196,646 research outputs found
Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions
No full textIF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set of membership functions by using extreme value theorem. The set of membership functions (fuzzy sets) is defined in this article to verifier our proofs before by Mizar [9], [10], [4]. Membership functions composed of triangle function, piecewise linear function and Gaussian function used in practice are formalized using existing functions. On the other hand, not only curve membership functions mentioned above but also membership functions composed of straight lines (piecewise linear function) like triangular and trapezoidal functions are formalized. Moreover, different from the definition in [3] formalizations of triangular and trapezoidal function composed of two straight lines, minimum function and maximum functions are proposed. We prove, using the Mizar [2], [1] formalism, some properties of membership functions such as continuity and periodicity [13], [8].This work has been partially supported in 2019-2020 by the domestic research grant of University of Marketing and Distribution Sciences in Kobe (Japan).University of Marketing and Distribution Sciences, Kobe, JapanGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, 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 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, 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):9–32, 2018. doi:10.1007/s10817-017-9440-6.Adam Grabowski. The formal construction of fuzzy numbers. Formalized Mathematics, 22(4):321–327, 2014. doi:10.2478/forma-2014-0032.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.Artur Korniłowicz and Yasunari Shidama. Inverse trigonometric functions arcsin and arccos. Formalized Mathematics, 13(1):73–79, 2005.Bo Li, Yanhong Men, Dailu Li, and Xiquan Liang. Basic properties of periodic functions. Formalized Mathematics, 17(4):245–248, 2009. doi:10.2478/v10037-009-0031-9.E. H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.Takashi Mitsuishi. Uncertain defuzzified value of periodic membership function. In 2018 International Electrical Engineering Congress (iEECON), pages 1–4, 2018. doi:10.1109/IEECON.2018.8712319.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.Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Basic properties of fuzzy set operation and membership function. Formalized Mathematics, 9(2):357–362, 2001.Takashi Mitsuishi, Noboru Endou, and Keiji Ohkubo. Trigonometric functions on complex space. Formalized Mathematics, 11(1):29–32, 2003.Takashi Mitsuishi, Takanori Terashima, Nami Shimada, Toshimichi Homma, Kiyoshi Sawada, and Yasunari Shidama. Continuity of defuzzification on L2 space for optimization of fuzzy control. In Active Media Technology, pages 73–81. Springer-Berlin-Heidelberg, 2012. ISBN 978-3-642-35236-2.Takashi Mitsuishi, Nami Shimada, Toshimichi Homma, Mayumi Ueda, Masayuki Kochizawa, and Yasunari Shidama. Continuity of approximate reasoning using fuzzy number under Łukasiewicz t-norm. In 2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pages 71–74, 2015. doi:10.1109/ICCIS.2015.7274550.29210311
Symmetrical Piecewise Linear Functions Composed by Absolute Value Function
No full textWe continue the formal development of the application of piecewise linear functions and centroids in the area of fuzzy set theory. The corresponding piecewise linear functions are symmetrical and composed by absolute function. In this paper we prove that the membership functions of isosceles triangle type and isosceles trapezoid type can be constructed by functions of this type.Faculty of Business and Informatics, Nagano University, JapanDidier Dubois and Henri Prade. Operations on fuzzy numbers. International Journal of Systems Science, 9(6):613–626, 1978. doi:10.1080/00207727808941724.Didier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.Ronald E. Giachetti and Robert E. Young. A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets and Systems, 91(2):185–202, 1997.
