实参软集理论及其与模糊集之间的联系

王兆浩; 李智荣; 董竹韵

doi:10.6040/j.issn.1671-9352.0.2025.270

山东大学学报(理学版) ›› 2026, Vol. 61 ›› Issue (5) : 114 -122. DOI: 10.6040/j.issn.1671-9352.0.2025.270

实参软集理论及其与模糊集之间的联系

王兆浩 ¹^,² ,
李智荣 ¹ ,
董竹韵 ¹

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

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摘要

针对软集理论中因不同软集的参数集互异而限制软集间运算与应用的问题,本文提出实参软集概念及运算法则,通过补充无效参数统一参数集,解决软集间运算受限的问题。证明模糊集可表述为一类特殊实参软集(划分软集),广义犹豫模糊集与实参软集之间存在一一对应关系,该对应关系既为实参软集理论的进一步扩展提供方向,也为犹豫模糊集的研究提供了新的视角。

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.

关键词

实参软集 / 软集 / 模糊集 / 犹豫模糊集

Key words

real-parameter soft set / soft set / fuzzy set / hesitant fuzzy set

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王兆浩,李智荣,董竹韵. 实参软集理论及其与模糊集之间的联系[J]. 山东大学学报(理学版), 2026, 61(5): 114-122 DOI:10.6040/j.issn.1671-9352.0.2025.270

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