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Volume 61 >>> № 5 SEPTEMBER — OCTOBER 2025

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UDC 519.8

S.O. Mashchenko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
s.o.mashchenko@gmail.com

LINEAR PROGRAMMING WITH A FUZZY SET OF FUZZY INEQUALITIES

Abstract. This paper investigates a linear programming problem with a fuzzy set (FS) of constraints in the form of fuzzy inequalities. It is shown that a solution to this problem forms a type-2 FS (T2FS). The corresponding type-2 membership function of this T2FS is given. We prove that a solution T2FS can be decomposed into a finite collection of FS based on secondary membership grades. Each of these is a solution to the corresponding fuzzy linear programming problem with a crisp set of constraints. This set is the corresponding cut of the initial FS of constraints. The illustrative example is also included for clarity.

Keywords: decision making, fuzzy linear programming problem, fuzzy optimization, type-2 fuzzy set.

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