doi:10.1016/S0165-0114(97)00140-1.Eikou Gonda, Hitoshi Miyata, and Masaaki Ohkita. Self-turning of fuzzy rules with different types of MSFs (in Japanese). Journal of Japan Society for Fuzzy Theory and
Intelligent Informatics, 16(6):540–550, 2004. doi:10.3156/jsoft.16.540.Adam Grabowski. The formal construction of fuzzy numbers. Formalized Mathematics, 22(4):321–327, 2014. doi:10.2478/forma-2014-0032.Adam Grabowski. Fuzzy implications in the Mizar system. In 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, Luxembourg, July 11–14, 2021, pages
1–6. IEEE, 2021. doi:10.1109/FUZZ45933.2021.9494593.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 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 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. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Mizar in a nutshell. Journal of Formalized Reasoning, 3(2):153–245, 2010.Tetsuro Katafuchi, Kiyoji Asai, and Hiroshi Fujita. Investigation of deffuzification in fuzzy inference: Proposal of a new defuzzification method (in Japanese). Medical Imaging and Information Sciences, 18(1):19–30, 2001. doi:10.11318/mii1984.18.19.Ebrahim H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.Takashi Mitsuishi. Some properties of membership functions composed of triangle functions and piecewise linear functions. Formalized Mathematics, 29(2):103–115, 2021. doi:10.2478/forma-2021-0011.Takashi Mitsuishi. Definition of centroid method as defuzzification. Formalized Mathematics, 30(2):125–134, 2022. doi:10.2478/forma-2022-0010.Takashi Mitsuishi. Isosceles triangular and isosceles trapezoidal membership functions using centroid method. Formalized Mathematics, 31(1):59–66, 2023. doi:10.2478/forma-2023-0006.Takashi Mitsuishi, Takanori Terashima, Nami Shimada, Toshimichi Homma, and Yasunari Shidama. Approximate reasoning using LR fuzzy number as input for sensorless fuzzy control. In 2016 IEEE Symposium on Sensorless Control for Electrical Drives (SLED), pages 1–5, 2016. doi:10.1109/SLED.2016.7518804.Masaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990.Timothy J. Ross. Fuzzy Logic with Engineering Applications. John Wiley and Sons Ltd, 2010.Luciano Stefanini and Laerte Sorini. Fuzzy arithmetic with parametric LR fuzzy numbers. In Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, pages 600–605, 2009.Werner Van Leekwijck and Etienne E. Kerre. Defuzzification: Criteria and classification. Fuzzy Sets and Systems, 108(2):159–178, 1999.Lotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. doi:10.1016/S0019-9958(65)90241-X.31129930
Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method
No full textSince isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f +· g, or f +* g using Mizar formalism, where f, g are affine mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agreement of the same function expressed with different parameters and formalized those centroids with parameters. In addition, various properties of membership functions on intervals where the endpoints of the domain are fixed and on general intervals are formalized in Mizar [1], [2]. Our formal development contains also some numerical results which can be potentially useful to encode either fuzzy numbers [7], or even fuzzy implications [5], [6] and extends the possibility of building hybrid rough-fuzzy approach in the future [8].Faculty of Business and Informatics, Nagano University, JapanGrzegorz 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.Grzegorz 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.Ronald E. Giachetti and Robert E. Young. A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets and Systems, 91(2):185–202, 1997.
doi:https://doi.org/10.1016/S0165-0114(97)00140-1. Fuzzy Arithmetic.Eikou Gonda, Hitoshi Miyata, and Masaaki Ohkita. Self-turning of fuzzy rules with different types of MSFs (in Japanese). Journal of Japan Society for Fuzzy Theory and
Intelligent Informatics, 16(6):540–550, 2004. doi:10.3156/jsoft.16.540.Adam Grabowski. On fuzzy negations generated by fuzzy implications. Formalized Mathematics, 28(1):121–128, 2020. doi:10.2478/forma-2020-0011.Adam Grabowski. Fuzzy implications in the Mizar system. In 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, Luxembourg, July 11–14, 2021, pages
1–6. IEEE, 2021. doi:10.1109/FUZZ45933.2021.9494593.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 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.Tetsuro Katafuchi, Kiyoji Asai, and Hiroshi Fujita. Investigation of deffuzification in fuzzy inference: Proposal of a new defuzzification method (in Japanese). Medical Imaging and Information Sciences, 18(1):19–30, 2001. doi:10.11318/mii1984.18.19.Ebrahim H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.Takashi Mitsuishi. Some properties of membership functions composed of triangle functions and piecewise linear functions. Formalized Mathematics, 29(2):103–115, 2021. doi:10.2478/forma-2021-0011.Takashi Mitsuishi. Definition of centroid method as defuzzification. Formalized Mathematics, 30(2):125–134, 2022. doi:10.2478/forma-2022-0010.Masaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990.Timothy J. Ross. Fuzzy Logic with Engineering Applications. John Wiley and Sons Ltd, 2010.Luciano Stefanini and Laerte Sorini. Fuzzy arithmetic with parametric LR fuzzy numbers. In Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, pages 600–605, 2009.Werner Van Leekwijck and Etienne E. Kerre. Defuzzification: Criteria and classification. Fuzzy Sets and Systems, 108(2):159–178, 1999.311596
Definition of Centroid Method as Defuzzification
