Affiliations: [a]
Department of Mathematics, Hunan University ofScience and Engineering, Hunan, China
| [b]
Shool of Mathematics and Computational Science, Xiangtan University, Hunan, China
| [c]
School of Mathematics and Computational Science, Wuyi University, Guangdong, China
Correspondence:
[*]
Corresponding author. Xiu-Yun Wu, Department of Mathematics, Hunan University of
Science and Engineering, Hunan, China. Tel.: +86 18374601897; Fax: +86 0746 6381374; E-mail: wuxiuyun2000@126.com.
Abstract: In this paper, decompositions of L-fuzzy natural numbers and cut sets of L-fuzzy sets on finite sets are presented. Then, based on some unified nature of L-fuzzy natural numbers, the notions of ℕβL-nested mappings and ℕαL-nested mappings are introduced and some representations of them are obtained. It is showed that if a ℕβL-nested mapping (resp. ℕαL-nested mapping) is generated by an L-fuzzy natural number, then its representation is exactly equal to itself. As for applications, the addition and the exponentiation of two ℕβL-nested mappings (resp. two ℕαL-nested mappings) are introduced. It is also showed that, given two ℕβL-nested mappings (resp. two ℕαL-nested mappings), cut sets that correspond to the representations of their addition (or, their exponentiation) are equal to cut sets of the addition (or, the exponentiations) of the given mappings.
