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Academic literature on the topic 'Fuzzy logic theory'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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Journal articles on the topic "Fuzzy logic theory"

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Takeuti, Gaisi, and Satoko Titani. "Fuzzy logic and fuzzy set theory." Archive for Mathematical Logic 32, no. 1 (January 1992): 1–32. http://dx.doi.org/10.1007/bf01270392.

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GAO, XIAOYU, Q. S. GAO, Y. HU, and L. LI. "A PROBABILITY-LIKE NEW FUZZY SET THEORY." International Journal of Pattern Recognition and Artificial Intelligence 20, no. 03 (May 2006): 441–62. http://dx.doi.org/10.1142/s0218001406004697.

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In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory — it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world — are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory — it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory — is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set theories, C-fuzzy set theory and probability-like fuzzy set theory, the N-fuzzy set theory, are proposed. The two are equivalent, and both overcome the error and shortcoming of Zadeh's fuzzy set theory, and they are consistent with normal, natural and classical thinking, logic and concepts. The similarities of N-fuzzy set theory with probability theory are also examined.

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Ching, Hugh. "The Fuzzy Completeness Theory." Journal of Research in Philosophy and History 4, no. 1 (February 24, 2021): p52. http://dx.doi.org/10.22158/jrph.v4n1p52.

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The Two Incompleteness Theorems of Kurt Friedrich Gödel and the Impossibility Theorem of Kenneth Arrow claim that logic, the most reliable of human knowledge, is incomplete or can be inconsistent. The Fuzzy Completeness Theory states that the Fuzzy Logic of Lotfi A. Zadeh has resolved the incompleteness and impossibility in logic and made logic complete and knowledge reliable with the new concept of Range of Tolerance, within which logic is still complete and knowledge, valid. In the Age of Reason about 300 years ago just prior to the Age of Science, reasoning is free for all, without the constraint of the laws of nature, which would be discovered in the Age of Science. However, the Scientific Method of reasoning by empirical verification depends so much on faith that it is logically and empirically dismissed by mathematicians and logicians, especially, after the exposure by Thomas Kuhn and Paul Feyerabend that a scientific advancement is akin to a religious conversion. On the other hand, mathematicians and logicians have been working steadily to find the limit of reliable knowledge. In the current state of knowledge, Kurt Gödel has the last word with his Two Incompleteness Theorems, which conclude that the most reliable of human knowledge, logic, is incomplete, casting doubt whether knowledge is completely reliable. Gödel’s view is further supported by the Impossibility Theorem of Kenneth Arrow. However, Zadeh and the author of this paper extend Zadeh’s concept of Range of Value in Fuzzy Logic to that of Range of Tolerance. Accordingly, Fuzzy Logic deals with the sacrifice of precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility of an uncertain future. In knowledge, incompleteness in logic can be resolved by the Range of Tolerance covering the incomplete part or ignoring the infrequent impossibilities, and, thus, making logic valid, again. Knowledge is derived generally from reason. Technically, the Fuzzy Completeness Theory classifies 16 Methods of Reason. The 16 Methods are the combination of the 4 basic Methods of Reason: 1) Logic, 2) Mathematics, 3) Empirical Verification, and 4) Others, each of which has 2 forms: 1) Fuzzy and 2) Exact and two types: 1) Complete and 2) Incomplete. Gödel, Arrow, and the Author agree that no matter how rigorous is the Method of Reason the reason cannot be complete, when the reason is Exact. When a solution is newly defined as an answer within the Range of Tolerance of the solution, Fuzzy Logic resolves the incompleteness in logic and becomes the new foundation of knowledge, replacing Exact Logic. With this definition of a solution, Fuzzy Logic covers the incomplete or the impossible parts of the solution by expanding sufficiently the Range of Tolerance to make reason complete and knowledge reliable, but only within the Range of Tolerance. To summarize, even though the world’s leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still operating smoothly, and science has even demonstrated the power of knowledge. The conflict between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, reality is fuzzy, not exact. The breakthrough impact of this paper centers around completeness theory and Fuzzy Logic. In the early 21st century, the mainstream knowledge is still not aware that the supply and demand model is incomplete, and that the DNA-protein system resembles computer science based on logic more than science based on experimentation. The current computer is based on exact logic and is designed for temporary existence, while the living system is design for permanent existence and must depend on the Range of Tolerance based on Fuzzy Logic to survive permanently in an uncertain future. Financial crises will be caused by the unstable investment return, which is the incomplete part in the supply demand model. Complexity crises will be caused by the lack of the requirement of permanence or complete automation, which is the ultimate solution to unlimited complexity. The 16 Methods of Reason correspond roughly to Culture Level Quotient (CLQ), which is a non-technical measure of a person, a people or a nation.

