Decompositions and representations of L-fuzzy natural numbers

作者：Wu, Xiu-Yun^*; Bai, Shi-Zhong

来源：Journal of Intelligent and Fuzzy Systems, 2016, 31(1): 333-344.

DOI：10.3233/IFS-162146

• L-fuzzy natural number
• cut set
• N-beta(L)-nested mapping
• N-alpha(L)-nested mapping
• addition
• exponentiation

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 N-beta(L)-nested mappings and N-alpha(L)-nested mappings are introduced and some representations of them are obtained. It is showed that if a N-beta(L)-nested mapping (resp. N-alpha(L)-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 N-beta(L)-nested mappings (resp. two N-alpha(L)-nested mappings) are introduced. It is also showed that, given two N-beta(L)-nested mappings (resp. two N-alpha(L)-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.

• 出版日期2016
• 单位五邑大学; 湘潭大学; 湖南科技学院