Dana scott, patrick suppes, foundational aspects of theories of measurementcausey, robert l. Siam journal on control and optimization siam society for. The reason is that, first this approach is most obvious and, second, theory of fuzzy and ordinary differential inclusions is well found and is rapidly developed at the present time 2734. The book fuzzy differential equations in various approaches focuses on fuzzy differential equations fdes and explains the basics of various approaches of fdes. Fdes are known as an ideal mathematical modeling of realworld problems whereby uncertainties and randomness exist. Abstract in this article we consider fuzzy integral equations and prove the existence and uniqueness theorem. Theory of fuzzy differential equations and inclusions crc. The full averaging of fuzzy differential inclusions. Research article numerical solution of firstorder linear. Fuzzy interval arithmetic is very simple to compute because it is applicable to the endpoints of an interval, and this leads to an estimate of the con. The theory of fuzzy differential inclusion is used to produce a solution of the model and a.
Boundary value problems for semilinear fuzzy impulsive. In this article we consider some properties of the fuzzy rsolution of the control linear fuzzy integro differential inclusions and research the timeoptimal problems for it. Full averaging of control fuzzy integrodifferential. An existence of the solutions for one system of fuzzy differential inclusions is proved by using. Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems, moreaus sweeping process, linear and nonlinear complementarity dynamical systems, discontinuous ordinary differential equations, switching dynamical systems, and. The first study of differential equations with multivalued. We introduce a hypograph metric in the space of fuzzy sets and prove a theorem on. On new solutions of fuzzy differential equations victor ayala. Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems, moreaus sweeping process, linear and nonlinear complementarity dynamical systems, discontinuous ordinary differential equations, switching dynamical systems, and fuzzy set arithmetic.
Citescore measures the average citations received per document published in this title. By means of semigroup properties, stacking approach and the fixed point theorem for multivalued map due to dhage, the existence results for fuzzy solution are established. Under the tangential condition, a global viable solution for a fuzzy delay differential inclusion is proved to exist. In this paper, we show some properties of the fuzzy rsolution of the control linear fuzzy integrodifferential inclusions and the timeoptimal problems for it. Fuzzy differential equations in various approaches luciana. On linear fuzzy differential equations by differential inclusions approach. Pdf the generalized solutions of the fuzzy differential inclusions. Fuzzy differential functions are applicable to realworld problems in engineering, computer science, and social science. Early approaches in fdes modeling were hukuhara derivative and. Pdf in this article we introduce the definition of the generalized solution of the fuzzy differential inclusion and find the conditions when this. Introduction the topics of numerical methods for solving fuzzy differential equations have been rapidly growing in recent years. These results generalize the results of 17,20 for differential inclusions with. Theory of fuzzy differential equations and inclusions book.
Recently published articles from fuzzy sets and systems. Fuzzy differential inclusions in atmospheric and medical cybernetics. Full averaging of control fuzzy integrodifferential inclusions with terminal criterion of quality andrej v. Differential inclusions and fuzzy differential inclusions are two topics that are very interesting but they do not constitute the subject of the. Important notes for a fuzzy boundary value problem in. Fuzzy integrodifferential inclusion, fuzzy systems, method. The fdes are special type of interval differential equations ides. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. Stability theorems of filippovs type in the convex and nonconvex case are proved under a onesided lipschitz condition, which extends the notions of lipschitz continuity, dissipativity, and the uniform onesided lipschitz condition for setvalued mappings. Ordinary differential and functional differential inclusions with compact righthand sides are considered. Baidosov, differential inclusions with fuzzy righthand side, dokl. It presents, in a unified way, a number of results scattered in the li. Partial averaging of fuzzy hyperbolic differential. Pdf fuzzy differential inclusions and nonprobabilistic.
Using a formal approach to such information, in accordance with the theory of fuzzy sets fs, we introduce the notation of a differential inclusion di with a fuzzy. Full averaging of fuzzy hyperbolic differential inclusions. P x is the set of fuzzy subsets of the space x 1, 2, is the membership function for. For consider problems we receive necessary such conditions of optimality. Partial averaging of fuzzy differential equations with maxima. Also obviously, these equations can be written in as fuzzy partial differential inclusions. The main goal of this paper is to show that the concept of generalized differentiability introduced by the authors in 2 allows to obtain new solutions to the fuzzy differential equations. Numerical methods for fuzzy differential inclusions core. Also the substantiation of a possibility of application of partial averaging method for hyperbolic differential inclusions with the fuzzy righthand side with the small parameters is considered.
