A proposed method for solving fuzzy system of linear equations.
Reza Kargar1, Tofigh Allahviranloo1, Mohsen Rostami-Malkhalifeh1
1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 18558-17556, Iran.
Thescientificworldjournal
|September 13, 2014
Summary
This study introduces a novel method for solving fuzzy linear systems with crisp coefficients and fuzzy or interval right-hand sides. The approach utilizes linear programming to determine the existence and find fuzzy or interval solutions for m x n systems.
Area of Science:
- Numerical Analysis
- Fuzzy Mathematics
- Operations Research
Background:
- Solving linear systems is fundamental in various scientific and engineering disciplines.
- Traditional methods are often insufficient for systems involving uncertainty, such as fuzzy or interval parameters.
- Existing approaches for fuzzy linear systems may lack efficiency or general applicability.
Purpose of the Study:
- To propose a new, practical method for solving fuzzy systems of linear equations.
- To address systems with a crisp coefficient matrix and fuzzy or interval right-hand side.
- To establish conditions for the existence of fuzzy or interval solutions.
Main Methods:
- The proposed method is founded upon formulating and solving linear programming problems.
- Derivation of conditions ensuring the existence of fuzzy or interval solutions.
- Development and detailed explanation of a practical algorithm.
Main Results:
- A novel algorithm is presented for solving fuzzy linear systems (FLS).
- Conditions for the existence of fuzzy or interval solutions for m x n systems are derived.
- The method's applicability is demonstrated through numerical examples.
Conclusions:
- The proposed linear programming-based method offers an effective approach to solving fuzzy linear systems.
- The derived conditions provide theoretical support for solution existence.
- The method is practical and applicable to real-world problems involving uncertainty.
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