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Solving Linear Fractional Programming Problems in Uncertain Environments: A Novel Approach with Grey Parameters | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 9، دوره 9، شماره 1، مرداد 2024، صفحه 169-183 اصل مقاله (468.92 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2023.67881.1235 | ||
| نویسندگان | ||
| Farid Pourofoghi* 1؛ Davood Darvishi Salokolaei2 | ||
| 1Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University (PNU), P.O. Box19395-4697, Tehran, Iran. | ||
| چکیده | ||
| Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In practical scenarios, uncertainties often make it challenging to determine precise coefficients for mathematical models. Consequently, utilizing indefinite coefficients instead of definite ones is recommended in such cases. Grey systems theory, along with probability theory, randomness, fuzzy logic, and rough sets, is an approach that addresses uncertainty. In this study, we address the problem of linear fractional programming with grey coefficients in the objective function. To tackle this problem, a novel approach based on the variable change technique proposed by Charnes and Cooper, along with the convex combination of intervals, is employed. The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers, thus capturing the uncertainty inherent in the objective function. To demonstrate the effectiveness of the proposed method, an example is solved using the suggested approach. The result is compared with solutions obtained using the whitening method, employing Hu and Wong's technique and the Center and Greyness Degree Ranking method. The comparison confirms the superiority of the proposed method over the whitening method, thus suggesting adopting the grey system approach in such situations. | ||
| کلیدواژه‌ها | ||
| Uncertainty؛ Optimization؛ Fractional programming؛ Grey system؛ Grey interval numbers | ||
| مراجع | ||
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