One of them solves differential equations using zadehs extension principle buckleyfeuring 30, while another approach interprets fuzzy differential equations through differential inclusions. One dimensional fuzzy differential inclusions have been discussed. The ides are differential equations used to handle interval uncertainty that appears in. The concept of fuzzy derivative was first introduced by chang and zadeh in 1. View full text full text pdf 283 kb full text epub 183 kb. Differential equations with fuzzy parameters via differential.
We introduce a hypograph metric in the space of fuzzy sets and prove a. Fuzzy differential equations and applications for engineers. Theory of fuzzy differential equations and inclusions, taylor francis, 2003. P x is the set of fuzzy subsets of the space x 1, 2, is the membership function for a fs m, and fuzzy differential inclusions are introduced and studied. Differential inclusions and fuzzy differential inclusions have already been. Stability theorems of filippovs type in the convex and nonconvex case are proved under a. If the inline pdf is not rendering correctly, you can download the pdf file here.
In this case, the transmission rate is considered as a fuzzy set. In this paper the substantiation of a possibility of application of partial averaging method for hyperbolic differential inclusions with the fuzzy righthand side with the small parameters is considered. Differential inclusions with a fuzzy righthand side. Comparation between some approaches to solve fuzzy differential. Fuzzy integrodifferential inclusion, fuzzy systems, method of. Existence of local and global solutions of fuzzy delay. The theory of fuzzy differential inclusion is used to produce a solution of the model and a comparison between this solution and the one proposed by the deterministic model is made too. Numerical methods for fuzzy differential inclusions. Numerical solution of firstorder linear differential equations in fuzzy environment by rungekuttafehlberg method and its application sankarprasadmondal, 1 susmitaroy, 1 andbiswajitdas 2. In this article we consider fuzzy integral equations and prove the existence and uniqueness theorem.
Fdishave turned out to be great tools to tackle complexity due to uncertainty in an fds 9, 10. If you need to make more complex queries, use the tips below to guide you. Partial averaging of fuzzy hyperbolic differential inclusions. This field is in its growing age, and it interacts with many researchers. In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. Tatyana alexandrovna komleva 1, irina vladimirovna molchanyuk 2, andrej viktorovich plotnikov 2, liliya ivanovna plotnikova 3.
Fuzzyvalued mappings fuzzy functions were initially. Series in mathematical analysis and applications, v. In the present paper, we show the some properties of the fuzzy rsolution of the control linear fuzzy differential inclusions and research the optimal time problems for it. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy d. By this algorithm a second order fuzzy differential inclusion has been solved and simulation result has been presented. The averaging of fuzzy hyperbolic differential inclusions. The development of impulsive fuzzy differential equations was initiated by 34, and was extended to impulsive functional differential inclusions in 33. The local and global existence theorems under different conditions are proved by using selection theorems and kakutanis fixed point theorem. Tatyana alexandrovna komleva, irina vladimirovna molchanyuk, andrej viktorovich plotnikov, liliya ivanovna plotnikova, partial averaging of fuzzy hyperbolic differential inclusions, international journal of systems science and applied mathematics. Komleva 2 department of applied mathematics, odessa state academy of civil engineering and architecture, didrihsona street. Research article the partial averaging of fuzzy differential inclusions on finite interval andrejv. The study of fuzzy differential equations fdes has been interested by many researchers in recent years. Fuzzy differential inclusions formulation of fuzzy differential inclusions differential inclusions fuzzy differential inclusions the variation of constants formula fuzzy volterra integral equations.
Sufficient references are given at the end of each chapter and a small index is provided in the book. Fuzzy delay differential inclusions are introduced and studied in this paper. The model is examined by comparing three fuzzy differential approaches, namely hukuhara differential, generalized hukuhara differential and fuzzy differential inclusions. The main objective of this survey is to study convergence properties of difference methods applied to differential inclusions. Analysis and computation of fuzzy differential equations. An efficient and easy to implement algorithm to solve them has been devised. Fuzzy differential equations in various approaches. In 1990, aubin and baidosov 2, 3 introduced differential inclusions with the fuzzy righthand side. Boundary value problems for semilinear fuzzy impulsive differential. Applications of fuzzy arithmetic concepts to the models lead to a deterministic alphacut systems, which are solved using extended rungekutta method. The uniqueness of the solution of a fddi is proved under different conditions.
Theory of fuzzy differential equations and inclusions 1st. Theory of fuzzy differential equations and inclusions. We use an averaging method of krylovbogolyubov and set in correspondence to the given problem the mayers fullaveraged fuzzy problem that is more simple for solving. In this paper, a scheme of partial averaging of fuzzy differential equations with maxima is considered. In the litreture, there are several approaches to study fuzzy differential equations. Existence of local and global solutions of fuzzy delay differential. Existence and uniqueness theorem for fuzzy integral equation. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory. These fuzzy solutions are constructed from the solution. Pdf the full averaging of fuzzy differential inclusions. If you do not already have an account you will need to register here.
