Fuzzification fuzzification12 is a process of making a crisp quantity into fuzzy quantity. However, there are many situations, where considering the uncertainty as t1fss may not be possible due to different. In this paper system of linear equations has been discussed in intuitionistic fuzzy environment. One can look for solutions of fuzzy linear systems in two ways.
A1jis a one of the fuzzy set of the fuzzy partition for x1 a2kis a one of the fuzzy set of the fuzzy partition for x2 om i is a one of the fuzzy set of the fuzzy partition for y for a given pair of crisp input values x1 and x2 the antecedents are the degrees of membership obtained during the fuzzification. Minimal solution of singular lr fuzzy linear systems. A fuzzy number vector, given by parametric form,, is called a solution of the fuzzy linear system if in order to solve the system given by. Liu, on the solution of fully fuzzy linear systems, international journal of computational and mathematical sciences, vol. The fuzzy linear programming problem with fuzzy decision variables is a dif. They introduce new notions for solution of a fls and transform the fls to a crisp linear system. Global stability of generalized additive fuzzy systems. Solving fully fuzzy linear system of equations in general form. Allahviranloo 4 proposed solution of a fuzzy linear system by using iterative.
Numerical methods for solving fuzzy linear systems mdpi. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including and not restricted to aggregation operations, a generalized theory of relations, specific measures of information content, a. In this paper, the main is to develop a method to solve an arbitrary inconsistent fuzzy linear system by using the embedding approach. For the ffls, we investigate its solution and develop a new approximate method for. Following 4 we represent an arbitrary fuzzy number by an ordered pair of functions ur, ir, 0 linear system of equations. Introduction the system of linear equations has applications in various areas of science such as operational research, physics, statistics, engineering, and social sciences. Design of fuzzy logic controller for a traffic control system a fuzzy logic controller for a nonlinear traffic system has been proposed and implemented using the fuzzy logic techniques.
Solving fuzzy linear systems of equations 209 x21 fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. A uzawasor method is presented for solving fuzzy linear system whose coefficient matrix is crisp and the righthand side column is arbitrary fuzzy number vector. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. It finds the solution of a fully fuzzy linear system by using interval operations. Koam 2, id and nawab hussain 3 id 1 department of mathematics, university of the punjab, new campus, lahore 54590, pakistan 2 department of mathematics, college of science, jazan university, new campus, p. Solving fuzzy linear systems of equations 209 x21 0 a fuzzy complex linear 2systems. A fuzzy number vector, given by parametric form,, is called a solution of the fuzzy linear system if in order to solve the system given by, friedman et al. We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. Pdf solving fuzzy linear programming problems with fuzzy.
Fuzzy system of linear equations fsle plays a major role in various areas such as operational research, physics, statistics, economics, engineering, and. Here we have solved both systems respectively by using the concept of strong and weak. A general fuzzy linear system is investigated using the embedding approach. In the first way, a fuzzy number vector t x,x n 1 2 is called to be a solution of the system if the fuzzy numbers x,x. Design of fuzzy logic controller for a nonlinear system. Applications in fuzzy linear programming, multivalued logic, fuzzy matrix equations or inequalities, fuzzy. In this paper we have used another approach to solve fuzzy linear system and fully fuzzy linear system.
It is known that the wellknown existence and uniqueness theorem of a strong fuzzy solution is. A rapid growth of interest in circuit theory and simulation is seen in recent decade. Some methods for solving these systems can be found in 47. The introduction of fuzzy block in to the structure of linear pid controller resulted fuzzy pid controller. An application of interval arithmetic for solving fully fuzzy. Zadeh, outline of a new approach to the analysis of complex systems and decision. In recent years fuzzy logic control techniques have been applied to a wide range of systems. As part of a control system, a fuzzy systemcontroller usually processes numerical inputs to numerical outputs. The both input variables and control action are given in linguistic forms for fuzzy pid controller. St decomposition method for solving fully fuzzy linear. Strong solutions of the fuzzy linear systems arxiv. Global stability of generalized additive fuzzy systems bart kosko, member, ieee abstract this paper explores the stability of a class of feedback fuzzy systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including and not restricted to aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Muhammad 33 developed the solution of bipolar fuzzy system of linear equations with polynomial parametric form.
Lu decomposition method for a crisp matrix is well known in. With the advent of neural networks, fuzzy models, and modern structure opti mization techniques a much wider class of systems can be handled. Systems of simultaneous linear equations play a major role in various areas as such as mathematics, physics, statistics, neural network and etc. Numerical solution of interval and fuzzy system of linear. Indian institute of engineering science and technology, shibpur, howrah711103, west bengal, india. This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Northholland publishing company systems of linear fuzzy constraints didier dubois school of electrical engineering, purdue university, west lafayette, in, u. Solving fully fuzzy linear system with the necessary and. A linear system is called a fully fuzzy linear system ffls if quantities in this system are all fuzzy numbers. Fifteen years ago, nonlinear system identification was a field of several adhoc approaches, each applicable only to a very restricted class of systems. Sanhita banerjee, suvankar biswas and tapan kumar roy.
