Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers

Ibrahim, Sabreen; Marabeh, M. A. A.; Qarariyah, Ammar

doi:10.1007/s41066-021-00262-6

Cited by 11 publications

(2 citation statements)

References 30 publications

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“…Strong arbitrary solutions were covered in (Ahlatcioglu et al, 2016;Kocken et al, 2016;Albayrak, 2017) for square and non-square systems with triangular and trapezoidal coefficients, using mixed integer programming. Both trapezoidal and hexagonal coefficients were taken into account in (Ziqan et al, 2022). Chanas and Nowakowski (1988) proposed an approach that enables assigning a precise numerical value to a fuzzy variable by simulating values of uniform random variables related to the fuzzy variable.…”

Section: Introductionmentioning

confidence: 99%

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

GÜNAY AKDEMİR

2023

Karadeniz Fen Bilimleri Dergisi

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In this paper, a new method is proposed to find the approximate solutions to fully fuzzy systems of linear equations (FFSLEs). The technique integrates a bisection method with Fuzzy Numerical Simulation (FNS). The procedure starts with generating single values of fuzzy parameters and solving the resulting crisp problems repeatedly to determine the lower and upper bounds of the solutions. After computing the mean lower and upper bound values, the obtained supremum and infimum values are considered to be the lower and upper bounds of the solutions, respectively. It is attempted to improve solutions by considering an error function related to the sum of the absolute differences between the corresponding lower and upper bounds of the left and right sides of the equalities. When very large intervals are obtained for the solutions, the bisection algorithm is applied to reduce the error value. The method intends to solve square systems of large dimensions for arbitrary fuzzy numbers (FNs) by removing non-negativity confinements of the variables and/or coefficients to be more realistic. After the computational method is presented thoroughly, some benchmark examples are finally provided.

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Section: Introductionmentioning

confidence: 99%

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

GÜNAY AKDEMİR

2023

Karadeniz Fen Bilimleri Dergisi

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“…Recently, Abbasi and Allahviranloo [20] investigated and reported a new concept based on transmission-average-based operations for solving the FFSLE. In addition, the FFSLE with trapezoidal and hexagonal fuzzy numbers was studied by Ziqan et al [21].…”

Section: Introductionmentioning

confidence: 99%

Computational Technique for Solving Imprecisely Defined Non-negative Fully Fuzzy Algebraic System of Linear Equations

Behera

Chakraverty

2022

IJFIS

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This study proposes a new straightforward approach for solving a fully fuzzy algebraic system of linear equations. The proposed technique was based on a convex combination approach. Here, elements of the fuzzy coefficients matrix, fuzzy unknown vector, and right-hand side fuzzy vector are considered non-negative. Using the fuzzy arithmetic and convex combination concepts, the fuzzy system is converted into an equivalent crisp system. After solving the corresponding system for any two distinct parametric values of the convex combination, the final solution is obtained. Various example problems were solved and compared with existing results for validation.

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A Novel Approach for Generalized Decagonal Neutrosophic Linear Programming Problem

Lachhwani

2024

Lecture Notes in Networks and Systems

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Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers

Cited by 11 publications

References 30 publications

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

Computational Technique for Solving Imprecisely Defined Non-negative Fully Fuzzy Algebraic System of Linear Equations

A Novel Approach for Generalized Decagonal Neutrosophic Linear Programming Problem

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