Next Article in Journal
Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints
Next Article in Special Issue
Two Classes of Entropy Measures for Complex Fuzzy Sets
Previous Article in Journal
Cournot-Bayesian General Equilibrium: A Radon Measure Approach
Previous Article in Special Issue
Characterizations of Right Weakly Regular Semigroups in Terms of Generalized Cubic Soft Sets
Open AccessArticle

Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets

Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Mathematics 2019, 7(1), 11; https://doi.org/10.3390/math7010011
Received: 20 November 2018 / Revised: 9 December 2018 / Accepted: 20 December 2018 / Published: 22 December 2018
(This article belongs to the Special Issue Fuzziness and Mathematical Logic )
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. View Full-Text
Keywords: dual decomposition theorem; dual fuzzy sets; dual arithmetics; lower α-level sets; upper α-level sets dual decomposition theorem; dual fuzzy sets; dual arithmetics; lower α-level sets; upper α-level sets
MDPI and ACS Style

Wu, H.-C. Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets. Mathematics 2019, 7, 11.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop