On the new solutions for a fully fuzzy linear system

Allahviranloo, Tofigh; Hosseinzadeh, Ali; Ghanbari, M.; Haghi, E.; Nuraei, Rahele

doi:10.1007/s00500-013-1037-3

Cited by 16 publications

(9 citation statements)

References 19 publications

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“…Reference [14] proposed the possibilistic regression approach where the fuzzy linear regression with fuzzy coefficients and crisp input variables was introduced. Both of the approaches to fuzzy regression analysis have been investigated extensively [15]- [18]; however, they are sensitive to outliers [19]. Reference [20] suggested the least absolute deviation estimators to construct the fuzzy regression model and showed that the proposed approach is more robust than the least squares deviation method when the data contains fuzzy outliers.…”

Section: A Methodology For Compensating the Non-homogeneity Of Dmusmentioning

confidence: 99%

Efficiency Measurement for Non-homogeneous Units in a Fuzzy Environment

Yeh¹,

Hu²,

Liu³

et al. 2020

IJTEF

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Data envelopment analysis (DEA) assumes homogeneity among the decision-making units (DMUs) for measuring the relative efficiency of DMUs. In actual practice the efficiency scores generated by DEA may reflect the underlying differences in environments rather than true operational efficiency when DMUs do not operate under similar conditions. This work considers measuring the relative efficiency of non-homogeneous DMUs in a fuzzy environment. A two-stage analysis incorporating imprecise environmental factors into DEA model for measuring the relative efficiency of non-homogeneous units is proposed. A fuzzy regression analysis is employed for adjusting the data of DMUs to account for variations in the fuzzy causes of non-homogeneity. DEA with fuzzy residual errors is then performed to construct a scalar measure of efficiency for all DMUs. An example of the performance assessment of municipalities' solid waste recycling and disposal channels is included. This is the first attempt to estimate the relative efficiency for non-homogeneous DMUs in a fuzzy environment.

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Section: A Methodology For Compensating the Non-homogeneity Of Dmusmentioning

confidence: 99%

Efficiency Measurement for Non-homogeneous Units in a Fuzzy Environment

Yeh¹,

Hu²,

Liu³

et al. 2020

IJTEF

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“…are column vectors of trapezoidal fuzzy numbers. Allahviranloo et al [14] defined the following solution sets for FFLS (27):…”

Section: A Methods For Solving a Fully Fuzzy Linear Systemmentioning

confidence: 99%

“…(iii) Controllable trapezoidal fuzzy solution set: Now, we aim to propose a practical method to obtain the suitable solution of an FFLS. The suitable solution is defined in [14] as solution x ∈ UTFSS. To find such a solution x ∈ UTFSS, it is sufficient to solve the following two interval linear systems:…”

Section: A Methods For Solving a Fully Fuzzy Linear Systemmentioning

confidence: 99%

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An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers

Siahlooei

Fazeli

2018

Advances in Fuzzy Systems

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We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. This new method uses a decomposition technique to convert a fully fuzzy linear system into two types of decomposition in the form of interval matrices. It finds the solution of a fully fuzzy linear system by using interval operations. This new method uses interval arithmetic and two new interval operations ⊖ and ⊘. These new operations, which are inverses of basic interval operations + and ×, will be presented in the middle of this paper. Some numerical examples are given to illustrate the ability of proposed methods.

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“…Fuzzy linear system whose coefficient matrix is crisp and right hand side column is an arbitrary fuzzy number was first proposed by Friedman et al [4]. A linear system is called a fully fuzzy linear system (FFLS) if all coefficients in the system are all fuzzy numbers .Several direct and iterative methods based on numerical algorithms were used for solving fuzzy linear systems have been introduced by many authors [1,2,3,8].…”

Section: Introductionmentioning

confidence: 99%