454 research outputs found
BEST CO-APPROXIMATIONANDBESTSIMULTANEOUS CO-APPROXIMATION ININTUITIONISTIC FUZZY NORMED LINEARSPACES
The main purpose of this paper is to study the t-best co-approximation and t-best simultaneous co-approximation in intuitionistic fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed by us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets
Best Co-Approximation In Weighted Space
In this paper, we present best co- approximation in weighted space. The results considered are these of existence of functions of best co- approximation, specifications of co-a proximal and specification co- Chebyshev subspaces
Nonlinear Analysis and Optimization with Applications
Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world
Representations for Morphological Image Operators and Analogies with Linear Operators
1.1 Why a representation theory?...............................
Multi-layer functional approximation of non-linear unsteady aerodynamic response
Non-linear unsteady aerodynamic effects present major modelling difficulties in the analysis of aeroelastic response and in the subsequent design of appropriate controllers. As the direct use of the basic fluid mechanic equations is still not practical for aeroelastic applications, approximate models of the non-linear unsteady aerodynamic response are required. A rigorous mathematical framework, that can account for the complex non-linearities and time-history effects of the unsteady aerodynamic response, is provided by the use of functional representations. A recent development, based on functional approximation theory, has provided a new functional form; namely, multi-layer functionals. Moreover, the multi-layer functional representation for time-invariant, infinite memory systems is shown to be realisable in terms of temporal neural networks.
In this work, a multi-layer functional representation of non-linear motion-induced unsteady aerodynamic response is presented. A discrete-time, finite memory temporal neural network, in the form of a finite impulse response (FIR) neural network, is used as a practical realisation of a multi-layer functional. This model form permits the identification of parametric input-output models of the non-linear motion-induced unsteady aerodynamic response. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process using multiple sets of motion-induced unsteady aerodynamic response. The training process is based on a conventional genetic algorithm to optimise the FIR neural network architecture, and is combined with a simplification of the simulated annealing algorithm to update weight and bias values
Fuzzy Mathematics
This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value
Fuzzy Sets, Fuzzy Logic and Their Applications 2020
The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity
The six blinds and the elephant or an interdisciplinary selection of measurement features
We propose here selected actual features of measurement problems based on our
concerns in our respective fields of research. Their technical similarity in
apparently disconnected fields motivate this common communication. Problems of
coherence and consistency, correlation, randomness and uncertainty are exposed
in various fields including physics, decision theory and game theory, while the
underlying mathematical structures are very similar.Comment: 28 pages, 11 figures, 1 table. Proceedings of the XL Workshop on
Geometric Methods in Physics, Bialowieza, 202
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