Abstract
In this study, the authors extended the concept of spherical fuzzy optimization models by considering different parameters of spherical fuzzy linear programming problem as symmetric and asymmetric spherical numbers. Eight spherical fuzzy linear programming models are discussed by converting decision variables, parameters, and coefficients of objective function and constraints into symmetric and asymmetric spherical fuzzy numbers. To verify the validity and efficiency of this study in contrast with a linear programming numerical and a physical energy optimization model for the textile industry is considered. The application of these symmetric and asymmetric spherical fuzzy optimization models is discussed along with the postoptimal analysis of the best optimization models that provide the feasible and most optimal solution.
Highlights
Growing urbanization is directly related to the increase in energy demands, usage, and cost
Other than decision variables, all the other factors are considered in the spherical fuzzy number, whereas in the fourth model, the cost and demand are in SF numbers
We considered cost and demand a symmetric spherical fuzzy number. e spherical fuzzy energy optimization model for the textile industry according to this model is as follows: min α⋎ m Csjsf⊛xj, j 1
Summary
Growing urbanization is directly related to the increase in energy demands, usage, and cost. According to National Electric Power Regulatory Authority’s (NEPRA) report, one energy unit fluctuation cost causes almost 4 to 5 hours closure in the production of textile’s products [6] To overcome this loss, it is best to optimize the usage and wastage of energy as much as possible. E most extensively adopted procedure for the optimal solution of modeled problem was linear programming (LP) due to its easy applicable nature that was first introduced by Kantorovich [7]. We are presenting symmetric and asymmetric energy optimization models inspired by the work of Ahmad and Adhami [17] For this purpose, the LP model for the textile industry is considered in the spherical fuzzy environment as a numeric example to validate the working of generated energy optimization models in the SF environment. Conclusions are based on the application of these spherical fuzzy models on the energy optimization model. e postoptimal analysis of the best feasible optimized SF model is discussed
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