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<p>A linear programming problem with a fuzzy set (FS) of constraints in the form of fuzzy inequalities is analyzed. The solution to such a problem is shown to form a type-2 FS (T2FS). A corresponding membership function of type 2 is provided. It is shown that the T2FS of the solution can be decomposed into a finite collection of FS based on secondary membership grades. Each of these FS is a solution to the corresponding fuzzy linear programming problem with a crisp set of constraints. This set corresponds to a certain cut of the original FS of constraints. An illustrative example is presented.</p>

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Linear Programming with a Fuzzy Set of Fuzzy Constraints

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • S. O. Mashchenko

摘要

A linear programming problem with a fuzzy set (FS) of constraints in the form of fuzzy inequalities is analyzed. The solution to such a problem is shown to form a type-2 FS (T2FS). A corresponding membership function of type 2 is provided. It is shown that the T2FS of the solution can be decomposed into a finite collection of FS based on secondary membership grades. Each of these FS is a solution to the corresponding fuzzy linear programming problem with a crisp set of constraints. This set corresponds to a certain cut of the original FS of constraints. An illustrative example is presented.