JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 125-132.doi: 10.6040/j.issn.1671-9352.0.2024.234

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The generalized form of P-fuzzy set and its application

LIU Jiqin, HAO Xiumei   

  1. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
  • Published:2025-05-19

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Abstract: By using the concept of fuzzy element transfer, a generalized internal P-fuzzy set A(-overF) contracting inward and a generalized outer P-fuzzy set AF expanding outward are constructed in the same universe of discourse. The mathematical structure of the generalized P-fuzzy set is given. Based on the generalized P-fuzzy set, the generalized P-fuzzy dependence degree is defined, and its characteristics are analyzed. The relationship between the generalized P-fuzzy set and Zadeh fuzzy set is further discussed, and their relationship theorems are given. Several forms of generated P-set from the generalized P-fuzzy set are obtained. It is concluded that the generalized P-fuzzy set is a generalization of Zadeh fuzzy set and the P-set, and both Zadeh fuzzy set and the P-set are special cases of the generalized P-fuzzy set. Finally, an application of the generalized P-fuzzy set in the venture capital management system is given.

Key words: generalized P-fuzzy set, Zadeh fuzzy set, P-fuzzy set, fuzzy element transfer, generalized P-fuzzy dependency degree

CLC Number: 

  • O144
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