Concept

T-norm fuzzy logics

T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics. In order to generate a well-behaved implication, the t-norms are usually required to be left-continuous; logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity, (A → B) ∨ (B → A). Both propositional and first-order (or higher-order) t-norm fuzzy logics, as well as their expansions by modal and other operators, are studied. Logics that restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued Łukasiewicz logics) are usually included in the class as well. Important examples of t-norm fuzzy logics are monoidal t-norm logic (MTL) of all left-continuous t-norms, basic logic (BL) of all continuous t-norms, product fuzzy logic of the product t-norm, or the nilpotent minimum logic of the nilpotent minimum t-norm. Some independently motivated logics belong among t-norm fuzzy logics, too, for example Łukasiewicz logic (which is the logic of the Łukasiewicz t-norm) or Gödel–Dummett logic (which is the logic of the minimum t-norm). As members of the family of fuzzy logics, t-norm fuzzy logics primarily aim at generalizing classical two-valued logic by admitting intermediary truth values between 1 (truth) and 0 (falsity) representing degrees of truth of propositions. The degrees are assumed to be real numbers from the unit interval [0, 1]. In propositional t-norm fuzzy logics, propositional connectives are stipulated to be truth-functional, that is, the truth value of a complex proposition formed by a propositional connective from some constituent propositions is a function (called the truth function of the connective) of the truth values of the constituent propositions.

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https://en.wikipedia.org/wiki/T-norm_fuzzy_logics

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Monoidal t-norm logic

In mathematical logic, monoidal t-norm based logic (or shortly MTL), the logic of left-continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic of commutative bounded integral residuated lattices (known as Höhle's monoidal logic, Ono's FLew, or intuitionistic logic without contraction) by the axiom of prelinearity. In fuzzy logic, rather than regarding statements as being either true or false, we associate each statement with a numerical confidence in that statement.

Łukasiewicz logic

In mathematics and philosophy, Łukasiewicz logic (ˌluːkəˈʃɛvɪtʃ , wukaˈɕɛvitʂ) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as infinitely-many-valued (א0-valued) variants, both propositional and first order. The א0-valued version was published in 1930 by Łukasiewicz and Alfred Tarski; consequently it is sometimes called the ŁukasiewiczTarski logic.

T-norm

In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize the triangle inequality of ordinary metric spaces.

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Official source

https://en.wikipedia.org/wiki/T-norm_fuzzy_logics

About this result

Related lectures (5)

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Explores weak solutions of differential equations and their properties.

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Jean-Louis Scartezzini

Director of EPFL Solar Energy and Building Physics Laboratory (1994-present); Founder & Director of ENAC Institute of Infrastructures, Resources and Environment (2002-2009); Founder & Director of EPFL Doctoral Program in Environment (2002-2009); Co-Director of EPFL Institute of Building Technology (1994-1997); Associate Professor of Building Physics at EPFL (1994-1997); Associate Professor of Building Physics at University of Geneva (1990-1997); Group Leader & Research Fellow at the EPFL Solar Energy Research Group (1981-1989); Research Fellow at the Applied Geophysics Institute of University of Lausanne (1980-1981).

Alexandre Schmid

Alexandre Schmid received the M.Sc. degree in microengineering and the Ph.D. degree in electrical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1994 and 2000, respectively. Since 1994, he has been with the EPFL, working with the Integrated Systems Laboratory as a Research and Teaching Assistant, and with the Electronics Laboratories as a Postdoctoral Fellow. In 2002, he was a Senior Research Associate with the Microelectronic Systems Laboratory, where he has been conducting research in the fields of bioelectronic interfaces and implantable biomedical electronics, nonconventional signal processing and neuromorphic hardware, and reliability of nanoelectronic devices, and also teaches with the Microengineering and Electrical Engineering Departments of EPFL. Since 2011, he is a Maître d'Enseignement et de Recherche (MER) Faculty Member with EPFL. He is a coauthor of two books, Reliability of Nanoscale Circuits and Systems, Methodologies and Circuit Architectures, Springer, 2011, and Wireless Cortical Implantable Systems, Springer, 2013, and a coeditor of one book, as well as over 100 articles published in journals and conferences. Dr. Schmid has served as the General Chair of the Fourth International Conference on Nano-Networks in 2009 and has been serving as an Associate Editor of the Institute of Electrical, Information, and Communication Engineers Electronics Express since 2009.

Mihai Adrian Ionescu

Adrian M. Ionescu is Full Professor at the Swiss Federal Institute of Technology, Lausanne, Switzerland. He received the B.S./M.S. and Ph.D. degrees from the Polytechnic Institute of Bucharest, Romania and the National Polytechnic Institute of Grenoble, France, in 1989 and 1997, respectively. He has held staff and/or visiting positions at LETI-CEA, Grenoble, France and INP Grenoble, France and Stanford University, USA, in 1998 and 1999. Dr. Ionescu has published more than 600 articles in international journals and conferences. He received many Best Paper Awards in international conferences, the Annual Award of the Technical Section of the Romanian Academy of Sciences in 1994 and the Blondel Medal in 2009 for contributions to the progress in engineering sciences in the domain of electronics. He is the 2013 recipient of the IBM Faculty Award in Engineering. He served the IEDM and VLSI conference technical committees and was the Technical Program Committee (Co)Chair of ESSDERC in 2006 and 2013. He is a member of the SATW. He is director of the Laboratory of Micro/Nanoelectronic Devices (NANOLAB).

Kamiar Aminian

Kamiar Aminian received the M.S. degree in electrical engineering in 1982, the Ph.D degree in biomedical engineering in 1989 and the Postgraduate degree on technical computing in 1993 from Ecole Polytechnique Fédérale de Lausanne (EPFL). He was assistant professor (1994-1996) with Sharif University of Technology (Tehran). He joint EPFL in 1996 where he is currently Professor of medical instrumentation and the director of the Laboratory of Movement Analysis and Measurement in the Institute of Bioengineering of EPFL. His research interests include methodologies for human movement monitoring and analysis in real world conditions mainly based on wearable technologies and inertial sensors with emphasis on gait, physical activity and sport. His research aims to perform outcome evaluation in orthopaedics, to improve motor function and intervention programs in aging and patients with movement disorders and pain, and to identify metrics of performance in sport science. Kamiar Aminian is a member of the International Society of Posture and Gait Research, the Institute of Electrical and Electronics Engineers, the European Society of Movement Analysis in Adults and Children, the Prevention of fall Network Europe, the Intentional Society of Biomechanics and the President of the 3D analysis of the human movement group. He is author or co-author of more than 450 scientific papers published in reviewed journals and presented at international conferences and holds 10 patents related to medical devices. Full CV ORCID

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