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Journals / Turkish Journal of Mathematics / 2002 / Cilt: 26 - Sayı: 4

Solving fuzzy linear programming problems with linear membership functions

Rafail N. GASIMOV
Kürşat YENİLMEZ
Pages
375–396
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give illustrative examples and their numerical solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers.
📊
Key Findings & Data:The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems.
💡
Conclusion & Impact:Finally, we give illustrative examples and their numerical solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the ``modified subgradient method'' and use it for solving these problems. We also compare the new proposed method with well known ``fuzzy decisive set method''. Finally, we give illustrative examples and their numerical solutions.

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Cite This Article

GASIMOV, R. N., YENİLMEZ, K. (2022). Solving fuzzy linear programming problems with linear membership functions. Turkish Journal of Mathematics, Cilt: 26 - Sayı: 4, 375–396. https://ajindex.com/articles/608840

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