Sum of Discrete Fuzzy Numbers with Fuzzy Set of Summands

Sum of Discrete Fuzzy Numbers with Fuzzy Set of Summands

The author analyzes the operation of addition of discrete fuzzy numbers with a fuzzy set of summand subscripts as a generalization of the sum operation with a crisp set of operands. The result of this operation is shown to be a type-2 fuzzy set (T2FS). The author generates the type-2 membership func...

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Veröffentlicht in:Cybernetics and systems analysis 2021-05, Vol.57 (3), p.374-382
1. Verfasser: Mashchenko, S. O.
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Artificial Intelligence
Control
Fuzzy sets
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
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description The author analyzes the operation of addition of discrete fuzzy numbers with a fuzzy set of summand subscripts as a generalization of the sum operation with a crisp set of operands. The result of this operation is shown to be a type-2 fuzzy set (T2FS). The author generates the type-2 membership function of this set and introduces the concept of a T2FS of a sum of discrete numbers with a fuzzy set of summand subscripts. The sum T2FS can be decomposed, according to secondary membership grades, into the corresponding set of fuzzy numbers. It helps to represent the resultant T2FS in a form convenient for a proper understanding and application. Illustrative examples are given.
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subjects Artificial Intelligence
Control
Fuzzy sets
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
title Sum of Discrete Fuzzy Numbers with Fuzzy Set of Summands
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