Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

In the present study, we investigate the existence of the solutions to a type of uncertain differential equations subject to nonlocal derivatives. The approach is based on the application of an extended Krasnosel’skii fixed point theorem valid on fuzzy metric spaces. With this theorem, we deduce that the problem of interest has a fuzzy solution, which is defined on a certain interval. Our approach includes the consideration of a related integral problem, to which the above-mentioned tools are applicable. We finish with some physical motivationsWe are grateful to the Editor and the anonymous Referees for their comments and suggestions that helped to improve the paper. The research of J.J.N. and R.R.L. is supported by grant numbers PID2020-113275GB-I00 (AEI/FEDER, UE), MTM2016-75140-P (AEI/FEDER, UE), and ED431C 2019/02 (GRC Xunta de Galicia). The visit of A.K. to the University of Santiago de Compostela has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P; and by Xunta de Galicia under grant ED431C 2019/02. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS

Algebraic description of spacetime foam

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.Comment: 34 pages, LaTeX2e, the section concerning classical spacetimes in the limit essentially correcte

Zadeh's Centenary

This is the introductory paper in a special issue on fuzzy logic dedicated to the centenary of the birth of Lotfi A. Zadeh published by International Journal of Computers Communications & Control (IJCCC). In 1965, Lotfi A. Zadeh published in the journal „Information and Control” the article titled „Fuzzy sets”, which today reaches over 117 thousand citations. The total sum of citations for all his papers is above 253 thousand. Based on the notion of fuzzy sets, fuzzy logic and the concept of soft computing emerged, bringing extremely important implications to the field of Artificial Intelligence (AI). In 2017, I published, whith F.G. Filip and M.J. Manolescu, a 42-page long paper in the IJCCC about the life and masterwork of Lotfi A. Zadeh, from which I will use some information in this material [15]

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue “Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences”, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc

Handling congestion in crowd motion modeling

We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We limit our approach to very basic principles in terms of behavior, to focus on the particular problems raised by the non-smooth character of the models. We consider that individuals tend to move according to a desired, or spontanous, velocity. We account for congestion by assuming that the evolution realizes at each time an instantaneous balance between individual tendencies and global constraints (overlapping is forbidden): the actual velocity is defined as the closest to the desired velocity among all admissible ones, in a least square sense. We develop those principles in the microscopic and macroscopic settings, and we present how the framework of Wasserstein distance between measures allows to recover the sweeping process nature of the problem on the macroscopic level, which makes it possible to obtain existence results in spite of the non-smooth character of the evolution process. Micro and macro approaches are compared, and we investigate the similarities together with deep differences of those two levels of description

Application of new homotopy analysis method and optimal homotopy asymptotic method for solving fuzzy fractional ordinary differential equations

Physical phenomena that are complex and have hereditary features as well as uncertainty are recognized to be well-described using fuzzy fractional ordinary differential equations (FFODEs). The analytical approach for solving FFODEs aims to give closed-form solutions that are considered exact solutions. However, for most FFODEs, the analytical solutions are not easily derived. Moreover, most complex physical phenomena tend to lack analytical solutions. The approximation approach can handle this drawback by providing open-form solutions where several FFODEs are solvable using the approximate-numerical class of methods. However, those methods are mostly employed for linear or linearized problems, and they cannot directly solve FFODES of high order. Meanwhile, the approximate-analytic class of methods under the approximation approach are not only applicable to nonlinear FFODEs without the need for linearization or discretization, but also can determine solution accuracy without requiring the exact solution for comparison. However, existing approximateanalytical methods cannot ensure convergence of the solution. Nevertheless, to solve non-fuzzy fractional ordinary differential equations, there exist perturbation-based methods: the fractional homotopy analysis method (F-HAM) and the optimal homotopy asymptotic method (F-OHAM), that possess convergence-control ability. Therefore, this research aims to develop new convergence-controlled approximateanalytical methods, fuzzy F-HAM (FF-HAM) and fuzzy F-OHAM (FF-OHAM), for solving first-order and second-order fuzzy fractional ordinary initial value problems and fuzzy fractional ordinary boundary value problems. In the theoretical development, the establishment of the convergence of the solutions is done based on the convergence-control parameters. In the experimental work, the convergence of solutions is determined using properties of fuzzy numbers. FF-HAM and FF-OHAM are not only able to solve difficult nonlinear problems but are also able to solve highorder problems directly without reducing them into first-order systems. The developed methods demonstrate the excellent performance of the developed methods in comparison to other methods, where FF-HAM and FF-OHAM are individually superior in terms of accuracy

Fuzzy Systems

This book presents some recent specialized works of theoretical study in the domain of fuzzy systems. Over eight sections and fifteen chapters, the volume addresses fuzzy systems concepts and promotes them in practical applications in the following thematic areas: fuzzy mathematics, decision making, clustering, adaptive neural fuzzy inference systems, control systems, process monitoring, green infrastructure, and medicine. The studies published in the book develop new theoretical concepts that improve the properties and performances of fuzzy systems. This book is a useful resource for specialists, engineers, professors, and students