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Maseleno, Andino, Md Mahmud Hasan, and Norjaidi Tuah. "Combining Fuzzy Logic and Dempster-Shafer Theory." TELKOMNIKA Indonesian Journal of Electrical Engineering 16, no. 3 (December 1, 2015): 583. http://dx.doi.org/10.11591/tijee.v16i3.1651.

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This research aims to combine the mathematical theory of evidence with the rule based logics to refine the predictable output. Integrating Fuzzy Logic and Dempster-Shafer theory by calculating the similarity between Fuzzy membership function. The novelty aspect of this work is that basic probability assignment is proposed based on the similarity measure between membership function. The similarity between Fuzzy membership function is calculated to get a basic probability assignment. The Dempster-Shafer mathematical theory of evidence has attracted considerable attention as a promising method of dealing with some of the basic problems arising in combination of evidence and data fusion. Dempster-Shafer theory provides the ability to deal with ignorance and missing information. The foundation of Fuzzy logic is natural language which can help to make full use of expert information.

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Arfi, Badredine. "Linguistic Fuzzy-Logic Game Theory." Journal of Conflict Resolution 50, no. 1 (February 2006): 28–57. http://dx.doi.org/10.1177/0022002705284708.

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Rouvray, Dennis H. "Fuzzy sets and fuzzy logic: Theory and applications." Endeavour 20, no. 1 (January 1996): 44. http://dx.doi.org/10.1016/s0160-9327(96)90083-6.

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Wedding, Donald K. "Fuzzy sets and fuzzy logic: Theory and applications." Neurocomputing 14, no. 3 (February 1997): 302–3. http://dx.doi.org/10.1016/s0925-2312(97)88327-0.

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Simon, Dan. "Fuzzy sets and fuzzy logic: Theory and applications." Control Engineering Practice 4, no. 9 (September 1996): 1332–33. http://dx.doi.org/10.1016/0967-0661(96)81492-4.

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Lakov, Dimiter. "Fuzzy sets and fuzzy logic, theory and applications." Fuzzy Sets and Systems 84, no. 1 (November 1996): 114. http://dx.doi.org/10.1016/0165-0114(96)82406-7.

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Lano, K. "Intuitionistic modal logic and set theory." Journal of Symbolic Logic 56, no. 2 (June 1991): 497–516. http://dx.doi.org/10.2307/2274696.

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The mathematical treatment of the concepts of vagueness and approximation is of increasing importance in artificial intelligence and related research. The theory of fuzzy sets was created by Zadeh [Z] to allow representation and mathematical manipulation of situations of partial truth, and proceeding from this a large amount of theoretical and applied development of this concept has occurred. The aim of this paper is to develop a natural logic and set theory that is a candidate for the formalisation of the theory of fuzzy sets. In these theories the underlying logic of properties and sets is intuitionistic, but there is a subset of formulae that are ‘crisp’, classical and two-valued, which represent the certain information. Quantum logic or logics weaker than intuitionistic can also be adopted as the basis, as described in [L]. The relationship of this theory to the intensional set theory MZF of [Gd] and the global intuitionistic set theory GIZF of Takeuti and Titani [TT] is also treated.

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Dissertations / Theses on the topic "Fuzzy logic theory"

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Peters, Barry. "Stable fuzzy logic controllers for uncertain dynamic systems." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/18223.

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Wang, Haibin. "Interval neutrosophic sets and logic theory and applications in computing /." unrestricted, 2005. http://etd.gsu.edu/theses/available/etd-11172005-131340/.

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Thesis (Ph. D.)--Georgia State University, 2005.
1 electronic text (119 p. : ill.) : digital, PDF file. Title from title screen. Rajshekhar Sunderraman, committee chair; Yan-Qing Zhang, Anu Bourgeois, Lifeng Ding, committee members. Description based on contents viewed Apr. 3, 2007. Includes bibliographical references (p. 112-119).

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Al-Assaf, Y. "Self-tuning control : Theory and applications." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235033.

