Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets

Hsien-Chung Wu
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan

Mathematics, 2018, vol. 7, issue 1, 1-24

Abstract: The conventional concept of α -level sets of fuzzy sets will be treated as the upper α -level sets. In this paper, the concept of lower α -level sets of fuzzy sets will be introduced, which can also be regarded as a dual concept of upper α -level sets of fuzzy sets. We shall also introduce the concept of dual fuzzy sets. Under these settings, we can establish the so-called dual decomposition theorem. We shall also study the dual arithmetics of fuzzy sets in R and establish some interesting results based on the upper and lower α -level sets.

Keywords: dual decomposition theorem; dual fuzzy sets; dual arithmetics; lower ? -level sets; upper ? -level sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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