. (s. f.). The curvature-velocity method for local obstacle avoidance. Proceedings of IEEE International Conference on Robotics and Automation. doi:10.1109/robot.1996.51102

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, κ£, connected with Łukasiewicz [14], and extend this research for two additional RIFs: κ 1, and κ 2, following a paper by Gomolińska [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 Białystok, PolandAnna Gomolinska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 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 117–135, 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 142–151, 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 35–55. 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-Kęplicz, 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 215–226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371–385, 2014. doi:10.3233/FI-2014-1129.Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In Tamás Mihálydeák, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo Düntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225–238, 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 – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.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 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 Michał Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183–191, 2018. doi:10.2478/forma-2018-0016.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. 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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

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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