Duality in Fuzzy Sets
Hsien-Chung Wu · 2024
This chapter deals with the concept of duality of fuzzy sets by considering the lower alpha-level sets. The conventional alpha-level sets are treated as upper alpha-level sets in this chapter. The so-called dual extension principle and dual decomposition theorem are established based on the lower alpha-level sets. Also, the so-called dual arithmetics of fuzzy sets are also proposed using on the lower alpha-level sets in which a duality relation with the conventional arithmetics of fuzzy sets is established.