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Wang, Haibin. "Interval Neutrosophic Sets and Logic: Theory and Applications in Computing." Digital Archive @ GSU, 2006. http://digitalarchive.gsu.edu/cs_diss/2.

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A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the set-theoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the set-theoretic operators and relation-theoretic operators of fuzzy relations and paraconsistent relations to neutrosophic relations. We propose the generalized SQL query constructs and tuple-relational calculus for Neutrosophic Data Model. We also design an architecture of Semantic Web Services agent based on the interval neutrosophic logic and do the simulation study.

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Polkinghorne, Martyn Neal. "A self-organising fuzzy logic autopilot for small vessels." Thesis, University of Plymouth, 1994. http://hdl.handle.net/10026.1/1100.

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Currently small vessels use autopilots based on the Proportional plus Integral plus Derivative (PID) algorithm which utilises fixed gain values. This type of autopilot is known to often cause performance difficulties, a survey is therefore carried out to identify the alternative autopilot methods that have been previously investigated. It is shown that to date, all published work in this area has been based on large ships, however, there are specific difficulties applicable to the small vessel which have therefore not been considered. After the recognition of artificial neural networks and fuzzy logic as being the two most suitable techniques for use in the development of a new, and adaptive, small vessel autopilot design, the basic concepts of both are reviewed and fiizzy logic identified as being the most suitable for this application. The remainder of the work herein is concerned with the development of a fuzzy logic controller capable of a high level of performance in the two modes of coursekeeping and course-changing. Both modes are integrated together by the use of nonlinear fuzzy input windows. Improved performance is then obtained by using a nonlinear fuzzy rulebase. Integral action is included by converting the fuzzy output window to an unorthodox design described by two hundred and one fuzzy singletons, and then by shifting the identified fuzzy sets to positive, or negative, in order that any steady-state error may be removed from the vessel's performance. This design generated significant performance advantages when compared to the conventional PID autopilot. To develop further into an adaptive form of autopilot called the self-organising controller, the single rulebase was replaced by two enhancement matrices. These are novel features which are modified on-line by two corresponding performance indices. The magnitude of the learning was related to the observed performance of the vessel when expressed in terms of its heading error and rate of change of heading error. The autopilot design is validated using both simulation, and full scale sea trials. From these tests it is demonstrated that when compared to the conventional PID controller, the self-organising controller significantly improved performance for both course-changing and course-keeping modes of operation. In addition, it has the capability to learn on-line and therefore to maintain performance when subjected to vessel dynamic or environmental disturbance alterations.

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Jin, Gang-Gyoo. "Intelligent fuzzy logic control of processes with time delays." Thesis, Cardiff University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388058.

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Ribeiro, Maria Rita Sarmento de Almeida. "Application of support logic theory to fuzzy multiple attribute decision problems." Thesis, University of Bristol, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357891.

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Hill, Carla. "Mass assignments for inductive logic programming." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325748.

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Guyot, Nicolas E. "Fuzzy logic and utility theory for multiobjective optimization of automotive joints." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-08292008-063415/.

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Ornelas, Gilbert. "Set-valued extensions of fuzzy logic classification theorems /." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2007. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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Books on the topic "Fuzzy logic theory"

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Bo, Yuan, ed. Fuzzy sets and fuzzy logic: Theory and applications. Upper Saddle River, N.J: Prentice Hall PTR, 1995.

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Nicola, Olivetti, and Gabbay Dov M. 1945-, eds. Proof theory for fuzzy logics. [Dordrecht]: Springer, 2009.

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H, St Clair Ute, and Yuan Bo, eds. Fuzzy set theory: Foundations and applications. Upper Saddle River, NJ: Prentice Hall, 1997.

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1949-, Fedrizzi Mario, and Fullér Robert 1958-, eds. Fuzzy logic in management. Boston: Kluwer Academic, 2004.

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Fuzzy logic for beginners. Singapore: World Scientific, 2001.

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Atanassov, Krassimir T. On Intuitionistic Fuzzy Sets Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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1949-, Ryan Michael, and Power James, eds. Using fuzzy logic: Towards intelligent systems. New York: Prentice Hall, 1994.

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Li, Zhong. Integration of fuzzy logic and chaos theory. Berlin [u.a.]: Springer, 2010.

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Li, Zhong, Wolfgang A. Halang, and Guanrong Chen, eds. Integration of Fuzzy Logic and Chaos Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-32502-6.

