Inverse packet fuzzy sets and its characteristics

Article type: Research Article

Authors: Yu, Xiuqing^* | Shen, Yanfeng | Li, Qiuping

Affiliations: School of Mathematics and Big Data, Dezhou University, Dezhou, Shandong, China

Correspondence: [*] Corresponding author: Xiuqing Yu, School of Mathematics and Big Data, Dezhou University, Dezhou, Shandong 253023, China. Tel.: +86 13969231258; E-mail: [email protected].

Abstract: Based on inverse packet sets and fuzzy set, the concept of inverse packet fuzzy sets is proposed in this paper by means of introducing dynamic characteristics into a fuzzy set A and improving the fuzzy set A. The inverse packet fuzzy sets is composed of a pair of fuzzy sets generated by the fuzzy set A and has dynamic characteristic and fuzzy characteristic. Furthermore, on certain conditions, it can be restored to the fuzzy set A or the inverse packet sets generated by the Cantor set X=ker⁡(A). As a result, an inverse packet fuzzy sets can be expressed as a series of inverse packet sets by defining its scalar multiplication and its cut sets. Meanwhile some attribute-dependent characteristics of inverse packet fuzzy sets are obtained. The new set model will both enrich the set theory and provide a new basic tool for further practical applications.

Keywords: Inverse packet sets, fuzzy set, inverse packet fuzzy sets, attribute-dependent characteristics

DOI: 10.3233/JCM-226188

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 22, no. 5, pp. 1493-1502, 2022