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Volume 57 >>> № 3 MAY — JUNE 2021

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UDC 519.8

S.O. Mashchenko¹

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

s.o.mashchenko@gmail.com

SUM OF DISCRETE FUZZY NUMBERS WITH FUZZY SET OF SUMMANDS

Abstract. We investigate the operation of addition of discrete fuzzy numbers with a fuzzy set of summand indices. This is a generalization of the sum operation with a crisp set of operands. We show that the result of this operation is a type-2 fuzzy set of (T2FS). We construct the type-2 membership function of this set. We introduce the concept of a sum T2FS of discrete numbers with a fuzzy set of summand indices. The sum T2FS can be decomposed according to secondary membership grades into the corresponding collection of fuzzy numbers. It helps to represent the resultant T2FS in a form which is convenient for a proper understanding and applications. Illustrative examples are given.

Keywords: fuzzy number, discrete fuzzy number, fuzzy set.

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