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Li, Zhong, Wolfgang A. Halang, and Guanrong Chen, eds. Integration of Fuzzy Logic and Chaos Theory. Berlin/Heidelberg: Springer-Verlag, 2006. http://dx.doi.org/10.1007/b103243.

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Book chapters on the topic "Fuzzy logic theory"

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Lowen, R. "Fuzzy Logic." In Fuzzy Set Theory, 169–239. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8741-9_6.

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Li, Zhong, and Xu Zhang. "On Fuzzy Logic and Chaos Theory." In Fuzzy Logic, 79–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-71258-9_5.

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Ahmed, Jameel, Mohammed Yakoob Siyal, Shaheryar Najam, and Zohaib Najam. "Fuzzy Logic Theory." In Fuzzy Logic Based Power-Efficient Real-Time Multi-Core System, 47–62. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-3120-5_5.

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Warner, M. W. "Towards a Mathematical Theory of Fuzzy Topology." In Fuzzy Logic, 83–94. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2014-2_8.

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Klement, Erich Peter, Radko Mesiar, and Endre Pap. "Fuzzy set theory." In Trends in Logic, 249–64. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9540-7_12.

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Gottwald, Siegfried. "Basic fuzzy set theory." In Fuzzy Sets and Fuzzy Logic, 37–96. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-86812-1_2.

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Kruse, Rudolf, Jörg Gebhardt, and Frank Klawonn. "Numerical and Logical Approaches to Fuzzy Set Theory by the Context Model." In Fuzzy Logic, 365–76. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2014-2_34.

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Dubois, Didier, and Henri Prade. "Fuzzy Sets and Possibility Theory : Some Applications to Inference and Decision Processes." In Fuzzy Logic, 66–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-78023-3_4.

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Bede, Barnabas. "Possibility Theory." In Mathematics of Fuzzy Sets and Fuzzy Logic, 201–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35221-8_11.

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D’Ambrosio, Bruce. "Fuzzy Logic Control." In Qualitative Process Theory Using Linguistic Variables, 5–15. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4613-9671-0_2.

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Conference papers on the topic "Fuzzy logic theory"

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"SATISFIABILITY DEGREE THEORY FOR TEMPORAL LOGIC." In International Conference on Fuzzy Computation Theory and Applications. SciTePress - Science and and Technology Publications, 2011. http://dx.doi.org/10.5220/0003672804970500.

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Castillo, Oscar, Patricia Melin, Janusz Kacprzyk, and Witold Pedrycz. "Type-2 Fuzzy Logic: Theory and Applications." In 2007 IEEE International Conference on Granular Computing (GRC 2007). IEEE, 2007. http://dx.doi.org/10.1109/grc.2007.118.

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Castillo, Oscar, Patricia Melin, Janusz Kacprzyk, and Witold Pedrycz. "Type-2 Fuzzy Logic: Theory and Applications." In 2007 IEEE International Conference on Granular Computing (GRC 2007). IEEE, 2007. http://dx.doi.org/10.1109/grc.2007.4403084.

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Leon, Teresa, and Vicente Liern. "Fuzzy logic helps to integrate music theory and practice." In 2010 IEEE International Conference on Fuzzy Systems. IEEE, 2010. http://dx.doi.org/10.1109/fuzzy.2010.5584652.

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"FUZZY LOGIC BASED QUALITY OF SERVICE MODELS." In International Conference on Fuzzy Computation Theory and Applications. SciTePress - Science and and Technology Publications, 2011. http://dx.doi.org/10.5220/0003694305160519.

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Brown, M. Q. "The theory and development of a neurofuzzy PID controller." In IEE Colloquium on Fuzzy Logic Controllers in Practice. IEE, 1996. http://dx.doi.org/10.1049/ic:19961130.

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Akey, Mark L. "Fuzzy logic ABS control: sizing theory to implementation." In Aerospace/Defense Sensing and Controls, edited by Bruno Bosacchi and James C. Bezdek. SPIE, 1996. http://dx.doi.org/10.1117/12.243262.

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Jain, Manisha, Leandro Gomes, Alexandre Madeira, and Luis S. Barbosa. "Towards a specification theory for fuzzy modal logic." In 2021 International Symposium on Theoretical Aspects of Software Engineering (TASE). IEEE, 2021. http://dx.doi.org/10.1109/tase52547.2021.00031.

