Open Access

ARTICLE

On Parametric Fuzzy Linear Programming Formulated by a Fractal

Rafid A. Al-Saeedi¹, Rabha W. Ibrahim², Rafida M. Elobaid^3,*

1 School of Mathematical Sciences, University Sciences Malaysia 11800 USM, Penang, Malaysia
2 IEEE: 94086547, Kuala Lumpur, 59200, Malaysia
3 Department of General Sciences, Prince Sultan University, Riyadh, Saudi Arabia

* Corresponding Author: Rafida M. Elobaid. Email:

(This article belongs to this Special Issue: Recent Trends in Computational Methods for Differential Equations)

Intelligent Automation & Soft Computing 2021, 30(3), 1073-1084. https://doi.org/10.32604/iasc.2021.018011

Received 21 February 2021; Accepted 26 May 2021; Issue published 20 August 2021

Abstract

Fractal strategy is an important tool in manufacturing proposals, including computer design, conserving, power supplies and decorations. In this work, a parametric programming, analysis is proposed to mitigate an optimization problem. By employing a fractal difference equation of the spread functions (local fractional calculus operator) in linear programming, we aim to analyze the restraints and the objective function. This work proposes a new technique of fractal fuzzy linear programming (FFLP) model based on the symmetric triangular fuzzy number. The parameter fuzzy number is selected from the fractal power of the difference equation. Note that this number indicates the fractal parameter, denoting by λ ε [0, 1]. Accordingly, we specify the objective function to the fractional case, utilizing the fractal difference equation. We apply the suggested model in an application under the oil market. Based on the fractal fuzzy set theory, the fuzzy demand, transportations, management, inventory and buying cost are explained and formulated in a unique fractal fuzzy linear programming model. This model is presented to obtain a maximal profit production approach with an evaluation. The costs indicate that the proposed model can bring valued solutions for developing profit-effective oil refinery methods in a fuzzy fractal situation. Some examples are illustrated in the sequel.

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Keywords

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