To date, investigations conducted on flss are restricted to those in which the uncertainty is assumed to be modeled by type1 fuzzy sets t1fss. They are used in several wideranging fields, including. Conditions for the existence of a unique fuzzy solution to n. Fuzzy systems for control applications engineering. Notes on fuzzy linear systems world academic union. The convergence is analyzed and numerical example is given to illustrate the. An application of interval arithmetic for solving fully. Since triangular fuzzy numbers is a special case of trapezoidal fuzzy numbers, hence in this paper we considered fully fuzzy linear system with trapezoidal fuzzy numbers.
Fuzzy set theoryand its applications, fourth edition. The applicability of the proposed model is illustrated with examples. Fuzzy system of linear equation is a wellknown linear system where the parameters are fuzzy numbers. Iterative methods for solving a system of linear equations. Some conditions for the existence of a fuzzy or interval solution of m. Fuzzy expert systems a fuzzy expert system is an expert system that uses fuzzy logic instead of boolean logic. The inference engine forms the core of the information processing components. Nonlinear system identification from classical approaches.
Zahmatkesh, huang method for solving fully fuzzy linear system of equations, the journal of mathematics and computer science, vol. This new method uses interval arithmetic and two new interval. Interval, fuzzy, linear simultaneous equation, fuzzy number msc 2010. Minimal solution of fuzzy linear system of differential. Allahviranloo proposed solution of a fuzzy linear system by using an iterative method and later suggested various numerical methods to solve fuzzy linear systems. Fuzzy logic control the basic ideaof fuzzy logic control flc was suggested by prof. The subject of fuzzy system of linear equations fsles with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the. In the first way, a fuzzy number vector t x,x n 1 2 is called to be a solution of the system if the fuzzy numbers x,x, x n 1 2 satisfy each equation of the system 1. Pdf on the new solutions for a fully fuzzy linear system.
Lu decomposition method for solving fully fuzzy linear. Fuzzy numbers in the next section we will investigate the fuzzy linear system, define a solution fuzzy vector and propose a procedure for calculating it. Vehicle dynamics and braking systems are complex and behave strongly non linear which causes difficulties in developing a classical controller for abs. Pdf numerical methods for solving fuzzy linear systems. Equivalence between fuzzy pid controller and a linear control structure can be established by tuning method. Iterative methods for solving a system of linear equations in. In the fully fuzzy linear system all the parameters are considered to be fuzzy numbers. In this paper, a novel method to find the solutions in which 0 is not the inner point of supports, of fully fuzzy linear systems shown as ffls is proposed, if they exist by an analytic approach. Fuzzy expert systems are the most common use of fuzzy logic. Pdf in this paper, we propose a new method to present a fuzzy trapezoidal solution, namely suitable solution, for a fully fuzzy linear system ffls. To display the validity of these iterative schemes, an illustrative example with known exact solution is considered. Askerzade 1 abstract we consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the righthand side.
Solving fully fuzzy linear system with the necessary and suf. Some authors are proposed different approach to solve the fuzzy linear systems. Fuzzy linear system has been studied by several authors 1,2,4,14,15, 16, 17,18. With the use of the parametric form of type1 fuzzy numbers t1fnswhich are a class of possibility distribution functionsand by replacing the original fuzzy \n \times n\ linear system by a crisp \2n \times 2n\ linear system proposed, friedman et al. Minimal solution of nonsquare fuzzy linear systems core. Article iterative methods for solving a system of linear equations in a bipolar fuzzy environment muhammad akram 1 id, ghulam muhammad 1 and ali n. Equations of this type are necessary to solve for the involved. Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. This paper presentation deals with study antilockbraking system abs using fuzzy logic. Vehicle dynamics and braking systems are complex and behave strongly nonlinear which causes difficulties in developing a classical controller for abs. Circuits can be modeled in the form of fuzzy complex system of linear equations fcsle. Strong solutions of the fuzzy linear systems sahin emrah amrahov 1 and iman n. The convergence properties of these iterative schemes have been discussed. As part of a control system, a fuzzy system controller usually processes numerical inputs to numerical outputs.
Pdf in this paper, the main aim is to develop a method for solving an arbitrary general fuzzy linear system by using the embedding approach. Later, a system, called fully fuzzy linear system ffls, is introduced wherein elements in the coefficient matrix. Pdf solutions of the fully fuzzy linear system naser. In this article, three numerical iterative schemes, namely. Minimal solution of fuzzy linear system of differential equations. Fuzzy linear systems flss are used in practical situations, where some of the systems parameters or variables are uncertain.
163 735 795 320 862 1680 1491 1045 1661 318 439 1510 1600 842 1595 1605 965 438 229 1146 73 1446 1001 1301 1172 157 77 1286 727 575 899 1564 1494 65 83 1072 239 251 653 101 1047 1374 776