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2019 | OriginalPaper | Buchkapitel

On the Issue of Comparison of Fuzzy Numbers

verfasst von : Viktor Ukhobotov, Irina Stabulit, Konstantin Kudryavtsev

Erschienen in: Mathematical Optimization Theory and Operations Research

Verlag: Springer International Publishing

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Abstract

In the class of decision-making problems with fuzzy information concerning criterion values, the problem of comparing fuzzy numbers is relevant. There are various approaches to solving it. They are determined by the specific character of the problem under consideration. This paper proposes one approach to comparing fuzzy numbers. The proposed approach is as follows. At first, a rule is constructed for comparing a real number with a level set of a fuzzy number. Then, with the help of a procedure for constructing the exact lower approximation for the collection of sets, a fuzzy set is constructed. This fuzzy set determine the rule for comparing a real number with a fuzzy number. Using this rule and the approach based on separating two fuzzy numbers with a real number, the procedure is chosen for comparing two fuzzy numbers. As an example, fuzzy numbers with trapezoidal membership functions are considered, and the geometric interpretation of the results being given.

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Titel: On the Issue of Comparison of Fuzzy Numbers
verfasst von: Viktor Ukhobotov
Irina Stabulit
Konstantin Kudryavtsev
Verlag: Springer International Publishing
Buch: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-33393-5

Electronic ISBN: 978-3-030-33394-2

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-33394-2_45

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