No full textIn this study, using the Mizar system [1], [2], we reuse formalization efforts in fuzzy sets described in [5] and [6]. This time the centroid method which is one of the fuzzy inference processes is formulated [10]. It is the most popular of all defuzzied methods ([11], [13], [7]) – here, defuzzified crisp value is obtained from domain of membership function as weighted average [8]. Since the integral is used in centroid method, the integrability and bounded properties of membership functions are also mentioned to fill the formalization gaps present in the Mizar Mathematical Library, as in the case of another fuzzy operators [4]. In this paper, the properties of piecewise linear functions consisting of two straight lines are mainly described.Faculty of Business and Informatics, Nagano University, JapanGrzegorz 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.Grzegorz 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.Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93–102, 1999.Adam Grabowski. Fuzzy implications in the Mizar system. In 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, Luxembourg, July 11–14, 2021, pages
1–6. IEEE, 2021. doi:10.1109/FUZZ45933.2021.9494593.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.Tetsuro Katafuchi, Kiyoji Asai, and Hiroshi Fujita. Investigation of deffuzification in fuzzy inference: Proposal of a new defuzzification method (in Japanese). Medical Imaging and Information Sciences, 18(1):19–30, 2001. doi:10.11318/mii1984.18.19Ebrahim H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Basic properties of fuzzy set operation and membership function. Formalized Mathematics, 9(2):357–362, 2001.Masaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990.Timothy J. Ross. Fuzzy Logic with Engineering Applications. John Wiley and Sons Ltd, 2010.Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195–200, 2004.Werner Van Leekwijck and Etienne E. Kerre. Defuzzification: Criteria and classification. Fuzzy Sets and Systems, 108(2):159–178, 1999.30212513
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States" By M. Carey.
No full text"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States: containing bried sketches of the moral and political character of those states.
By M. Carey, member of the American philosophical, and of the American Antiquarian Society, and author of The Olive Branch, Cindiciae Hibernicae, essays on banking, on political economy, and on internal improvement.
To which are now added the English editor's comments on the subject; together with Important Advice to Emigrants, and Cautions Against Impositions Practiced in the Outports
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Efficient deep processing of japanese
No full textWe present a broad coverage Japanese grammar written in the HPSG formalism with MRS semantics. The grammar is created for use in real world applications, such that robustness and performance issues play an important role. It is connected to a POS tagging and word segmentation tool. This grammar is being developed in a multilingual context, requiring MRS structures that are easily comparable across languages
Dr. Glendon Swarthout
No full textHosted by Roger M. Busfield, MSU Assistant Professor of Speech and Theater, Meet the Author is designed to introduce a general audience to a contemporary author and their work through in-depth interviews. This episode features a conversation between Dr. Glendon Swarthout, prolific author and English professor at MSU, and assistant professors Sam S. Baskett and Theodore B. Strandness
Simulation of thermal plant optimization and hydraulic aspects of thermal distribution loops for large campuses
No full textFollowing an introduction, the author describes Texas A&M University and its utilities system. After that, the author presents how to construct simulation models for chilled water and heating hot water distribution systems. The simulation model was used in a $2.3 million Ross Street chilled water pipe replacement project at Texas A&M University. A second project conducted at the University of Texas at San Antonio was used as an example to demonstrate how to identify and design an optimal distribution system by using a simulation model. The author found that the minor losses of these closed loop thermal distribution systems are significantly higher than potable water distribution systems. In the second part of the report, the author presents the latest development of software called the Plant Optimization Program, which can simulate cogeneration plant operation, estimate its operation cost and provide optimized operation suggestions. The author also developed detailed simulation models for a gas turbine and heat recovery steam generator and identified significant potential savings. Finally, the author also used a steam turbine as an example to present a multi-regression method on constructing simulation models by using basic statistics and optimization algorithms. This report presents a survey of the author??s working experience at the Energy Systems Laboratory (ESL) at Texas A&M University during the period of January 2002 through March 2004. The purpose of the above work was to allow the author to become familiar with the practice of engineering. The result is that the author knows how to complete a project from start to finish and understands how both technical and nontechnical aspects of a project need to be considered in order to ensure a quality deliverable and bring a project to successful completion. This report concludes that the objectives of the internship were successfully accomplished and that the requirements for the degree of Degree of Engineering have been satisfied
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