Quantum fuzzy genetic algorithm with Turing to solve DE (original) (raw)
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Journal of Al-Qadisiyah for computer science and mathematics, 2019
In this paper, we introduce a hybrid method to use fuzzy differential equation, and Genetic Turing Machine developed for solving nth order fuzzy differential equation under Seikkala differentiability concept [14]. The Errors between the exact solutions and the approximate solutions were computed by fitness function and the Genetic Turing Machine results are obtained. After comparing the approximate solution obtained by the GTM method with approximate to the exact solution, the approximate results by Genetic Turing Machine demonstrate the efficiency of hybrid methods for solving fuzzy differential equations (FDE).
Journal of Computers, 2012
This paper proposes a new approach based on quantum inspired evolutionary algorithm (QIEA) for effective selection and definition of fuzzy if-then control rules as well as the shapes of membership functions (MFs) to design fuzzy logic controllers (FLCs). The majority of works done on designing FLCs rely on the knowledge base derived from imprecise heuristic knowledge of experienced operators or persons. These traditional methods, however, are cumbersome to implement and very time consuming to evaluate. Our proposed approach is a self-learning adaptive method and decomposes a problem in such a way that leads to more effective knowledge acquisition and improved control performance with the FLCs. In order to verify the effectiveness of this self-learning adaptive method, a standard test-bed, the truck backer-upper problem, is considered as the test problem. During each generation, the rules are updated and the MFs' parameters are altered using a complementary double mutation operator (CDMO) and a discrete crossover (DC). This paper also demonstrates the effect of different fuzzification and defuzzification methods on the response of the FLC. The center of gravity (COG) and modified COG are used as defuzzifier to analyze the results of the fuzzy controller. The experimental results show that the proposed approach with different fuzzification and MCOG to design FLCs performs better than the traditional methods with triangular fuzzification and COG in terms of required time to backing up the truck.
Fuzzy Analysis of Particle movement in Quantum Mechanics
International journal of multidisciplinary and current research, 2016
Direct measurement of variables in classic mechanics is not applicable to whole of real-deterministic areas like nonlinear functions of quantum mechanics; and corporation of beneficent methods like fuzzy logic can predict the behavior of particles in the fields that, there is not much access for experience of all possible states in physics. Thus, based on Shrödinger equation and momentum of particles in a 2-D surface with a wave-liked function, the hidden aspects of behavior is forecasted and for any given state as input, fuzzy controller indicates the characteristics as well.
Utilizing quantum genetic algorithm with TM to solve DEs
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In this paper a proposed approach to solve the DEs utilizing the TM with quantum Genetic algorithms. The aim of the proposed approach is to use the series functions of form quantum genetic to solve the DEs by decreasing the number of iterations and more increase by utilizing automata more with enhancement of TM.
The general approach for quantum algorithm (QA) simulation on classical computer is introduced. Efficient fast algorithm and corresponding SW for simulation of Grover's quantum search algorithm (QSA) in large unsorted database and fuzzy simulation is presented. Comparison with common QA simulation approach is demonstrated. Hardware (HW) design method of main quantum operators that are used in simulation of QA and fuzzy operators is described. Grover's QSA as Benchmark of HW design method application is presented. This approach demonstrates the possibility of classical efficient simulation of quantum algorithm gates (QAG) and in general fuzzy simulation approaches.
INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences, 2012
A novel Quantum-behaved Particle Swarm Optimization Algorithm with comprehensive learning and cooperative learning approach (CCQPSO) was introduced to improve the global convergence property of QPSO. In the proposed algorithm, the updating method of local attractor, particle's previous best position and swarm's global best position were performed in each dimension of the solution vector to avoid loss some components that had moved closer to the global optimal solution in the vector. Then the novel algorithm was applied to parameter optimization of fuzzy neural networks. The introduction of cooperative learning strategy is the originality in the proposed method. The results of prediction of chaotic time series experiment show that the proposed technique can converge more rapidly than other evolutionary computation methods, and the novel method is effective and efficient.
The Study of Fuzzy Differential Equations Expanding as New Branch of Fuzzy Mathematics
Partial differential equations are used for modeling various physical phenomena. Unfortunately, many problems are dynamical and too complicated, developing an accurate differential equation model for such problems require complex and time consuming algorithms hardly implementable in Leveque R. J (2005). For a long time, scientist goal was to develop constructive and effective methods that reliably compute the partial differential equation with more accuracy as possible. In classical mathematics, various kinds of transforms (Fourier, Laplace, integral, wavelet) are used as powerful methods for construction of approximation models and for solution of differential or integral-differential equations Perfilieva I. (2004). Fuzzy set theory is composed of an organized body of mathematical tools particularly well-suited for handling incomplete information, the un-sharpness of classes of objects or situations, or the gradualness of preference profiles, in a flexible way. It offers a unifying framework for modeling various types of information ranging from precise numerical, interval-valued data, to symbolic and linguistic knowledge, with a stress on semantics rather than syntax. Zimmermann H. J (2001) Achieving high levels of precision is a very important subject in all science fields, getting a satisfied precision depending basically on the way we deal with elements in the problem Universe. For many years we were depended on crisp set theory "classical set theory " to deal with elements and sets which belong to the problem Universe, but in real world there are many application problems which can't be described nor handled by the crisp set theory Leondes C. (1998).The study of fuzzy differential equations is rapidly expanding as a new branch of fuzzy mathematics. Both theory and applications have been actively discussed over the last few years. According to Vorobiev and Seikkala (1986), the term 'fuzzy differential equation' was first coined in 1978. Since then, it has been a subject of interest among scientists and engineers. In the literature, the study of fuzzy differential equations has several interpretations. The first one is based on the notion of Hukuhara derivative (R. Goetschel (1986 et al)). Under this interpretation, the existence and uniqueness of the solution of fuzzy differential equations have been extensively studied by (S. Song,(2000), S. Seikkala, (1987))The concept of Hukuhara derivative was further explored by Kaleva (1987) and Seikkala (1986). Subsequently, the theory of fuzzy differential equations has been developed and fuzzy initial value problems have been studied. However, this approach produces many solutions that have an increasing length of support as the independent variable increases (T.G. Bhaskar,et al (2012)). Moreover, different formulations of the same fuzzy differential equation might lead to different solutions.
Introduction of the numerical methods in quantum calculus with uncertainty
2021
The aim of this study is the introduction of the numerical methods for solving the fuzzy qqq-differential equations that many real life problems can be modelized in the form of these equations. qqq-Taylor's expansion method is among important and famous methods for solving these problems. In this paper, applications of the fuzzy qqq-Taylor's expansion, the fuzzy local qqq-Taylor's expansion and the fuzzy qqq-Euler's method, based on the generalized Hukuhara qqq-differentiability are illustrated which are two numerical methods for finding approximate solution of the fuzzy initial value qqq-problems (for short FIVq-Ps).
The paper gives a review of the application of fuzzy set ideas in quantum logics. After a brief introduction to the fuzzy set theory, the historical development of the main attempts to utilize fuzzy set ideas in quantum logics are presented. Results of investigations of all major researchers (except the Italian group discussed elsewhere), who work or worked in the field, are discussed.