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Subba Reddy, P. Venkata. "Fuzzy predicate logic for Knowledge Representation." In 2013 International Conference on Fuzzy Theory and Its Applications (iFUZZY). IEEE, 2013. http://dx.doi.org/10.1109/ifuzzy.2013.6825407.

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Guller, Dušan. "Hyperresolution for Propositional Product Logic." In 8th International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0006044300300041.

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Reports on the topic "Fuzzy logic theory"

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Smith, James F., and III. A Fuzzy Logic Multisensor Association Algorithm: Theory and Simulation. Fort Belvoir, VA: Defense Technical Information Center, September 1997. http://dx.doi.org/10.21236/ada330176.

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Tsidylo, Ivan M., Serhiy O. Semerikov, Tetiana I. Gargula, Hanna V. Solonetska, Yaroslav P. Zamora, and Andrey V. Pikilnyak. Simulation of intellectual system for evaluation of multilevel test tasks on the basis of fuzzy logic. CEUR Workshop Proceedings, June 2021. http://dx.doi.org/10.31812/123456789/4370.

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The article describes the stages of modeling an intelligent system for evaluating multilevel test tasks based on fuzzy logic in the MATLAB application package, namely the Fuzzy Logic Toolbox. The analysis of existing approaches to fuzzy assessment of test methods, their advantages and disadvantages is given. The considered methods for assessing students are presented in the general case by two methods: using fuzzy sets and corresponding membership functions; fuzzy estimation method and generalized fuzzy estimation method. In the present work, the Sugeno production model is used as the closest to the natural language. This closeness allows for closer interaction with a subject area expert and build well-understood, easily interpreted inference systems. The structure of a fuzzy system, functions and mechanisms of model building are described. The system is presented in the form of a block diagram of fuzzy logical nodes and consists of four input variables, corresponding to the levels of knowledge assimilation and one initial one. The surface of the response of a fuzzy system reflects the dependence of the final grade on the level of difficulty of the task and the degree of correctness of the task. The structure and functions of the fuzzy system are indicated. The modeled in this way intelligent system for assessing multilevel test tasks based on fuzzy logic makes it possible to take into account the fuzzy characteristics of the test: the level of difficulty of the task, which can be assessed as “easy”, “average", “above average”, “difficult”; the degree of correctness of the task, which can be assessed as “correct”, “partially correct”, “rather correct”, “incorrect”; time allotted for the execution of a test task or test, which can be assessed as “short”, “medium”, “long”, “very long”; the percentage of correctly completed tasks, which can be assessed as “small”, “medium”, “large”, “very large”; the final mark for the test, which can be assessed as “poor”, “satisfactory”, “good”, “excellent”, which are included in the assessment. This approach ensures the maximum consideration of answers to questions of all levels of complexity by formulating a base of inference rules and selection of weighting coefficients when deriving the final estimate. The robustness of the system is achieved by using Gaussian membership functions. The testing of the controller on the test sample brings the functional suitability of the developed model.

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Lavrentieva, Olena O., Ihor O. Arkhypov, Olexander I. Kuchma, and Aleksandr D. Uchitel. Use of simulators together with virtual and augmented reality in the system of welders’ vocational training: past, present, and future. [б. в.], February 2020. http://dx.doi.org/10.31812/123456789/3748.

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The article discusses the theory and methods of simulation training, its significance in the context of training specialists for areas where the lack of primary qualification is critical. The most widespread hardware and software solutions for the organization welders' simulation training that use VR- and AR- technologies have been analyzed. A review of the technological infrastructure and software tools for the virtual teaching-and-production laboratory of electric welding has been made on the example of the achievements of Fronius, MIMBUS, Seabery. The features of creating a virtual simulation of the welding process using modern equipment based on studies of the behavioral reactions of the welder have been shown. It is found the simulators allow not only training, but also one can build neuro-fuzzy logic and design automated and robotized welding systems. The functioning peculiarities of welding's simulators with AR have been revealed. It is shown they make it possible to ensure the forming basic qualities of a future specialist, such as concentration, accuracy and agility. The psychological and technical aspects of the coaching programs for the training and retraining of qualified welders have been illustrated. The conclusions about the significant advantages of VR- and AR-technologies in comparison with traditional ones have been made. Possible directions of the development of simulation training for welders have been revealed. Among them the AR-technologies have been presented as such that gaining wide popularity as allow to realize the idea of mass training in basic professional skills.

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