A new method for solving real and complex fuzzy systems of linear equations

Behera, Diptiranjan; Chakraverty, Snehashish

doi:10.1007/s10598-012-9152-z

Cited by 49 publications

(23 citation statements)

References 12 publications

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“…Proceeding as in Equation (7) The results obtained are same as that of Ref. [3]. The plot for x 1 and x 2 are given in Fig.…”

Section: Numerical Examplesmentioning

confidence: 91%

“…Recently Guo and Gong [8] presented a block Gaussian elimination approach for the fuzzy linear system. Behera and Chakraverty [3] very recently proposed a new method which can handle both real and complex fuzzy system of linear equations. Garg and Singh [7] applied numerical approach to solve fuzzy system of linear equations using Gaussian membership function.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy system of linear equations with crisp coefficients

Chakraverty

Behera

2013

Journal of Intelligent &Amp; Fuzzy Systems

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This paper proposed a new and simple solution approach to solve a general fuzzy system of linear equations. In the original system, the coefficient matrix is considered as real crisp whereas the unknown variable vector and right hand side vector are considered as fuzzy. Here, three different types of fuzzy numbers viz. triangular, trapezoidal and Gaussian fuzzy numbers are taken into consideration. First the system is solved in term of fuzzy centre then this solution is used with width to get the final solution of the original system. Solution theorems are stated and proved related to the proposed method. The method is also used to solve some known example problems found in the references and the results are compared to show the efficacy of the proposed method.

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“…Proceeding as in Equation (7) The results obtained are same as that of Ref. [3]. The plot for x 1 and x 2 are given in Fig.…”

Section: Numerical Examplesmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Fuzzy system of linear equations with crisp coefficients

Chakraverty

Behera

2013

Journal of Intelligent &Amp; Fuzzy Systems

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“…The result for fuzzy system of linear equations (15) obtained by Friedman et al (1998) and Behera and Chakraverty (2012)…”

Section: Examples Of Solving Fuzzy Linear Systems With Horizontal Fuzmentioning

confidence: 99%

“…Lodwick and Dubois (2015) wrote that improper intervals are not accepted. Changing the borders in x 2 and x 3 , the indicator of "solution" Table 3 Spans for r = 0 of the solution obtained using horizontal fuzzy numbers and of the "weak solution" by methods presented in (Friedman et al 1998;Behera and Chakraverty 2012) Solution Span of the solution using HFN The "weak solution"…”

Section: Examples Of Solving Fuzzy Linear Systems With Horizontal Fuzmentioning

confidence: 99%

Method with horizontal fuzzy numbers for solving real fuzzy linear systems

Landowski

2018

Soft Comput

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The paper presents a method for solving real fuzzy systems of linear equations with the usage of horizontal fuzzy numbers (HFNs). Based on the multidimensional RDM interval arithmetic and a fuzzy number in a parametric form, the definition of a horizontal fuzzy number with nonlinear left and right borders was given. Additionally, the paper presents the properties of basic algebraic operations on these numbers. The usage of horizontal fuzzy numbers with linear and nonlinear borders was illustrated in the examples with n × n fuzzy linear systems. The obtained results are multidimensional and satisfy the fuzzy linear systems. Calculated solutions of fuzzy linear systems were compared with the results of other methods. The solution obtained with horizontal fuzzy numbers satisfies any equivalent form of fuzzy linear system, whereas the results of existing methods do not satisfy the equivalent forms of the system. The presented examples also show that the method with HFN delivers a full multidimensional solution (direct solution). The analyzed results of standard methods, which are only a part of span (indicator, indirect solution) of a full solution and/or include values that do not satisfy the fuzzy linear systems, are underestimated or overestimated. The proposed method gives a possibility to obtain a crisp solution together with a crisp system of equations; other methods do not possess these properties.

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“…However, the expressions used in [2,3] can also be corrected in this way for complex fuzzy number and the related expressions can be derived accordingly. However, the expressions used in [2,3] can also be corrected in this way for complex fuzzy number and the related expressions can be derived accordingly.…”

Section: Corrections In Section 5 Of [1]mentioning

confidence: 99%