Fuzzy linear systems

Friedman, Menahem; Ma, Ming; Kandel, Abraham

doi:10.1016/s0165-0114(96)00270-9

Cited by 378 publications

(282 citation statements)

References 21 publications

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“…A particular type of fuzzy systems, Ax = b, where the coefficient matrix A is crisp, while b is a fuzzy number vector, is investigated by Friedman et al [10], Ma et al [15] and Allahviranloo [11][12][13], by using interval analysis techniques. Friedman et al [10] has used the embedding method given in [19], they replaced the original fuzzy linear system with a crisp linear system having a nonnegative coefficient matrix S, which may be singular even if A is nonsingular.…”

Section: Related Workmentioning

confidence: 99%

“…Friedman et al [10] has used the embedding method given in [19], they replaced the original fuzzy linear system with a crisp linear system having a nonnegative coefficient matrix S, which may be singular even if A is nonsingular. Allahviranloo [11][12][13] uses the iterative Jacobi and Gauss Siedel method, the Adomian method and the Successive over-relaxation method, respectively.…”

Section: Related Workmentioning

confidence: 99%

“…Dehghan and Hashemi [14,20] extended several well-known numerical algorithms such as Richardson, Extrapolated Richardson, Jacobi, JOR, Gauss-Seidel, EGS, SOR, AOR, ESOR, SSOR, USSOR, EMA and MSOR to solve system of linear equations. Ma et al [15], starting from the work by Friedman et al [10], analyzed the solution of fuzzy systems of the form A 1 x = A 2 x + b. They remarked that the system A 1 x = A 2 x + b is not equivalent to the system (A 1 -A 2 ) x = b, since for an arbitrary fuzzy number u there exists no element v such that u + v = 0.…”

Section: Related Workmentioning

confidence: 99%

“…In the previous work In the aforementioned works, real coefficients are discussed but in many applications as circuit analysis, while SLE includes complex coefficients and complex variables. Also we encountered situations in circuit solving that needs solving a FSLE model which has been solved by Friedman et al [10]. Therefore we present a Fuzzy Complex SLE, namely, FCSLE in this paper.…”

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confidence: 99%

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Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis

Rahgooy¹,

Yazdi²,

Monsefi³

2009

IJCEE

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I. INTRODUCTIONWide range of real world applications in many areas including economics, engineering and physics, are using linear system of equations for modeling and solving their respective problems. In many situations the estimation of the system parameters is imprecise and only some vague knowledge about the actual value of parameters is available, therefore to overcome this problem the vagueness of parameters is represented by fuzzy numbers. In many applications some of the parameters are usually represented by complex numbers which have fuzzy nature, thus it is important to develop mathematical models that would appropriately treat fuzzy complex linear systems. Circuits can be modeled in the form of fuzzy complex system of linear equations (FCSLE).A rapid growth of interest in circuit theory and simulation is seen in recent decade. A circuit simulation program (e.g., SPICES [1] and QPMDFSD [2, 3, and 4]) provides very good details in simulation of circuits. These types of software provide various facilities for obtaining best answer which is close to real form. Some contributions have been made in stability theory using functional analysis in the study of nonlinear systems, and computer-aided nonlinear network analysis [5, 6, 7, and 8]. But uncertainty in circuit parameters and environmental conditions lead to develop a new method which takes in to account uncertainty in circuit analysis. In the previous work In the aforementioned works, real coefficients are discussed but in many applications as circuit analysis, while SLE includes complex coefficients and complex variables. Also we encountered situations in circuit solving that needs solving a FSLE model which has been solved by Friedman et al. [10]. Therefore we present a Fuzzy Complex SLE, namely, FCSLE in this paper. This model works well in circuit solving. Major notes in this paper are presentation of FCSLE, and application of FSLE and FCSLE in circuit solving. Organization of this paper is as follows: Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis Taher Rahgooy, Hadi Sadoghi Yazdi, Reza MonsefiInternational Journal of Computer and Electrical Engineering, Vol. 1, No. 5 December, 2009 1793-8163 536 FSLE is explained in section III. Section IV appropriate to the proposed FCSLE and experimental results over circuit analysis are discussed in the section V. Final section includes the conclusion. III. FUZZY SYSTEM OF LINEAR EQUATIONS A. PreliminariesWe represented an arbitrary fuzzy number by an ordered pair of functions which should satisfy the following requirements:1.is a bounded left continuous nondecreasing function over [0,1]. 2.is a bounded left continuous nonincreasing function over [0,1]. 3. Fig. 1 A fuzzy numberFor example, the fuzzy number (1 + r, 4 -2r) is shown in Fig. 1. A crisp number α is simply represented by By appropriate definitions the fuzzy number space becomes a convex cone E 1 which is then embedded isomorphically and isometrically into a Banach space. Definition 1. The n × n linear system of equations Cons...

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

mentioning

confidence: 99%

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Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis

Rahgooy¹,

Yazdi²,

Monsefi³

2009

IJCEE

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“…Takagi and Sugeno [14] have presented first numerical approach of fuzzy systems. A general model has been proffered for solving a fuzzy linear system using embedding method by Friedman et al [7]. Further, Dubois and Prade [6] studied theoretical features of a fuzzy linear system .…”

Section: Introductionmentioning

confidence: 99%

Application of ANNs approach for solving fully fuzzy polynomials system

Novin¹,

Araghi²,

Amirfakhrian³

2017

Journal of Fuzzy Set Valued Analysis

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In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results.

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References

2019

Modeling and Control of Uncertain Nonlinear Systems With Fuzzy Equations and Z‐Number

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Fuzzy linear systems

Cited by 378 publications

References 21 publications

Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis

Fuzzy Complex System of Linear EquationsApplied to Circuit Analysis

Application of ANNs approach for solving fully fuzzy polynomials system

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