Goal programming approach to fully fuzzy fractional transportation problem

Anukokila, P.; Radhakrishnan, B.

doi:10.1080/16583655.2019.1651520

Cited by 15 publications

(6 citation statements)

References 25 publications

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“…Similar studies that use max-min operators within the extension principle applied to linear and linear fractional transportation problems can be found in the literature, see, for instance, [8][9][10][11][12][13][14][15][16]. Another related area is Data Enveloped Analysis (DEA) in fuzzy environments.…”

Section: Introductionmentioning

confidence: 87%

“…In what follows, we extend the LP problem to an FF-LP problem, referring only to its standard maximization form, without loosing any generality. Model (9) provides the full fuzzy extension to Model (8).…”

Section: Problem Formulation and Solution Approachmentioning

confidence: 99%

“…where the dimensions of parameters A, b, c are as given in Problem (8). The optimization is performed with respect to the variables x, a ij , b i , c j , δ ij , β i , γ j , i = 1, m, j = 1, n. With the help of the notation…”

Section: First Variantmentioning

confidence: 99%

“…The right side of the membership function of the fuzzy set representing the optimal objective value is determined by solving the optimization problem obtained by combining the dual of Problem (8) with the first four constraints of Problem (12).…”

Section: First Variantmentioning

confidence: 99%

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Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

Stanojević,

Nǎdǎban

2023

Mathematics

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Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the “product” operator instead of “min” within the definition of the solution concept. Our theoretical findings show that using a generalized “min” operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information.

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Section: Introductionmentioning

confidence: 87%

Section: Problem Formulation and Solution Approachmentioning

confidence: 99%

Section: First Variantmentioning

confidence: 99%

Section: First Variantmentioning

confidence: 99%

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Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

Stanojević,

Nǎdǎban

2023

Mathematics

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“…In recent years, the fractional calculus has gained the importance and popularity for the modelling of the real-world problems [22][23][24][25][26][27][28]. However, many scientists have shown that the conventional form of the fractional derivatives with singular kernel may not be able to characterize the nonlocal dynamics in an appropriate manner; hence, to better investigate the real-world phenomena with hereditary property, there is a need to apply new types of the fractional operators with nonsingular kernel.…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator

Ullah

Alzahrani

Băleanu

2019

Journal of Taibah University for Science

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The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag-Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.

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Solving the Problem of Fuzzy Transportation Using Linear Programming and Goal Programming

Ahmed¹

2021

Intelligent Systems Reference Library

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Goal programming approach to fully fuzzy fractional transportation problem

Cited by 15 publications

References 25 publications

Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator

Solving the Problem of Fuzzy Transportation Using Linear Programming and Goal Programming

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