JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (5): 114-122.doi: 10.6040/j.issn.1671-9352.0.2025.270

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The theory of real parameter soft sets and its connection with fuzzy sets

WANG Zhaohao1,2, LI Zhirong1, DONG Zhuyun1   

  1. 1. School of Mathematical Sciences, Shanxi Normal University, Taiyuan 030031, Shanxi, China;
    2. Shanxi Key Laboratory of Cryptography and Data Security, Shanxi Normal University, Taiyuan 030031, Shanxi, China
  • Published:2026-05-15

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Abstract: In response to the issue that the operations and application research among soft sets are restricted because of the different parameter sets of distinct soft sets in the soft set theory. The concept of a real-parameter soft set along with its operational rules is proposed. By supplementing invalid parameters to unify the parameter sets, the problem of limited inter-soft-set operations is resolved. Furthermore, the paper shows that fuzzy sets can be expressed as a special type of real-parameter soft set—partition soft sets. There exists a one-to-one correspondence between generalized hesitant fuzzy sets and real-parameter soft sets. This correspondence not only provides direction for the further extension of real-parameter soft set theory but also offers a new perspective for research on hesitant fuzzy sets.

Key words: real-parameter soft set, soft set, fuzzy set, hesitant fuzzy set

CLC Number: 

  • TP181
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