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

Fuzzy-logic-based control, filtering, and fault detection for networked systems: A Survey

This paper is concerned with the overview of the recent progress in fuzzy-logic-based filtering, control, and fault detection problems. First, the network technologies are introduced, the networked control systems are categorized from the aspects of fieldbuses and industrial Ethernets, the necessity of utilizing the fuzzy logic is justified, and the network-induced phenomena are discussed. Then, the fuzzy logic control strategies are reviewed in great detail. Special attention is given to the thorough examination on the latest results for fuzzy PID control, fuzzy adaptive control, and fuzzy tracking control problems. Furthermore, recent advances on the fuzzy-logic-based filtering and fault detection problems are reviewed. Finally, conclusions are given and some possible future research directions are pointed out, for example, topics on two-dimensional networked systems, wireless networked control systems, Quality-of-Service (QoS) of networked systems, and fuzzy access control in open networked systems.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374039, 61473163, and 61374127, the Hujiang Foundation of China under Grants C14002 andD15009, the Engineering and Physical Sciences Research Council (EPSRC) of the UK, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Applications of Soft Computing in Mobile and Wireless Communications

Soft computing is a synergistic combination of artificial intelligence methodologies to model and solve real world problems that are either impossible or too difficult to model mathematically. Furthermore, the use of conventional modeling techniques demands rigor, precision and certainty, which carry computational cost. On the other hand, soft computing utilizes computation, reasoning and inference to reduce computational cost by exploiting tolerance for imprecision, uncertainty, partial truth and approximation. In addition to computational cost savings, soft computing is an excellent platform for autonomic computing, owing to its roots in artificial intelligence. Wireless communication networks are associated with much uncertainty and imprecision due to a number of stochastic processes such as escalating number of access points, constantly changing propagation channels, sudden variations in network load and random mobility of users. This reality has fuelled numerous applications of soft computing techniques in mobile and wireless communications. This paper reviews various applications of the core soft computing methodologies in mobile and wireless communications

Extruder for food product (otak–otak) with heater and roll cutter

Food extrusion is a form of extrusion used in food industries. It is a process by which a set of mixed ingredients are forced through an opening in a perforated plate or die with a design specific to the food, and is then cut to a specified size by blades [1]. Summary of the invention principal objects of the present invention are to provide a machine capable of continuously producing food products having an’ extruded filler material of meat or similarity and an extruded outer covering of a moldable food product, such as otak-otak, that completely envelopes the filler material