The partial averaging of fuzzy differential inclusions on. The theory of fuzzy differential inclusion is used to produce a solution of the model and a comparison between this solution and. Fuzzy differential inclusions and nonprobabilistic likelihood article pdf available in dynamic systems and applications 14. Averaging method, fuzzy differential equation with maxima. Komleva3 1department of applied mathematics, odessastateacademy of civil engineering and architecture, odessa, 65029, ukraine. Ordinary differential and functionaldifferential inclusions with compact righthand sides are considered. Quasisolutions of fuzzy differential inclusions springerlink. Plotnikov et al full averaging of fuzzy hyperbolic differential inclusions to variation in a range. Differential inclusions with fuzzy righthand side, dokl.
And up till now the literature is mainly concerned with fuzzy ordinary differential equations, inclusions, and fuzzy partial differential equations, but in this paper we present a model for hyperbolic type partial fuzzy differential inclusion with integral local conditions. Existence results for fuzzy partial differential inclusions. We study fuzzy differential equations fde using the concept of generalized h differentiability. In the second case, fuzzy differential inclusions are frequently used to describe behavior of objects. And we verify the continuous dependence of the solutions of fddis through the convergence theorem. The timeoptimal problems for the fuzzy rsolution of the. We express this impreciseness and uncertainties in terms of fuzzy numbers. The local and global existence theorems under different conditions. Research article existence results for fuzzy partial. Fuzzy differential equations and applications for engineers and scientists crc press book differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In this article, we considered the fuzzy hyperbolic differential inclusions fuzzy darboux problem, introduced the concept of rsolution and proved the existence of such a solution.
The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy righthand side with a small parameter is considered. A further discussion about fuzzy delay differential inclusions fddis is presented in this paper. The solution of a differential inclusion is defined as the fs of motions. Analysis and computation of fuzzy differential equations via. A firstorder semilinear fuzzy differential inclusion with fuzzy impulse characteristics and linear boundary conditions is considered in separable banach spaces. That relevance makes for rapid development of new ideas and theories. Research article the partial averaging of fuzzy differential. It is well established that the fuzzy dynamical systems represented by a set of fuzzy differential inclusions fdi are very convenient tools for modeling and. It is established that the level set of this fs is identical with the bundle of solutions of an ordinary differential equation whose righthand side is given by the corresponding level set of the fuzzy righthand side. Citescore values are based on citation counts in a given year e. Keywordsdifferential inclusions, approximation methods, fuzzy initial value problem.
A new derivative concept for setvalued and fuzzyvalued functions. So we come across with fuzzy partial differential equations. We give the expression for the solution to some particular initial value problems in the space e 1 of fuzzy subsets of we deduce some interesting properties of the diameter and the midpoint of the solution and compare the solutions with the corresponding ones in the crisp case. These results generalize the results of 17, 20 for differential inclusions with hukuhara derivative and of 18 for fuzzy differential equations. Uniqueness and continuous dependence of the solutions of. Searching for just a few words should be enough to get started. Many others utilized a variety of approach for the fuzzy system of volterra integrodifferential equations based on a bloodline of differential inclusions. J they have been many suggestions for definition of fuzzy derivative to studyfuzzy differential equation.
A very general existence and uniqueness result of two solutions for the fuzzy differential equations with modified argument and based on generalized. One of the most efficient ways to model the propagation of epistemic uncertainties in dynamical environmentssystems encountered in applied sciences, engineering and even social sciences is to employ fuzzy differential equations fdes. Detailing the theory of fuzzy differential equations and inclusions and a systematic account of recent developments, this text provides preliminary material of fuzzy set theory. Keywords differential inclusions, approximation methods, fuzzy initial value problem. Fuzzy differential equations are interpreted as a family of differential inclusions. Fuzzy differential equations have been suggested as a way of modeling uncertain and incompletely specified systems and were studied by many researchers 7, 11, 15, 17, 19, 20. The term fuzzy differential equation was introduced in1987 by kandel. In this paper we consider the fuzzy control system with fuzzy terminalqualitycriterion mayers fuzzy problem when the behaviour of system is described by thefuzzy controlled integrodifferential inclusion with a small parameter. Existence results for the system of partial differential. One dimensional fuzzy differential inclusions, journal of. Research article existence results for fuzzy partial differential inclusions nayyarmehmood 1 andakbarazam 2 department of mathematics and statistics, international islamic university, h, islamabad, pakistan department of mathematics, comsats institute of information technology, islamabad, pakistan. Nov 04, 2016 partial averaging of fuzzy hyperbolic differential inclusions.